An experimental program with high duty-cycle polarized and unpolarized positron beams at Jefferson Lab
A. Accardi, A. Afanasev, I. Albayrak, S.F. Ali, M. Amaryan, J.R.M. Annand, J. Arrington, A. Asaturyan, H. Atac, H. Avakian, T. Averett, C. Ayerbe Gayoso, X. Bai, L. Barion, M. Battaglieri, V. Bellini, R. Beminiwattha, F. Benmokhtar, V.V. Berdnikov, J.C. Bernauer, V. Bertone, A. Bianconi, A. Biselli, P. Bisio, P. Blunden, M. Boer, M. Bondì, K.-T. Brinkmann, W.J. Briscoe, V. Burkert, T. Cao, A. Camsonne, R. Capobianco, L. Cardman, M. Carmignotto, M. Caudron, L. Causse, A. Celentano, P. Chatagnon, J.-P. Chen, T. Chetry, G. Ciullo, E. Cline, P.L. Cole, M. Contalbrigo, G. Costantini, A. D'Angelo, L. Darmé, D. Day, M. Defurne, M. De Napoli, A. Deur, R. De Vita, N. D'Hose, S. Diehl, M. Diefenthaler, B. Dongwi, R. Dupré, H. Dutrieux, D. Dutta, M. Ehrhart, L. El Fassi, L. Elouadrhiri, R. Ent, J. Erler, I.P. Fernando, A. Filippi, D. Flay, T. Forest, E. Fuchey, S. Fucini, Y. Furletova, H. Gao, D. Gaskell, A. Gasparian, T. Gautam, F.-X. Girod, K. Gnanvo, J. Grames, G.N. Grauvoge, P. Gueye, M. Guidal, S. Habet, T.J. Hague, D.J. Hamilton, O. Hansen, D. Hasell, M. Hattawy, D.W. Higinbotham, A. Hobart, T. Horn, C.E. Hyde, H. Ibrahim, A. Ilyichev, A. Italiano, K. Joo, S.J. Joosten, V. Khachatryan, N. Kalantarians, G. Kalicy, et al. (130 additional authors not shown)
ee + @JLab White Paper ∼ . ∼ . ∼ a r X i v : . [ nu c l - e x ] J u l n Experimental Program with Positron Beamsat Jefferson Lab A. Accardi , , A. Afanasev , I. Albayrak , S.F. Ali , M. Amaryan , J.R.M. Annand , J. Arrington ,A. Asaturyan , H. Avakian , T. Averett , C. Ayerbe Gayoso , L. Barion , M. Battaglieri , ,V. Bellini , F. Benmokhtar , V. Berdnikov , J.C. Bernauer , , A. Bianconi , , A. Biselli ,M. Boer , M. Bondì , K.-T. Brinkmann , W.J. Briscoe , V. Burkert , T. Cao , A. Camsonne ,R. Capobianco , L. Cardman , M. Carmignotto , M. Caudron , L. Causse , A. Celentano ,P. Chatagnon , T. Chetry , G. Ciullo , , E. Cline , P.L. Cole , M. Contalbrigo , G. Costantini , ,A. D’Angelo , , D. Day , M. Defurne , M. De Napoli , A. Deur , R. De Vita , N. D’Hose ,S. Diehl , , M. Diefenthaler , B. Dongwi , R. Dupré , D. Dutta , M. Ehrhart , L. El-Fassi ,L. Elouadrhiri , R. Ent , J. Erler , , I.P. Fernando , A. Filippi , D. Flay , T. Forest , E. Fuchey ,S. Fucini , Y. Furletova , H. Gao , D. Gaskell , A. Gasparian , T. Gautam , F.-X. Girod ,J. Grames , P. Gueye , M. Guidal , S. Habet , D.J. Hamilton , O. Hansen , D. Hasell ,M. Hattawy , D.W. Higinbotham , A. Hobart , T. Horn , C.E. Hyde , H. Ibrahim , A. Italiano ,K. Joo , S.J. Joosten , N. Kalantarians , G. Kalicy , D. Keller , C. Keppel , M. Kerver ,A. Kim , J. Kim , P.M. King , E. Kinney , V. Klimenko , H.-S. Ko , M. Kohl , V. Kozhuharov , ,V. Kubarovsky , T. Kutz , , L. Lanza , , M. Leali , , P. Lenisa , , N. Liyanage , Q. Liu ,S. Liuti , J. Mammei , S. Mantry , D. Marchand , P. Markowitz , L. Marsicano , , V. Mascagna , ,M. Mazouz , M. McCaughan , B. McKinnon , D. McNulty , W. Melnitchouk , Z.-E. Meziani ,M. Mihoviloviˇc , R. Milner , A. Mkrtchyan , H. Mkrtchyan , A. Movsisyan , M. Muhoza ,C. Muñoz Camacho , J. Murphy , P. Nadel-Turo ´nski , J. Nazeer , S. Niccolai , G. Niculescu ,R. Novotny , M. Paolone , L. Pappalardo , , R. Paremuzyan , E. Pasyuk , T. Patel , I. Pegg ,C. Peng , D. Perera , M. Poelker , K. Price , A.J.R. Puckett , M. Raggi , , N. Randazzo ,M.N.H. Rashad , M. Rathnayake , B. Raue , P.E. Reimer , M. Rinaldi , A. Rizzo , , J. Roche ,O. Rondon-Aramayo , G. Salmè , E. Santopinto , R. Santos Estrada , B. Sawatzky , A. Schmidt ,P. Schweitzer , S. Scopetta , V. Sergeyeva , M. Shabestari , A. Shahinyan , Y. Sharabian ,S. Širca , E. Smith , D. Sokhan , A. Somov , N. Sparveris , M. Spata , S. Stepanyan , P. Stoler ,I. Strakovsky , R. Suleiman , M. Suresh , H. Szumila-Vance , V. Tadevosyan , A.S. Tadepalli ,M. Tiefenback , R. Trotta , M. Ungaro , P. Valente , L. Venturelli , , H. Voskanyan , E. Voutier ,B. Wojtsekhowski , S. Wood , J. Xie , Z. Ye , M. Yurov , H.-G. Zaunick , S. Zhamkochyan ,J. Zhang , S. Zhang , S. Zhao , Z.W. Zhao , X. Zheng , C. Zorn + @JLab White Paper Thomas Jefferson National Accelerator Facility, 12000 Jefferson Avenue, Newport News, VA 23606, USA Laboratoire de Physique des 2 Infinis Irène Joliot-Curie, Université Paris-Saclay, CNRS/IN2P3, IJCLab, 15 rue GeorgesClémenceau, 91405 Orsay cedex, France The George Washington University, 221 I Street NW, Washington, DC 20052, USA Laboratory for Nuclear Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139,USA University of Virginia, Department of Physics, 382 McCormick Rd, Charlottesville, VA 22904, USA The University of North Georgia, 82 College Cir, Dahlonega, GA 30597, USA Duke University and Triangle Universities Nuclear Laboratory, Department of Physics, 134 Chapel Drive, Durham, NC27708, USA Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, Via E. Fermi 40 - 00044 Frascati, Italy Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Via Dodecaneso, 33 - 16146 Genova, Italy Università di Genova, Via Balbi, 5 - 16126 Genova, Italy Argonne National Laboratory, Physics Division, 9700 S Cass Ave., Lemont, IL, USA Institute für Physik, Johannes Gutenberg-Universität, 55099 Mainz, Germany PRISMA + Cluster of Excellence and Helmholtz Institute Mainz, Johannes Gutenberg-Universität, 55099 Mainz, Germany Universidad Nacional Autónoma de México, Instituto de Física, Departamento de Física Teórica, 04510 CDMX, México Mississippi State University, Mississippi State, MS 39762, USA Faculté des Sciences de Monastir, Avenue de l’Environnement 5019, Monastir, Tunisia Old Dominion University, 4600 Elkhorn Ave, Norfolk, VA 23529, USA Dipartimento di Fisica e Geologia, Università degli studi di Perugia, INFN Sezione di Perugia, via A. Pascoli snc, 06123Perugia, Italy Sapienza Università di Roma, Piazzale Aldo Moro 5 - 00185 Roma, Italy Stony Brook University, 100 Nicolls Road, Stony Brook, NY 11794, USA University of Connecticut, Department of Physics, 196 Auditorium Road, Storrs, CT 06269-3046, USA RIKEN-Brookhaven Research Center, Brookhaven National Lab, 98 Rochester St, Upton, NY 11973, USA Ohio University, Athens, OH 45701, USA Lamar University, Physics Department, 4400 MLK Boulevard, Beaumont, TX 77710, USA Tsinghua University, 30 Shuangqing Rd, Haidian District, Beijing 100084, P.R. China University of Colorado, Boulder, CO 80309, USA Università degli Studi di Brescia, Via Branze, 38 - 25121 Brescia, Italy Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via Santa Sofia, 64 - 95123 Catania, Italy University of New Hampshire, Durham, NH 03824, USA Facility for Rare Isotope Beams, Michigan State University, 640 South Shaw Lane, East Lansing, MI 48824, USA Fairfield University, 1073 N Benson Road, Fairfield, CT 06824, USA Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Saragat, 1 - 44122 Ferrara, Italy Università di Ferrara, Via Ludovico Ariosto, 35 - 44121 Ferrara, Italy Universität Gießen, Luwigstraße 23, 35390 Gießen, Germany Institut de Recherche sur les Lois Fondamentales de l’Univers, Commissariat à l’Energie Atomique, Université Paris-Saclay, e + @JLab White Paper | 3 Physics Department, Cairo University, Giza 12613, Egypt University of Glasgow, University Avenue, Glasgow G12 8QQ, United Kingdom North Carolina A&T State University, 1601 E Market Street, Greensboro, NC 27411, USA Hampton University, Physics Department, 200 William R. Harvey Way, Hampton, VA 23668, USA James Madison University, Harrisonburg, VA 22807, USA Akdeniz Üniversitesi, Pinarba¸si Mahallesi, 07070 Konyaalti/Antalya, Turkey New Mexico State University, 1780 E University Ave, Las Cruces, NM 88003, USA Univerza v Ljubljani, Faculteta za Matematico in Fiziko, Jadranska ulica 19, 1000 Ljubljana, Slovenia Florida International University, Modesto A. Maidique Campus, 11200 SW 8th Street, CP 204, Miami, FL 33199, USA Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Via Agostino Bassi, 6 - 27100 Pavia, Italy University of West Florida, 11000 University Pkwy, Pensacola, FL 32514, USA Temple University, Physics Department, 1925 N 12th Street, Philadelphia, PA 19122-180, USA Duquesne University, 600 Forbes Ave, Pittsburgh, PA 15208, USA Idaho State University, Pocatello, ID 83209, USA Virginia Union University, 1500 N Lombardy Street, Richmond, VA 23220, USA Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Piazzale A. Moro 2 - 00185 Roma, Italy Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tor Vergata, Via de la Ricerca Scientifica, 1 - 00133 Roma, Italy Università degli Studi di Roma Tor Vergata, Via Cracovia, 50 - 00133 Roma, Italy University of Sofia, Faculty of Physics, 5 J. Bourchier Blvd., 1164 Sofia, Bulgaria Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via P. Giuria, 1 - 10125 Torino, Italy The Catholic University of America, Washington, DC 20064, USA The College of William & Mary, Small Hall, 300 Ukrop Way, Williamsburg, VA 23185, USA University of Manitoba, 66 Chancellors Cir, Winnipeg, MB R3T2N2, Canada A. Alikhanyan National Laboratory, Yerevan Physics Institute, Yerevan 375036, Armenia + @JLab White Paper bstractPositron beams, both polarized and unpolarized, are identified as essential ingredients for the ex-perimental program at the next generation of lepton accelerators. In the context of the HadronicPhysics program at the Jefferson Laboratory (JLab), positron beams are complementary, even es-sential, tools for a precise understanding of the electromagnetic structure of the nucleon, in both theelastic and the deep-inelastic regimes. For instance, elastic scattering of (un)polarized electrons andpositrons off the nucleon allows for a model independent determination of the electromagnetic formfactors of the nucleon. Also, the deeply virtual Compton scattering of (un)polarized electrons andpositrons allows us to separate unambiguously the different contributions to the cross section of thelepto-production of photons, enabling an accurate determination of the nucleon Generalized Par-ton Distributions (GPDs), and providing an access to its Gravitational Form Factors. Furthermore,positron beams offer the possibility of alternative tests of the Standard Model through the search ofa dark photon, the precise measurement of electroweak couplings, or the investigation of lepton fla-vor violation. This white paper discusses the perspectives of an experimental program with positronbeams at JLab. e + @JLab White Paper | 5 xecutive Summary Introduction
Quantum Electrodynamics (QED) is one of the most powerful quantum physics theories. The highly accurate predictive powerof this theory allows not only to investigate numerous physics phenomena at the macroscopic, atomic, nuclear, and partonicscales, but also to test the validity of the Standard Model. Therefore, QED promotes electrons and positrons as unique physicsprobes, as demonstrated worldwide over decades of scientific research at different laboratories.Both from the projectile and the target point of views, spin appears nowadays as the finest tool for the study of the inner structureof matter. Recent examples from the experimental physics program developed at the Thomas Jefferson National AcceleratorFacility (JLab) include: the measurement of polarization observables in elastic electron scattering off the nucleon [1–3], thatestablished the unexpected magnitude and behaviour of the proton electric form factor at high momentum transfer (see [4]for a review); the experimental evidence, in the production of real photons from a polarized electron beam interacting withunpolarized protons, of a strong sensitivity to the electron beam helicity [5], that opened the investigation of the 3-dimensionalpartonic structure of nucleons and nuclei via the Generalized Parton Distributions (GPDs) [6] measured through the DeeplyVirtual Compton Scattering (DVCS) [7, 8]; the achievement of a unique parity violation experimental program [9–17] accessingthe smallest polarized beam asymmetries ever measured ( ∼ − ), which provided the first determination of the weak charge ofthe proton [17] and allowed for stringent tests of the Standard Model at the TeV mass-scale [18]; etc. Undoubtedly, polarizationbecame an important capability and a mandatory property of the current and next generation of accelerators.The combination of the QED predictive power and the fineness of the spin probe led to a large but yet limited variety ofimpressive physics results. Adding to this tool-kit charge symmetry properties in terms of polarized positron beams will providea more complete and accurate picture of the physics at play, independently of the size of the scale involved. In the contextof the experimental study of the structure of hadronic matter carried out at JLab, the electromagnetic interaction dominateslepton-hadron reactions and there is no intrinsic difference between the physics information obtained from the scattering ofelectrons or positrons off an hadronic target. However, when a reaction process is a combination of more than one elementaryQED-mechanism, the comparison between electron and positron scattering allows us to isolate their quantum interference.This is of particular interest for studying limitations of the one-photon exchange Born approximation in elastic and inelasticscatterings [19, 20]. It is also essential for the experimental determination of the GPDs where the interference between theknown Bethe-Heitler (BH) process and the unknown DVCS requires polarized and unpolarized electron and positron beamsfor a model independent extraction of the different contributions to the cross section [21]. Such polarized lepton beams alsoprovide the ability to test new physics beyond the frontiers of the Standard Model via the precise measurement of electroweakcoupling parameters [22] or the search for new particles linked to dark matter [23, 24].The production of high-quality polarized positron beams to suit these many applications remains however a highly difficulttask that, until recently, was feasible only at large scale accelerator facilities. Relying on the most recent advances in highpolarization and high intensity electron sources [25], the PEPPo (Polarized Electrons for Polarized Positrons) technique [26],demonstrated at the injector of the Continuous Electron Beam Accelerator Facility (CEBAF), provides a novel and widelyaccessible approach based on the production, within a high- Z target, of polarized e + e − pairs from the circularly polarizedbremsstrahlung radiation of a low energy highly polarized electron beam [27, 28]. As opposed to other schemes operating atGeV lepton beam energies [29–31], the operation of the PEPPo technique requires only energies above the pair-productionthreshold and is therefore ideally suited for a polarized positron beam at CEBAF.This white paper adresses the physics merits of an experimental program with high energy unpolarized and polarized positronbeams at JLab. It discusses 15 possible experiments illustrating the benefits of positron beams for the study of the partonicstructure of nucleons and nuclei, for the investigation of two-photon exchange mechanisms and other specfic effects, and fortesting the Standard Model. Deeply Virtual Compton Scattering
Quantum chromodynamics (QCD) has been established as the theory that describes the interaction between the quarks andthe gluons, the fundamental particles which form hadronic matter. However, at today exact QCD-based calculations cannotyet be performed to explain the properties of hadrons in terms of their constituents. One has to resort to phenomenologicalfunctions to interpret experimental measurements in order to understand how QCD works. GPDs are nowadays the object ofan intense effort of research, in the perspective of understanding nucleon structure. They allow to perform a tomography ofthe nucleon [32, 33], by correlating the longitudinal momentum and the transverse spatial position of the partons inside thenucleon, and give access to the contribution of the orbital momentum of the quarks to the nucleon spin [7].The nucleon GPDs are accessed in the measurement of the exclusive leptoproduction of a photon ( eN → eN γ or DVCS) orof a meson on the nucleon, at high momentum transfer. At leading order and leading twist, considering only the quark sector + @JLab White Paper nd quark-helicity conserving quantities, there are 4 GPDs for each quark flavor, and each depends on 3 kinematic variables.Moreover, the GPDs do not enter directly in the DVCS amplitude, but only as combinations of integrals over one of the variables( x ). These integrals are referred to as Compton Form Factors (CFFs). Therefore, given their complexity and the complicatelink to experimental observables, the measurement of GPDs is a highly non-trivial task. It calls for a long-term experimentalprogram comprising the measurement of different DVCS observables (to single out the contribution of each of the 4 GPDs), onthe proton and on the neutron (to disentangle the quark-flavor dependence of the GPDs): cross sections, beam-, longitudinal andtransverse target- single polarization observables, double polarization observables, as well as and beam-charge asymmetries.Such dedicated experimental program, concentrating on a proton target, has started worldwide in these past few years. Afterthe first observations of a sin φ dependence for ep → e p γ events (a signature of the interference of DVCS with the competingBethe Heitler process, BH) in low statistics beam-spin asymmetry measurements by HERMES [34] and CLAS [5], varioushigh-statistics DVCS experiments were performed. Polarized and unpolarized cross sections measured at Jefferson Lab HallA indicated, via a Q -scaling test, that the factorization and leading-twist approximations are valid already at relatively low Q (1 -2 (GeV/c) ) [35]. High-statistics and wide-coverage beam-spin asymmetries [36] and cross sections [37] measured inHall B with CLAS, brought important constraints for the parametrization, in particular, of the imaginary part of the CFF ofthe GPD H . These data were expanded with more results from JLab experiments at 6 GeV on the proton aimed to measurelongitudinally polarized target-spin asymmetries along with double-polarization observables, which provided a first look to theimaginary part of the CFF of the GPD ˜ H [38].The energy upgrade of the JLab CEBAF to 12 GeV was undertaken in order to pursue the experimental study of the confinementof quarks and of the 3-dimensional quark-gluon structure of the nucleons with a particular focus on the study of GeneralizedParton Distributions. An extensive program is ongoing in the Halls A, B, and C, on both proton and neutron DVCS observableswith polarized beam and targets, with wide acceptance (CLAS12) and luminosity (Halls A and C). The addition of a polarizedpositron beam to the CEBAF accelerator opens up the perspective of measuring new GPD-related observables, namely beam-charge asymmetries (BCAs). Beam-charge related observables have the unique property to permit the separation of the differentamplitudes of the eN γ reaction, particularly to isolate the contributions from the interference between the pure DVCS and theBethe-Heitler (BH) mechanism where the real photon is emitted by either the initial or the final electron. This is of upmostimportance since the interference terms have a linear dependence on the CFFs, which instead enter the pure DVCS terms asbilinear combinations.While beam and target single spin asymmetries are proportional to the imaginary part of the DVCS-BH interference amplitude,accessing the real part is significantly more challenging. It appears in the unpolarized cross-sections for which either the BHcontribution is dominant, or all three terms (pure BH, pure DVCS, and interference amplitudes) are comparable. The DVCSand interference terms can be separated in the unpolarized cross-sections by exploiting their dependencies on the incident beamenergy, a generalized Rosenbluth separation. This is an experimentally elaborated procedure, and necessitates some theoreticalhypothesis to extract the physics content [39]. The real part also appears in double spin asymmetries, but these can receivesignificant direct contribution from the BH process itself, and are also experimentally challenging. Unpolarized BCAs aredirectly proportional to the real part of the interference term, and receive no direct contribution from the BH process. As suchthey provide the cleanest access to this crucial observable, without the need for additional theoretical assumptions in the CFFextraction procedure.The availability of DVCS positron data does not merely have a quantitative impact on uncertainties: having a direct access tothe real part of the amplitude is a qualitative shift for related studies on nucleons and nuclei. The measurement of DVCS witha positron beam is a key factor for the completion of the ambitious scientific program of the understanding of the structure anddynamics of hadronic matter. Two-Photon Exchange Physics
Two-photon exchange (TPE) became a serious concern for high-precision determinations of the proton’s elastic form factorswith the advent of the technique of polarization transfer, in the early 2000s. Measurements of polarization transfer in elasticelectron-proton scattering at Jefferson Lab [1–3, 40–49] and elsewhere [50–52] produced surprising results: the proton’s formfactor ratio, µ p G E /G M , falls steadily with Q . This trend is contrary to decades-worth of observations made using Rosenbluthseparations of unpolarized cross section data [53–60]. This discrepancy may be the result of failing to fully account for two-photon exchange as a radiative correction [19, 20, 61]. Two-photon exchange, as well as other box-diagrams with an off-shellhadronic propagator, are difficult to calculate without model dependence, and so standard radiative corrections procedures, (e.g.,Refs. [62, 63]) have typically only included two-photon exchange in the soft-limit, in which one of the two photons carries non-negligible momentum. Quantifying the amount of hard TPE, beyond these soft-calculations is an important experimental goal.Until TPE can be decisively quantified over a wide kinematic range and this discrepancy conclusively resolved, it remainsan obstacle to refining our knowledge about proton structure, both for the push to high Q , and at low Q where significantuncertainty remains about the proton radius.While positron-scattering is not the only way to experimentally constrain hard two-photon exchange, it is one of the best. Sincethe interference term between one- and two-photon exchange changes sign between electron-scattering and positron scattering, e + @JLab White Paper | 7 PE induces asymmetries in many observables when measured with electrons versus positrons. In fact, three recent experimentswere conducted to measure the ratio of the unpolarized positron-proton to electron-proton elastic scattering cross sections, withthe goal of determining if TPE is the cause of the proton form factor discrepancy [64–67]. The results, while showing modestindications of hard TPE, were far from conclusive because of their limitation to low- Q kinematics ( Q < (GeV /c ) ) wherethe form factor discrepancy is small. More decisive measurements at higher Q and with larger beam energies are needed. Theregime between < Q < (GeV /c ) is particularly interesting because not only is the form factor discrepancy large, but italso sits between the regions where dispersive hadronic calculations [68, 69] and partonic calculations [70–72] are expected towork best.In addition, two-photon exchange is one of a larger class of hadronic box diagrams, along with the γZ -box, an importantcorrection in parity-violating electron scattering, as well as the γW ± -box, relevant for β -decay. All are troublesome to calculatebecause of their off-shell hadronic propagator. New experimental constraints, even just of TPE, are valuable for helping to tuneand improve model-dependent calculations of box-diagrams in general.Currently, of the facilities around the world that can produce positron beams, none possess both an accelerator of the energy ofCEBAF as well as detector systems in the same league as those operating in and planned for the Jefferson Lab experimentalHalls. This deficit renders a number of highly impactful potential measurements out of reach for now. A high-quality positronbeam in CEBAF would permit a diverse and exciting program of measurements of two-photon exchange that would providecrucial experimental constraints, help solidify our understanding of nucleons structure, and even help test the limits of thestandard model.Of the experimental concepts proposed in this white paper, three attempt to quantify two photon-exchange by comparing theunpolarized elastic positron-proton scattering cross section to that of electron-proton scattering. The most comprehensive mea-surement could be performed in Hall B with the CLAS-12 detector, where the enormous acceptance would provide unparalleledkinematic reach, and where the typical beam currents match what the proposed positron source could provide. This could com-plemented by a rapid two-week measurement, focusing on low- (cid:15) kinematics, in Hall A, where the planned Super BigBiteSpectrometer would allow higher luminosity running. The spectrometers in Hall C would be well-suited for performing aso-called super-Rosenbluth measurement with positrons, in which an L/T separation is performed from cross sections in whichonly the recoiling proton is detected. The results of a positron super-Rosenbluth measurement could be directly compared tothose of a previous measurement in Hall A, taken with electrons [60].Positrons would be valuable for constraining TPE through observables other than elastic cross sections. Polarization Transfer,while expected to be more robust to the effects of hard TPE, is sensitive to a different combination of generalized form fac-tors, and a measurement with both electrons and positrons provides new constraints. A 90-day measurement, at Q = . and3.4 (GeV /c ) would be possible in Hall A, using Super BigBite in a similar configuration to the upcoming GEp-V experi-ment [73]. Super BigBite would also be useful for a measurement of the target-normal single-spin asymmetry in positron-protonscattering. Transverse single-spin asymmetries are zero in the limit of one-photon exchange, and a non-zero asymmetry mea-surement can either be caused by an imaginary component in the TPE amplitude, or some unknown T-violating process. Ameasurement with electrons and positrons can distinguish between the two.Lastly, TPE in elastic lepton-nucleus scattering would be useful for helping to constrain nuclear models used for calculations of γW ± box diagrams, important radiative corrections in beta-decay. Beta-decay widths for a number of super-allowed transitionsare important inputs for tests of the unitarity of the first row of the CKM Matrix. Measurements of TPE via the unpolarized e + A/e − A cross section ratio on a number of specific isotopes can help improve the radiative corrections necessary to searchingfor new physics in the quark sector. A key to this measurement is the ability to resolve the events in which the nucleus remainsin the ground state, but resolution of the spectrometers in Halls A and C are more than sufficient, especially since the rateswould be low enough to permit the use of drift chambers for tracking. A 25-day measurement would be sufficient to cover sixdifferent nuclei in three different kinematics to 1% statistical precision.Two-photon exchange is important to measure not least of all to solidify our understanding of nucleon form factors, but alsobecause it touches on a number of open problems relating to radiative corrections in parity violation and beta-decay. For thetime being, a positron beam at CEBAF would be the only feasible avenue for pursuing the broad TPE program described in thisWhite Paper. Tests of the Standard Model
Electromagnetic and electroweak interactions with polarized electron and positron beams provide new possibilities to probe theexistence of physics beyond the Standard Model (SM).Electroweak neutral-current (NC) couplings are important parameters of the Standard Model of particle physics. The effectiveelectron-quark NC couplings, C q , C q , C q , measured in lepton scattering off a nucleon or nuclear target, provide stringenttests of the Standard Model and explore the possible existence of Beyond the Standard Model (BSM) physics. Recent parityviolation electron scattering experiments at Jefferson Lab have improved the precision of the C q and C q couplings. Thecross-section asymmetry between an electron and a positron beam deep inelastic scattering (DIS) of an isoscalar target would + @JLab White Paper rovide the first measurement of the C q . The different kinematic dependence of electroweak vs. higher-order electromagneticradiative corrections can be used to separate the two effects.While the CEBAF polarized positron beam program at JLAB is primarily focused on studies of the strong interaction and hadronstructure, it also provides an opportunity to probe Charged Lepton Flavor Violation (CLFV) through a search for the process e + N → µ + X . The discovery of neutrino oscillations provides conclusive evidence that lepton flavor is not a conserved quantity.However, lepton flavor violation in the charged lepton sector has never been observed. Many BSM scenarios, including thetree-level process of Leptoquark exchange, predict CLFV rates that are within reach of current or future planned experiments.A polarized positron beam can play an important role in the search for CLFV by improving on limits from HERA by up totwo orders of magnitude and complementing searches in other low energy experiments. This program with high luminositypolarized positrons will complement planned CLFV studies at the future Electron-Ion Collider (EIC), where e → τ CLFVtransitions will also be investigated, while still providing stronger constraints for CLFV transitions between the first two leptongenerations.The e + e − annihilation is a promising channel in search of the A or heavy photon, candidate of SM-Dark Matter (DM)interaction mediator. The combination of high energy and continuous, high intensity positron beam available at JLab wouldallow to probe large unexplored regions in the heavy photon parameter space. Two different experimental setups have beenproposed. The first makes use of a thin target to produce A s through the annihilation process e + e − → A γ . By measuringthe emitted photon, the mediator of the DM-SM interaction will be identified and its (missing) mass measured. The programproposed at JLab represents an extension of PADME experiment. This pioneering measurement is currently taking data with thelow energy positron beam available at LNF- Italy. The high energy positron beam available at JLab will extend the mass rangeby a factor of four with two order of magnitude better sensitivity in the DM-SM coupling constant. The second experiment usesa thick active target and a total absorption calorimeter to detect remnants of the light dark matter production in a missing energyexperiment. Exploting the A resonant production by positron annihilation on atomic electron, the A invisible decay will beidentified by the resulting peak in the missing energy distribution, providing a clear experimental signature for the signal. Thisexperiment has the potentiality to cover a wide area of the parameter space and hit the thermal target with sensitivity to confirmor exclude some of the preferred LDM scenarios. Beside the proposed program that does not rely on polarized positron,polarization observables are expected to leverage a significant role for suppressing background to identify the experimentalphysics signal of interest extending the reach of the above mentioned experiments.The availability of a positron beam will make JLab the ultimate facility to explore the Dark Sector and BSM physics. e + @JLab White Paper | 90 | e + @JLab White Paper eeply virtual Compton scattering cross sec-tions with NPS in Hall C C. Muñoz Camacho, J. Grames, M. Mazouz
We propose to use the High Momentum Spectrometer of Hall Ccombined with the Neutral Particle Spectrometer (NPS) to per-form high precision measurements of the Deeply Virtual Comp-ton Scattering (DVCS) cross section using a beam of positrons.The combination of measurements with oppositely charged in-cident beams is the only unambiguous way to disentangle thecontribution of the DVCS term in the photon electroproduc-tion cross section from its interference with the Bethe-Heitleramplitude. This provides a stronger way to constrain the Gen-eralized Parton Distributions of the nucleon. A wide range ofkinematics accessible with an 11 GeV beam off an unpolarizedproton target will be covered. The Q − dependence of each con-tribution will be measured independently. Introduction
Deeply Virtual Compton Scattering (DVCS) refers to thereaction γ ∗ ( q ) P ( p ) → P ( p ) γ ( q ) in the Bjorken limit ofDeep Inelastic Scattering (DIS). Experimentally, we canaccess DVCS through electroproduction of real photons e ( k ) P ( p ) → e ( k ) P ( p ) γ ( q ) , where the DVCS amplitudeinterferes with the so-called Bethe-Heitler (BH) process. TheBH contribution is calculable in QED since it corresponds tothe emission of the photon by the incoming or the outgoingelectron. DVCS is the simplest probe of a new class of light-cone (quark) matrix elements, called Generalized Parton Dis-tributions (GPDs). The GPDs offer the exciting possibilityof the first ever spatial images of the quark waves inside theproton, as a function of their wavelength [6–8, 74–76]. Thecorrelation of transverse spatial and longitudinal momentuminformation contained in the GPDs provides a new tool toevaluate the contribution of quark orbital angular momentumto the proton spin. Physics goals
In this experiment we propose to exploit the charge depen-dence provided by the use of a positron beam in order tocleanly separate the DVCS term from the DVCS-BH inter-ference in the photon electroproduction cross section.The photon electroproduction cross section of a polarizedlepton beam of energy E b off an unpolarized target of mass M is sensitive to the coherent interference of the DVCS am-plitude with the Bethe-Heitler amplitude. It can be writtenas: d σ ( λ, ± e ) d Φ = dσ dQ dx B (cid:12)(cid:12)(cid:12) T BH ( λ ) ± T DV CS ( λ ) (cid:12)(cid:12)(cid:12) / | e | = dσ dQ dx B (cid:20)(cid:12)(cid:12)(cid:12) T BH ( λ ) (cid:12)(cid:12)(cid:12) + (cid:12)(cid:12)(cid:12) T DV CS ( λ ) (cid:12)(cid:12)(cid:12) ∓ I ( λ ) (cid:21) e (1) dσ dQ dx B = α π ( s e − M ) x B √ (cid:15) (2) (cid:15) = 4 M x B /Q s e = 2 M E b + M where d Φ = dQ dx B dφ e dtdφ γγ , λ is the electron helicityand the + ( − ) stands for the sign of the charge of the leptonbeam. The BH contribution is calculable in QED, given our ≈ knowledge of the proton elastic form factors at smallmomentum transfer. The other two contributions to the crosssection, the interference and the DVCS terms, provide com-plementary information on GPDs. It is possible to exploit thestructure of the cross section as a function of the angle φ γγ between the leptonic and hadronic plane to separate up toa certain degree the different contributions to the total crosssection [77].Equation (1) shows how a positron beam, together with mea-surements with electrons, provides a way to separate with-out any assumptions the DVCS and BH-DVCS interferencecontributions to the cross section. With electrons alone, theonly approach to this separation is to use the different beamenergy dependence of the DVCS and BH-DVCS interfer-ence. This is the strategy that will be used in approvedexperiment E12-13-010. However, as recent results haveshown [39] this technique has limitations due to the need toinclude power corrections to fully describe the precise az-imuthal dependence of the DVCS cross sections. A positronbeam, on the other hand, will be able to pin down each indi-vidual term. The Q − dependence of each of them can laterbe used to study the nature of the higher twist contributionsby comparing it to the predictions of the leading twist dia-gram.A positron beam can also be used to measure the correspond-ing beam charge asymmetry defined as: A C ( φ γγ ) = dσ + ( φ γγ ) − dσ − ( φ γγ ) dσ + ( φ γγ ) + dσ − ( φ γγ ) , (3) which is easier experimentally. This measurement was pi-oneered by the HERMES collaboration [78]. A drawback,however, is that it depends non-linearly on the DVCS ampli-tudes because of the denominator. One can further project thebeam charge asymmetry on the various harmonics. Nonethe-less, because of the φ γγ -dependent denominator in Eq. (3),it is contaminated by all other harmonics as well [79]. Ab-solute cross-section measurements are thus needed to cleanlymeasure the interference term without any contamination.GPDs appear in the DVCS cross section under convolu-tion integrals, usually called Compton Form Factors (CFFs): F µν , where µ and ν are the helicity states of the virtual p-DVCS@NPS e + @JLab White Paper | 11 hoton and the outgoing real photon, respectively. The in-terference between BH and DVCS provides a way to inde-pendently access the real and imaginary parts of CFFs. Atleading-order, the imaginary part of the helicity-conserving F ++ is directly related to the corresponding GPD at x = ξ : R e F ++ = P Z − dx (cid:20) x − ξ − κ x + ξ (cid:21) F ( x, ξ, t ) , I m F ++ = − π [ F ( ξ, ξ, t ) + κF ( − ξ, ξ, t )] , (4) where κ = − if F ∈ { H, E } and if F ∈ { e H, e E } . Re-cent phenomenology uses the leading-twist (LT) and leading-order (LO) approximation in order to extract or parametrizeGPDs, which translates into neglecting F and F − + andusing the relations of Eq. 4 [80–82].The scattering amplitude is a Lorentz invariant quantity, butthe deeply virtual scattering process nonetheless defines apreferred axis (light-cone axis) for describing the scatteringprocess. At finite Q and non-zero t , there is an ambigu-ity in defining this axis, though all definitions converge as Q → ∞ at fixed t . Belitsky et al. [83] decompose the DVCSamplitude in terms of photon-helicity states where the light-cone axis is defined in the plane of the four-vectors q and P .This leads to the CFFs defined previously. Recently, Braun et al. [79] proposed an alternative decomposition which de-fines the light cone axis in the plane formed by q and q andargue that this is more convenient to account for kinematicalpower corrections of O ( t/Q ) and O ( M /Q ) . The bulk ofthese corrections can be included by rewriting the CFFs F µν in terms of F µν using the following map [79]: F ++ = F ++ + χ [ F ++ + F − + ] − χ F , (5) F − + = F − + + χ [ F ++ + F − + ] − χ F , (6) F = − (1 + χ ) F + χ [ F ++ + F − + ] , (7) where kinematic parameters χ and χ are defined as follows(Eq. 48 of Ref [79]): χ = √ Q e K √ (cid:15) ( Q + t ) ∝ √ t min − tQ , (8) χ = Q − t + 2 x B t √ (cid:15) ( Q + t ) − ∝ t min − tQ . (9) Within the F µν -parametrization, the leading-twist andleading-order approximation consists in keeping F ++ andneglecting both F and F − + . Nevertheless, as a conse-quence of Eq. (6) and (7), F and F − + are no longer equalto zero since proportional to F ++ . The functions that can beextracted from data to describe the three dimensional struc-ture of the nucleon become: F ++ = (1+ χ F ++ , F = χ F ++ , F − + = χ F ++ . (10) A numerical application gives χ = χ = Q =2 GeV , x B =0.36 and t = − . GeV . Consideringthe large size of the parameters χ and χ , these kinemati-cal power corrections cannot be neglected in precision DVCS phenomenology, in particular in order to unambiguously ex-tract the CFFs. Indeed, when the beam energy changes, notonly do the contributions of the DVCS-BH interference andDVCS terms change but also the polarization of the virtualphoton changes, thereby modifying the weight of the differ-ent helicity amplitudes.The calculation of power corrections to DVCS is one of themost important theory advances in DVCS in recent years.BMP [79] have convincingly shown that in JLab kinemat-ics target mass corrections can be sizeable and cannot be ne-glected. Experimental setup
We propose to make a precision coincidence setup measuringcharged particles (scattered positrons) with the existing HMSand photons using the Neutral Particle Spectrometer (NPS),currently under construction. The NPS facility consists of aPbWO crystal calorimeter and a sweeping magnet in orderto reduce electromagnetic backgrounds. A high luminosityspectrometer+calorimeter (HMS+PbWO ) combination pro-posed in Hall C is ideally suited for such measurements.The sweeping magnet will allow to achieve low-angle photondetection. Detailed background simulations show that thissetup allows for ≥ µA beam current on a 10 cm long cryo-genic LH2 target at the very smallest NPS angles, and muchhigher luminosities at larger γ, π angles [84]. High Momentum Spectrometer.
The magnetic spectrome-ters benefit from relatively small point-to-point uncertainties,which are crucial for absolute cross section measurements.In particular, the optics properties and the acceptance of theHMS have been studied extensively and are well understoodin the kinematic e between 0.5 and 5 GeV, as evidenced bymore than 200 L/T separations ( ∼ Photon detection: neutral particle spectrometer (NPS).
We will use the general-purpose and remotely rotatable NPSsystem for Hall C. A layout of NPS standing in the SHMScarriage is shown in Fig. 1. The NPS system consists of thefollowing elements:• A sweeping magnet providing 0.3 Tm field strength.• A neutral particle detector consisting of 1080 PbWO crystals in a temperature controlled frame.• Essentially deadtime-less digitizing electronics.• A new set of high-voltage distribution bases with built-in amplifiers for operation in high-rate environments.• A dedicated beam pipe with as large a critical angle aspractical.
12 | e + @JLab White Paper C. Muñoz Camacho et al. ig. 1. The DVCS detector in Hall C. The cylinder in the left is the (1 m diameter) vacuum chamber containing the 10-cm long liquid-hydrogen target. The NPS sweepingmagnet and calorimeter are standing on the yellow platform of the SHMS, which will be used as carriage to support them. The HMS (not shown) placed on the other side ofthe beam line will be used to detect the scattered positrons.
The PbWO electromagnetic calorimeter. The energy resolu-tion of the photon detection is the limiting factor of the exper-iment. Exclusivity of the reaction is ensured by the missingmass technique and the missing-mass resolution is dominatedby the energy resolution of the calorimeter.We plan to use a PbWO calorimeter 56 cm wide and 68 cmhigh. This corresponds to 28 by 34 PbWO crystals of 2.05by 2.05 cm (each 20.0 cm long). We have added one crystalon each side to properly capture showers, and thus designedour PbWO calorimeter to consist of 30 by 36 PbWO crys-tals, or 60 by 72 cm . This amounts to a requirement of 1080PbWO crystals.To reject very low-energy background, a thin absorber couldbe installed in front of the PbWO detector. The space be-tween the sweeper magnet and the proximity of the PbWO detector will be enclosed within a vacuum channel (with athin exit window, further reducing low-energy background)to minimize the decay photon conversion in air.Given the temperature sensitivity of the scintillation light out-put of the PbWO crystals, the entire calorimeter must bekept at a constant temperature, to within . ◦ to guarantee0.5% energy stability for absolute calibration and resolution.The high-voltage dividers on the PMTs may dissipate up toseveral hundred Watts, and this power similarly must not cre-ate temperature gradients or instabilities in the calorimeter.The calorimeter will thus be thermally isolated and be sur-rounded on all four sides by water-cooled copper plates.At the anticipated background rates, pile-up and the associ-ated baseline shifts can adversely affect the calorimeter res-olution, thereby constituting the limiting factor for the beamcurrent. The solution is to read out a sampled signal, and per-form offline shape analysis using a flash ADC (fADC) sys-tem. New HV distribution bases with built-in pre-amplifierswill allow for operating the PMTs at lower voltage and loweranode currents, and thus protect the photocathodes or dyn- odes from damage.The PbWO crystals are 2.05 x 2.05 cm . The typical posi-tion resolution is 2-3 mm. Each crystal covers 5 mrad, and theexpected angular resolution is 0.5-0.75 mrad, which is com-parable with the resolutions of the HMS and SOS, routinelyused for Rosenbluth separations in Hall C.To take full advantage of the high-resolution crystals whileoperating in a high-background environment, modern flashADCs will be used to digitize the signal. They continuouslysample the signal every 4 ns, storing the information in aninternal FPGA memory. When a trigger is received, the sam-ples in a programmable window around the threshold cross-ing are read out for each crystal that fired. Since the readoutof the FPGA does not interfere with the digitizations, the pro-cess is essentially deadtime free. Proposed kinematics and projections
The different kinematics settings are represented in Fig. 2 inthe Q – x B plane. The area below the straight line Q =(2 M p E b ) x B corresponds to the physical region for a max-imum beam energy E b = 11 GeV. Also plotted is the reso-nance region
W < GeV. We have performed detailed MonteCarlo simulation of the experimental setup and evaluatedcounting rates for each of the settings. In order to do this, wehave used a recent global fit of world data with LO sea evolu-tion by D. Müller and K. Kumeriˇcki [86]. This fit reproducesthe magnitude of the DVCS cross section measured in HallA at x B = 0 . and is available up to values of x B ≤ . .For our high x B settings we used a GPD parametrization byP. Kroll, H. Moutarde and F. Sabatié [87] fitted to Deeply Vir-tual Meson Production data, together with a code to computeDVCS cross sections, provided by H. Moutarde [88, 89]. No-tice that for DVCS, counting rates and statistical uncertaintieswill be driven at first order by the Bethe-Heitler (BH) cross p-DVCS@NPS e + @JLab White Paper | 13 ig. 2. Display of different kinematic setting proposed. The Q − x B settingscorrespond to the ones approved in experiment E12-13-010, which will measureDVCS cross sections using an electron beam. Shaded areas show the resonanceregion W < GeV and the line Q = (2 M p E b ) x B limits the physical region fora maximum beam energy E b = 11 GeV. section, which is well-known.Figure 3 shows the some projected results at x B = 0 . . Sta-tistical uncertainties are shown by error bars and systematicuncertainties are represented by the cyan bands. The DVCS term (which is φ independent at leading twist) can be verycleanly separated from the BH-DVCS interference contribu-tion, and this without any assumption regarding the leading-twist dominance. The Q − dependence of each term willbe measured and its dependence compared to the asymptoticprediction of QCD. The extremely high statistical and sys-tematic precision of the results illustrated in Fig. 3 will becrucial to disentangle higher order effects (higher twist ornext-to-leading order contributions) as shown by recent re-sults [39]. Constraints on Compton Form Factors
In order to quantify the impact of the proposed experiment onthe extraction of the nucleon Compton Form Factors, we havesimulated the extraction of the proton CFFs by using only ap-proved electron cross-section measurements (both helicity-dependent and helicity-independent) from upcoming experi-ment E12-13-010 and with the addition of the positron mea-surements proposed herein. Measurements with an unpolar-ized target as proposed herein have little sensitivity to GPDs E and e E . Therefore, only the CFFs corresponding to H and e H have been fitted. Prospects of measurements with polar-ized targets would be, of course, extremely exciting and com-plementary to these. Most importantly, as mentioned before,kinematics corrections of O ( t/Q ) and O ( M /Q ) cannotbe neglected in JLab kinematics. Therefore, all CFFs H ++ , H , H − + , e H ++ , e H and e H − + have been fitted.First of all, the DVCS cross sections measured in Hall A witha 6 GeV beam [39, 90] were fitted in order to extract somerealistic values of the CFFs. These values were then used Fig. 3.
Experimental projections for 2 t − bins at x B = 0 . , Q = 4 . GeV .Red points show the projected positron cross sections with statistical uncertainties.Electron cross sections that will be measured in experiment E12-13-010 are shownin magenta. The combination of e − and e + cross sections allow the separationof the DVCS contribution (blue) and the DVCS-BH interference (green). For ref-erence, the BH cross section is displayed in black. Systematic uncertainties areshown by the cyan band. to calculate projected cross sections. The CFFs are assumedconstant in t for this exercise and equal to the average valueof those extracted from 6 GeV data. The projected electronand positron cross sections are then fitted. In doing this, thestatistical and systematic uncertainties of the measurementswere added quadratically.Results of the CFFs extracted from the fits are shown inFig. 4. One can see the significant improvement of positrondata: a factor of 6 for R e ( H ++ ) and an average factor of 4 for
14 | e + @JLab White Paper C. Muñoz Camacho et al. (GeV t - - - - ) H e ( ´ - - ) (e+ & e- data) ++ H e( ´ ) (e- data only) ++ H e( ´ ) (GeV t - - - - ) H m ( ` - ) (GeV t - - - - ) H ~ e ( ´ - ) (GeV t - - - - ) H ~ m ( ` - ) (GeV t - - - - ) H e ( ´ - - ) (e+ & e- data) H e( ´ ) (e- data only) H e( ´ ) (GeV t - - - - ) H m ( ` - ) (GeV t - - - - ) H ~ e ( ´ - ) (GeV t - - - - ) H ~ m ( ` - ) (GeV t - - - - ) H e ( ´ - - ) (e+ & e- data) -+ H e( ´ ) (e- data only) -+ H e( ´ ) (GeV t - - - - ) H m ( ` - ) (GeV t - - - - ) H ~ e ( ´ - ) (GeV t - - - - ) H ~ m ( ` - ) (GeV t - - - - )) - , e + ( e H e ( ´d ) - ( e H e ( ´d ) ++ H e( ´ ) H e( ´ ) -+ H e( ´ ) (GeV t - - - - ) - , e + ( e H m ( `d ) - ( e H m ( `d ) (GeV t - - - - )) - , e + ( e H ~ e ( ´d ) - ( e H ~ e ( ´d ) (GeV t - - - - )) - , e + ( e H ~ m ( `d ) - ( e H ~ m ( `d Fig. 4.
CFFs extracted from the fits of projected cross sections. Left: the first column in the left shows the results of the helicity-conserving CFFs when both positron andelectron data are used in the fit (black), and when only the electron approved data is used (grey). The second and third columns show the same information for the helicity-flipCFFs. The solid horizontal lines indicate the input values used to generate the cross-section data. Right: ratio of the uncertainties between the fit using both electron andpositron data and the one using only electron data. R e ( e H ++ ) . There is also a factor ∼ p-DVCS@NPS e + @JLab White Paper | 156 | e + @JLab White Paper C. Muñoz Camacho et al. eam charge assymmetries for deeply virtualCompton scattering off the proton E. Voutier, V. Burkert, L. Elouadrhiri, F.-X. Girod, S. Niccolai
The unpolarized and polarized Beam Charge Asymmetries(BCAs) of the ~e ± p → e ± pγ process on unpolarized Hydrogenare discussed. We propose to measure BCAs with the CLAS12spectrometer, using polarized positron and electron beams at10.6 GeV. The azimuthal and t -dependences of the unpolarizedand polarized BCAs will be measured over a large ( x B , Q ) phase space, providing a direct access to the real part of theCompton form factor H . The validity of the Bethe-Heitler domi-nance hypothesis will also be investigated together with eventualeffects beyond the leading twist. Introduction
The mapping of the nucleon GPDs, and the detailed under-standing of the spatial quark and gluon structure of the nu-cleon, have been widely recognized as key objectives of Nu-clear Physics of the next decades. This requires a compre-hensive program, combining results of measurements of avariety of processes in eN scattering with structural infor-mation obtained from theoretical studies, as well as expectedresults from future lattice QCD calculations. Particularly,GPDs can be accessed in the lepto-production of real pho-tons lN → lN γ through the Deeply Virtual Compton Scat-tering (DVCS) corresponding to the scattering of a virtualphoton into a real photon after interacting with a parton ofthe nucleon. At leading twist-2, DVCS accesses the 4 quark-helicity conserving GPDs { H q , E q , e H q , e E q } defined for eachquark-flavor q ≡ { u, d, s... } . They enter the cross section withcombinations depending on the polarization states of the lep-ton beam and of the nucleon target, and are extracted fromthe modulation of experimental observables in terms of the φ out-of-plane angle between the leptonic and hadronic planes.The non-ambiguous extraction of GPDs from experimentaldata not only requires a large set of observables but also theseparation of the different reaction amplitudes contributing tothe lN γ reaction. Beam charge asymmetries
Fig. 5.
Lowest QED-order amplitude of the electroproduction of real photons offnucleons.
Deeply Virtual Compton Scattering.
Analogously to X-rays crystallography, the virtual light produced by a lep-ton beam scatters on the partons to reveal the details of the internal structure of the proton. For this direct accessto the parton structure, DVCS is the golden channel to ac-cess GPDs. This process competes with the known BH re-action [39] where real photons are emitted from the initialor final leptons. The lepton beam charge ( e ) and polariza-tion ( λ ) dependence of the eN γ differential cross section d σ ≡ d σ/dQ dx B dtdφ e dφ off proton is expressed [91] d σ eλ = d σ BH + d σ DV CS + λ d e σ DV CS + e (cid:0) d σ INT + λ d e σ INT (cid:1) (11) where the index
IN T denotes the BH - DV CS quan-tum interference contribution to the cross section;( d σ BH , d σ DV CS , d σ INT ) represent the beam po-larization independent contributions of the cross section, and( d e σ DV CS , d e σ INT ) are the beam polarization dependentcontributions. Combining lepton beams of opposite polari-ties and different polarization provides a perfect separation ofthe 4 unknown
IN T and
DV CS reaction amplitudes whichconsequently permits an unambiguous access to GPDs. Inabsence of such beams, the only possible approach to thisseparation is to take advantage of the different beam energysensitivity of the
DV CS and
IN T amplitudes. Recentresults [39] have shown that this Rosenbluth-like separationcannot be performed without assumptions because of highertwists and higher α s -order contributions to the cross section.Positron beams in comparison to electron beams offer to thisproblem an indisputable experimental method. Access to Generalized Parton Distributions.
GPDs areuniversal non-perturbative objects entering the description ofhard scattering processes. Although they are not a positive-definite probability density, GPDs correspond to the ampli-tude for removing a parton carrying some longitudinal mo-mentum fraction x and restoring it with a different longitu-dinal momentum.They enter the eN γ cross section throughCompton Form Factors (CFF) F (with F ≡ {H , E , e H , e E} ) de-fined as F ( ξ, t ) = P Z dx (cid:20) x − ξ ± x + ξ (cid:21) F + ( x, ξ, t ) − iπ F + ( ξ, ξ, t ) (12) where P denotes the Cauchy’s principal value integral, and F + ( x, ξ, t ) = X q (cid:16) e q e (cid:17) [ F q ( x, ξ, t ) ∓ F q ( − x, ξ, t )] (13) is the singlet GPD combination for the quark flavor q wherethe upper sign holds for vector GPDs ( H q , E q ) and the lowersign applies to axial vector GPDs ( ˜ H q , ˜ E q ) . Thus the imag-inary part of the CFF accesses GPDs along the diagonals p-DVCS@CLAS12 e + @JLab White Paper | 17 o ( f - - - @ E = 10.6 GeV CUU A -t=0.16 GeV =2.0 GeV =0.13 Q B x -t=0.51 GeV =1.7 GeV =0.24 Q B x -t=1.00 GeV =5.5 GeV =0.65 Q B xKM PARTONS VGG ) o ( f - - - - @ E = 10.6 GeV CLU A ) o ( f - - - )/2 @ E = 10.6 GeV -LU -A +LU - (A cLU A Fig. 6.
Beam charge asymmetry observables for typical kinematics and different GPD models. x = ± ξ while the real part probes a convoluted integral ofGPDs over the initial longitudinal momentum of the partons.At leading twist and leading order, the CFF combinations en-tering the DV CS and
IN T contributions are F DV CS = 4(1 − x B ) (cid:16) HH ? + e H e H ? (cid:17) − x B t M e E e E ? − x B (cid:16) HE ? + EH ? + e H e E ? + e E e H ? (cid:17) (14) − (cid:18) x B + (2 − x B ) t M (cid:19) E e E ? F INT = F H + ξ ( F + F ) e H − t M F E . (15) Separating the
IN T contribution to the eN γ cross sectionprovides then a direct access to a linear combination of CFFs,as compared to the more involved bilinear combination of the
DV CS contributions.Analytical properties of the
DV CS amplitude at the LeadingOrder (LO) approximation lead to a dispersion relationshipbetween the real and imaginary part of the CFFs [92–94] < e [ F ( ξ, t )] LO = D F ( t ) (16) + 1 π P Z dx (cid:18) ξ − x − ξ + x (cid:19) = m[ F ( x, t )] where D F ( t ) is the so-called D -term, a t -dependent subrac-tion constant. Originally introduced to restore the polyno-miality property of vector GPDs, the D -term [95] enters theparameterization of the non-forward matrix element of theEnergy-Momentum Tensor (EMT), which subsequently pro-vides access to the mechanical properties of the nucleon [96–99]. The independent experimental determination of the realand imaginary parts of the CFFs is a key feature for the un-derstanding of nucleon dynamics. Charge asymmetries.
Comparing polarized electron andpositron beams, the unpolarized Beam Charge Asymmetry (BCA) A CUU can be constructed following the expresssion A CUU = ( d σ ++ + d σ + − ) − ( d σ − + + d σ −− ) d σ ++ + d σ + − + d σ − + + d σ −− = d σ INT d σ BH + d σ DV CS (17) which, at leading twist-2, is proportionnal to the < e [ F INT ] CFF. It constitutes a selective CFF signal which becomes dis-torted in the case of the non-dominance of the BH amplitudewith respect to the polarization insensitive DV CS ampli-tude. Similarly, the polarized BCA A CLU can be constructedas A CLU = ( d σ ++ − d σ + − ) − ( d σ − + − d σ −− ) d σ ++ + d σ + − + d σ − + + d σ −− = λ d e σ INT d σ BH + d σ DV CS (18)(19) which, at leading twist-2, is proportionnal to the = m [ F INT ] CFF. As A CUU , A CLU is a selective CFF signal affected by thesame BH -non-dominance distortion. At leading twist-2 andin the BH -dominance hypothesis, A CLU is simply oppositesign to the Beam Spin Asymmetry (BSA) A − LU measuredwith polarized electrons, and equal to the BSA A + LU mea-sured with polarized positrons. The relationship A CLU = A + LU − A − LU (20) can be viewed as a signature of the BH -dominance hypoth-esis and provides a handle on its validity. In the case of sig-nificant differences, the neutral BSA A LU = ( d σ ++ + d σ − + ) − ( d σ + − + d σ −− ) d σ ++ + d σ + − + d σ − + + d σ −− = λ d e σ DV CS d σ BH + d σ DV CS , (21) which is a twist-3 observable, allows us to distinguish be-tween the possible origins of the breakdown of this hypothe-sis. BCA observables are shown on Fig. 6 for selected kine-matics at a 10.6 GeV beam energy. They are determined
18 | e + @JLab White Paper E. Voutier et al. ig. 7. CLAS12 in Hall B. The positron beam comes from the right and hits the target in the center of the solenoid magnet, which is at the core of the Central Detector (CD).It is largely hidden from view inside the HTCC ˇCerenkov counter. using the BM modeling of DVCS observables [100] and ei-ther the KM [80] CFFs, the PARTONS CFFs [101] CFFs,or a choice of VGG [102] CFFs. Asymmetries are generallysizeable and sensitive to the CFF model, particularly the un-polarized BCA. The BH-dominance hypothesis appears as akinematic- and model-dependent statement.
Experimental configuration
Detector.
The experiment will measure the DVCS process e ± p → e ± pγ with the CLAS12 spectrometer (Fig. 7) [103],alternating electron and positron beams over a period of 80days. When operating with positron beam, the experimentwill use the standard Hall B beam line with the electrical di-agnostics in reversed charge mode from operating the beamline and the experimental equipment with electron beam.This includes the nano-ampere beam position and currentmonitors, the beam line magnetic elements, and the chargeintegrating Faraday cup. The experimental setup will be iden-tical to the standard electron beam setup with both magnets,the Solenoid and the Torus magnet in reversed current modefrom electron scattering experiments. As the positron beamemittance at the target is expected to be larger than in stan-dard electron beam operation from the later driven gun, theliquid hydrogen target cell will be redesigned with increaseddiameter. Kinematic coverage.
The simultaneous kinematic cover-age of the DVCS process in the CLAS12 acceptance is shownin Fig. 8 from a subset of Run Group A (RGA) data and adetector configuration similar to the positron configuration.Scattered electrons/positrons will be detected in the CLAS12Forward Detectors including the high threshold ˇCerenkovCounter (HTCC), the drift chamber tracking system, the For-ward Time-of-Flight system (FTOF) and the electromagneticcalorimeter (ECAL). The latter consists of the pre-showercalorimeter (PCAL) and the EC-inner and EC-outer parts of the electromagnetic calorimeter (EC) providing a 3-fold lon-gitudinal segmentation. DVCS photons are measured in theCLAS12 ECAL that covers the polar angle range from about5 ◦ to 35 ◦ . Additionally, high energy photons are also de-tected in the Forward Tagger calorimeter FTCal, which spansthe polar angle range of 2.5 ◦ to 4.5 ◦ . Protons are detectedmostly in the CLAS12 Central Detector (CD) with momentaabove 300 MeV/ c , but a significant fraction is also detected inthe CLAS12 Forward Detector, especially those in the higher − t range. Fig. 8.
Kinematic coverage of exclusive DVCS/BH events in Q versus x B (top),and in − t (bottom) plotted versus the azimuthal φ -dependence, from a subset ofRGA data.p-DVCS@CLAS12 e + @JLab White Paper | 19 ystematic uncertainties. The expected positron beamproperties differ from the CEBAF electron beam essentiallyby a 4-5 times larger emittance. To control these effectsDVCS data with an electron beam having the same propertiesas the positron beam should be carried out. Such beam canbe made of the secondary electrons produced at the positronsource, which is expected to have similar properties in termsof ( x, y ) profile and emittance at the target position. This willallow for the elimination/correction of potential beam-relatedfalse asymmetries. Fig. 9.
The generic setup of the CLAS12 detector in Hall B viewed from upstreamdown the beam pipe. In this view the proton rotates in the opposite direction, fromthe case of the electron beam. When switching the solenoid field the electron andpositron experience different phi motions due to the opposite motion of electron andpositrons (left). When the solenoid field is reversed the electrons and positronsget kicks in the opposite azimuthal directions as seen that positrons and electronsswitch place in the forward detector. This potential asymmetry can be controlledwith elastic scattered electrons and positrons.
The experimental setup is generically shown in Fig. 9 in aview along the beam line looking downstream. For the scat-tered positron and for the DVCS photon the detector looksidentical to the situation when electrons are scattered off pro-tons and the magnetic fields in both magnets are reversed.This is not the case of the recoil proton, which will be bentin the solenoid field in the opposite direction compared to theelectron scattering case. This could result in systematic ef-fects due to potentially different track reconstruction efficien-cies and effective solid angles. Measuring simultaneously toDVCS a known process as the e ± p → e ± p elastic scatter-ing at small Q , i.e. in a region where 2-photon effects arevery small [104], and alternating the solenoid polarity willallow us to monitor the performance of the detector systemthroughout the experiment and to correct for detector relatedfalse-asymmetries. Impact of positron measurements
The importance of BCA observables for the extraction ofCFFs has been stressed numerous times in the literature (seeamong others [105], [106], or [107]). The methods for theextraction of CFFs from DVCS observables can be classifiedin two generic groups: GPD-model independent [108–110](local fit) and dependent [80, 111] (global fit) methods. Bothmethods are still depending on the cross section model andof further fitting hypotheses like the number of CFFs to beextracted from data. In an attempt of a necessarily model-dependent quantitative evaluation of the impact of positronmeasurements, we use a local fit to extract the H and e H CFFs.
Fig. 10.
Subset of projected A CUU and A CLU data in selected bins assuming 80days physics data tahing at a 10.6 GeV and a luminosity of 0.6 × cm − · s − ;blue points correspond to projected data smeared according to their statistical er-ror; red lines correspond to the model prediction used to generate experimentalobservables.20 | e + @JLab White Paper E. Voutier et al. ig. 11. Impact of the positron data on the extraction of < e[ H ] : projection of extracted < e[ H ] without (blue points) and with (red points) positron data compared to the modelvalue (line); ratios of errors on the extracted < e[ H ] with positron data with respect to electron data only (right). The blue points are slightly shifted in x for visual clarity. In absence of completed analysis or actual today existence ofexperimental data, we consider the parameters of approvedCLAS12 DVCS experiments using a polarized electron beamwith an unpolarized and longitudinally polarized proton tar-get. Projected data are determined for a 10.6 GeV beam en-ergy using the BM modeling of the cross section, and statis-tical errors are obtained from the approved data taking timeand expected luminosities. BCAs statistics assume 80 daysof physics running at a luminosity of 0.6 × cm − · s − . Asubset of projected data is shown on Fig. 10 for typical kine-matics exhibiting signals of different magnitude and shape.The results of the fit are reported on Fig. 11 for the full setof kinematics accessible with CLAS12, using the Ref. [112]parameterization of CFFs. The left panel shows the model < e[ H ] as a function of − t for different ( x B , Q ) bins (line),together with the extracted values without (blue points) andwith (red points) the positron data. The right panel showsthe ratios of CFF uncertainties. The impact of positron datais found to be particularly strong at small - t where they candecrease uncertainties on < e[ H ] by over a factor five. Theelectron data only scenario tends to provide values differentfrom the model values. By providing a pure interference sig-nal, positron data corrects for this deviation and allows thefitting procedure to recover the input model value. p-DVCS@CLAS12 e + @JLab White Paper | 212 | e + @JLab White Paper E. Voutier et al. eeply virtual Compton scattering on the neu-tron with positron beams S. Niccolai
Measuring DVCS on a neutron target is a necessary step todeepen our understanding of the structure of the nucleon interms of GPDs. The combination of neutron and proton targetsallows to perform a flavor decomposition of the GPDs. More-over, neutron-DVCS plays a complementary role to DVCS ona transversely polarized proton target in the determination ofthe GPD E , the least known and constrained GPD that entersJi’s angular momentum sum rule. A measurement of the beam-charge asymmetry (BCA) in the e ± d → e ± nγ ( p ) reaction cansignificantly impact the experimental determination of the realparts of the E and, to a lesser extent, e H GPDs.
Introduction
It is well known that the fundamental particles which formhadronic matter are the quarks and the gluons, whose interac-tions are described by the QCD Lagrangian. However, exactQCD-based calculations cannot yet be performed to explainall the properties of hadrons in terms of their constituents.Phenomenological functions need to be used to connect ex-perimental observables with the inner dynamics of the con-stituents of the nucleon, the partons. Typical examples ofsuch functions include form factors, parton densities, anddistribution amplitudes. The GPDs are nowadays the objectof intense research in the perspective of unraveling nucleonstructure. They describe the correlations between the longi-tudinal momentum and transverse spatial position of the par-tons inside the nucleon, they give access to the contribution ofthe orbital momentum of the quarks to the nucleon, and theyare sensitive to the correlated q - ¯ q components [6, 105, 113].The GPDs of the nucleon are the structure functions which Fig. 12.
The handbag diagram for the DVCS process on the nucleon eN → e N γ . Here x + ξ and x − ξ are the longitudinal momentum fractions ofthe struck quark before and after scattering, respectively, and t = ( N − N ) is the squared four-momentum transfer between the initial and final nucleons. ξ ’ x B / (2 − x B ) is proportional to the Bjorken scaling variable x B = Q / Mν ,where M us the nucleon mass and ν the energy transfer to the quark. are accessed in the measurement of the exclusive leptopro-duction of a photon (DVCS) or of a meson on the nucleon, at sufficiently large virtual-photon virtuality ( Q ) for the re-action to happen at the quark level. Figure 12 illustrates theleading process for DVCS, also called “handbag diagram”.At leading-order QCD and at leading twist, considering onlyquark-helicity conserving quantities and the quark sector, theprocess is described by four GPDs: H q , f H q , E q , f E q , one foreach quark flavor q , that account for the possible combina-tions of relative orientations of the nucleon spin and quarkhelicities between the initial and final states. H q and E q donot depend on the quark helicity and are therefore called un-polarized GPDs while f H q and f E q depend on the quark he-licity and are called polarized GPDs. H q and f H q conservethe spin of the nucleon, whereas E q and f E q correspond to anucleon-spin flip.The GPDs depend upon three variables, x , ξ and t : x + ξ and x − ξ are the longitudinal momentum fractions of the struckquark before and after scattering, respectively, and t is thesquared four-momentum transfer between the initial and finalnucleon (see caption of Fig. 12 for definitions). The trans-verse component of t is the Fourier-conjugate of the trans-verse position of the struck parton in the nucleon. Amongthese three variables, only ξ and t are experimentally acces-sible with DVCS.The DVCS amplitude is proportional to combinations of in-tegrals over x of the form Z − dx F ( ∓ x, ξ, t ) (cid:20) x − ξ + i(cid:15) ± x + ξ − i(cid:15) (cid:21) , (22) where F represents one of the four GPDs. The top com-bination of the plus and minus signs applies to unpolarizedGPDs ( H q , E q ), and the bottom combination of signs appliesto the polarized GPDs ( f H q , f E q ). Each of these 4 integrals, orCompton Form Factors (CFFs), can be decomposed into itsreal and imaginary parts, as following: < e [ F ( ξ, t )] = P Z − dx (cid:20) F ( x, ξ, t ) x − ξ ∓ F ( x, ξ, t ) x + ξ (cid:21) (23) = m [ F ( ξ, t )] = − π [ F ( ξ, ξ, t ) ∓ F ( − ξ, ξ, t )] , (24) where P is Cauchy’s principal value integral and the signconvention is the same as in Eq. 22. The information thatcan be extracted from the experimental data at a given ( ξ, t )point depends on the measured observable. < e[ F ] is accessedprimarily measuring observables which are sensitive to thereal part of the DVCS amplitude, such as double-spin asym-metries, beam-charge asymmetries or unpolarized cross sec-tions. = m[ F ] can be obtained measuring observables whichare sensitive to the imaginary part of the DVCS amplitude,such as single-spin asymmetries or the difference of polarizedcross-sections. However, knowing the CFFs does not define n-DVCS@CLAS12 e + @JLab White Paper | 23 he GPDs uniquely. A model input is necessary to deconvo-lute their x -dependence. The DVCS process is accompaniedby the Bethe-Heitler (BH) process, in which the final-statereal photon is radiated by the incoming or scattered electronand not by the nucleon itself. The BH process, which is notsensitive to GPDs, is experimentally indistinguishable fromDVCS and interferes with it at the amplitude level. However,considering that the nucleon form factors are well known atsmall t , the BH process is precisely calculable. Neutron GPDs and flavor separation
The importance of neutron targets in the DVCS phenomenol-ogy was clearly established in the pioneering Hall A experi-ment, where the polarized-beam cross section difference off aneutron, from a deuterium target, was measured [114]. Mea-suring neutron GPDs in complement to proton GPDs allowsfor a quark-flavor separation. For instance, the E -CFF of theproton and the neutron can be expressed as E p ( ξ, t ) = 49 E u ( ξ, t ) + 19 E d ( ξ, t ) (25) E n ( ξ, t ) = 19 E u ( ξ, t ) + 49 E d ( ξ, t ) (26) (and similarly for H , e H and e E ). From this it follows that E u ( ξ, t ) = 915 [4 E p ( ξ, t ) − E n ( ξ, t )] (27) E d ( ξ, t ) = 915 [4 E n ( ξ, t ) − E p ( ξ, t )] . (28) An extensive experimental program dedicated to the mea-surement of the DVCS reaction on a proton target hasbeen approved at Jefferson Lab, in particular with CLAS12.Single-spin asymmetries with polarized beam and/or linearlyor transversely polarized proton targets, as well as unpolar-ized and polarized cross sections, will be measured with highprecision over a vast kinematic coverage. If a similar pro-gram is performed on the neutron, the flavor separation ofthe various GPDs will be possible. The beam-spin asym-metry for nDVCS, particularly sensitive to the GPD E n iscurrently being measured at CLAS12, using an experimen-tal technique different from the initial Hall A measurementand involving the neutron detection. Additionally, the mea-surement of single- and double-spin asymmetries with a lon-gitudinally polarized deuteron target is also foreseen for thenearby future with CLAS12. Here we focus on the extractionof one more observable, the beam-charge asymmetry. Thenext section outlines the benefits of this observable for theCFFs determination. Beam charge asymmetry
Considering unpolarized electron and positron beams, thesensitivity of the cross-section to the lepton beam charge canbe expressed with the beam charge asymmetry observable A C ( φ ) = d σ + − d σ − d σ + + d σ − = d σ I UU d σ BH UU + d σ DVCS UU (29) which isolates the BH-DVCS interference contribution at thenumerator and the DVCS amplitude at the denominator. Fol-lowing the harmonic decomposition proposed in Ref. [105], d σ I UU = K P ( φ ) P ( φ ) X n =0 c I n, unp cos( nφ ) (30) d σ DVCS UU = K Q X n =0 c DVCS n, unp cos( nφ ) , (31) where K i ’s are kinematical factors, and P i ( φ ) ’s are the BHpropagators. Because of the /Q kinematical suppressionof the DVCS amplitude, the dominant contribution to the de-nominator originates from the BH amplitude. This approx-imation depends on the kinematics and, in the most generalcase, the DVCS contribution in the denominator complicatesthe extraction of CFFs. At leading twist, the dominant coef-ficients of the numerator are c I0 , unp and c I1 , unp c I0 , unp ∝ − √− tQ c I1 , unp (32) c I1 , unp ∝ < e (cid:20) F H + ξ ( F + F ) e H − t M F E (cid:21) . (33) Given the relative strength of F and F at small t for a neu-tron target, the beam charge asymmetry becomes A C ( φ ) ∝ F < e (cid:20) ξ e H n − t M E n (cid:21) . (34) Therefore, the BCA is mainly sensitive to the real part of theGPD E n , and, for selected kinematics, to the real part of theGPD f H n . Extraction of Compton form factors
In order to establish the impact of a beam-charge asymmetrymeasurement on the nDVCS experimental program plannedwith CLAS12 at Jefferson Lab, projections for four kinds ofasymmetries (beam-spin asymmetry, BSA, longitudinal sin-gle, TSA, and double targe-spin asymmetry, DSA, and theBCA) were produced using the VGG model and realisticcount rates and acceptances. The projected observables werethen processed using a fitting procedure [108, 115] to extractthe neutron CFFs. This approach is based on a local-fittingmethod at each given experimental ( Q , x B , − t ) kinematicpoint. In this framework, there are eight real CFF-relatedquantities F Re ( ξ, t ) = < e [ F ( ξ, t )] (35) F Im ( ξ, t ) = − π = m [ F ( ξ, t )]= [ F ( ξ, ξ, t ) ∓ F ( − ξ, ξ, t )] , (36) where the sign convention is the same as for Eq. 22. TheseCFFs are the almost-free parameters to be extracted from The values of the CFFs are allowed to vary within ± times the valuespredicted by the VGG model [108]
24 | e + @JLab White Paper S. Niccolai VCS observables using the well-established theoretical de-scription of the process based on the DVCS and BH mech-anisms. The BH amplitude is calculated exactly while theDVCS one is determined at the QCD leading twist [116]. Asthere are eight CFF-related free parameters, including moreobservables, measured at the same kinematic points, will re-sult in tighter constraint on the fit and will increase the num-ber and accuracy of the extracted CFFs. In the adopted ver-sion of the fitter code, g E Im ( n ) is set to zero, as f E n is as-sumed to be purely real. Thus, seven out of the eight real andimaginary parts of the CFFs are left as free parameters in thefit. The results for the 7 neutron CFFs are shown in Figs. 19-16, as a function of − t , and for each bin in Q and x B . Theblue points are the CFFs resulting from the fits of the fourobservables, while the red ones are the CFFs obtained fittingonly the projections of the currently approved n-DVCS ex-periments. The error bars reflect both the statistical precisionof the fitted observables and their sensitivity to that particu-lar CFFs. Only results for which the error bars are non zero,and therefore the fits properly converged, are included in thefigures.The major impact of the BCA measurement is, as expected,on E Re ( n ) , for which the already approved projections havehardly any sensitivity. Thanks to the BCA, E Re ( n ) can beextracted over basically the whole phase. A considerable ex-tension in the coverage can be also obtained for ˜ H Re ( n ) . Anoverall improvement to the precision on the other CFFs, aswell as an extension in their kinematic coverage can also beinduced by the nDVCS BCA dataset. Summary
The strong sensitivity to the real part of the GPD E q of thebeam-charge asymmetry for DVCS on a neutron target makesthe measurement of this observable particularly important forthe experimental GPD program of Jefferson Lab. This sensi-tivity is maximal for values of x B which are attainable onlywith a 11 GeV beam. Model predictions show that for possi-ble CLAS12 kinematics, this asymmetry can be comparablein size to the BSA obtained for p-DVCS.The addition of the beam-charge asymmetry to the alreadyplanned measurements with CLAS12, permits the model-independent extraction of the real parts of the E n and f H n CFFs of the neutron over the whole available phase space.Combining all the neutron and the proton CFFs, obtainedfrom the fit of n-DVCS and p-DVCS observables to be mea-sured at CLAS12, will ultimately allow the quark-flavor sep-aration of all GPDs. ) ( G e V Q B x0.1 0.2 0.3 0.4 0.5 0.6 0.7 ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E - - Fig. 13. E Re ( n ) as a function of − t , for all bins in Q and x B . The blue pointsare the results of the fits including the proposed BCA while the red ones includeonly already approved experiments. ) ( G e V Q B x0.1 0.2 0.3 0.4 0.5 0.6 0.7 ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H ~ - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H ~ - - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H ~ - - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H ~ - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H ~ - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H ~ - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H ~ - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H ~ - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H ~ - - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H ~ - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H ~ - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H ~ - - - Fig. 14. ˜ H Re ( n ) as a function of − t , for all bins in Q and x B . The blue pointsare the results of the fits including the proposed BCA while the red ones includeonly already approved experiments. ) ( G e V Q B x0.1 0.2 0.3 0.4 0.5 0.6 0.7 ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e H - - Fig. 15. H Re ( n ) as a function of − t , for all bins in Q and x B . The blue pointsare the results of the fits including the proposed BCA while the red ones includeonly already approved experiments.n-DVCS@CLAS12 e + @JLab White Paper | 25 ( G e V Q B x0.1 0.2 0.3 0.4 0.5 0.6 0.7 ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E ~ - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E ~ - - - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E ~ - - - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E ~ - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E ~ - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E ~ - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E ~ - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E ~ - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E ~ - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E ~ - - - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E ~ - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E ~ - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) R e E ~ - - - - Fig. 16. ˜ E Re ( n ) as a function of − t , for all bins in Q and x B . The blue pointsare the results of the fits including the proposed BCA while the red ones includeonly already approved experiments. ) ( G e V Q B x0.1 0.2 0.3 0.4 0.5 0.6 0.7 ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m E - - - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m E - - - - - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m E - - - - - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m E - - - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m E - - - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m E - - - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m E - - - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m E - - - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m E - - - - - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m E - - - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m E - - - - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m E - - - - - - Fig. 17. E Im ( n ) as a function of − t , for all bins in Q and x B . The blue pointsare the results of the fits including the proposed BCA while the red ones includeonly already approved experiments. ) ( G e V Q B x0.1 0.2 0.3 0.4 0.5 0.6 0.7 ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H ~ - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H ~ - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H ~ - - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H ~ - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H ~ - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H ~ - - - Fig. 18. ˜ H Im ( n ) as a function of − t , for all bins in Q and x B . The blue pointsare the results of the fits including the proposed BCA while the red ones includeonly already approved experiments. ) ( G e V Q B x0.1 0.2 0.3 0.4 0.5 0.6 0.7 ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H - - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H - - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H - - - ) -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H - - - -t (GeV0.2 0.4 0.6 0.8 1 ( n ) I m H - - - Fig. 19. H Im ( n ) as a function of − t , for all bins in Q and x B . The blue pointsare the results of the fits including the proposed BCA while the red ones includeonly already approved experiments.26 | e + @JLab White Paper SubFiles/S. Niccolai eeply virtual Compton scattering off heliumnuclei with positron beams S. Fucini, M. Hattawy, M. Rinaldi, S. Scopetta
The relevance of using positron beams in deeply virtual Comp-ton scattering (DVCS) off He and He is addressed. The waythe so-called d − term could be extracted from the real part ofthe relevant Compton form factor, using as an example coher-ent DVCS on He, is summarized, and the importance and nov-elty of this measurement is described. Analogous measurementsare addressed for He tagets, which could be very useful even ina standard unpolarized setup, measuring beam spin asymme-tries and charge beam asymmetries only. The role of incoher-ent DVCS processes, in particular tagging the internal target bymeasuring slow recoiling nuclei, and the unique possibility of-fered by positron beams for the investigation of Compton formfactors of higher twist, are also briefly addressed.
Introduction
The possibility to shed light on the EMC effect, i.e., thenuclear modifications of the nucleon parton structure [117,118], as well as the feasibility to distinguish coherentand incoherent channels, have been recently experimentallydemonstrated by the CLAS collaboration at JLab using a Hegaseous target [119, 120]. Those measurements have led toa growing interest on nuclear deeply virtual Compton scat-tering (DVCS). Let us analyze the impact that measurementsof positron initiated DVCS on He and He may have, sepa-rately for the coherent an incoherent channels.
Coherent DVCS
To fix the ideas on how positron beams could help in thisfield, let us think first to coherent DVCS off He. We re-call that He has only one Compton Form Factor (CFF),corresponding to one chiral-even generalized parton distri-bution (GPD) at leading twist. In the EG6 experiment ofthe CLAS collaboration, Ref. [119], the crucial measured ob-servable was the beam-spin asymmetry A LU , which can beextracted from the reaction yields with the two electron he-licities ( N ± ): A LU = 1 P B N + − N − N + + N − , (37) where P B is the degree of longitudinal polarization of the in-cident electron beam. In the accessible phase space of theEG6 experiment, the cross section of real photon electro-production is dominated by the BH contribution, while theDVCS contribution is very small. However, the DVCS con-tribution is enhanced in the observables sensitive to the in-terference term, e.g. A LU , which depends on the azimuthalangle φ between the ( e, e ) and ( γ ∗ , He ) planes. The asym-metry A LU for a spin-zero target can be approximated at leading-twist as A LU ( φ ) = α ( φ ) = m ( H A ) den ( φ ) , (38) den ( φ ) = α ( φ ) + α ( φ ) < e ( H A )+ α ( φ ) (cid:0) < e ( H A ) + = m ( H A ) (cid:1) . (39) The kinematic factors α i are known (see, e.g., Ref. [105,121]). In the experimental analysis, using the different con-tributions proportional to sin( φ ) and cos( φ ) in Eq. (39), boththe real and imaginary parts of the so-called Compton FormFactor H A , < e ( H A ) and = m ( H A ) , respectively, have beenextracted by fitting the A LU ( φ ) distribution. Results of theimpulse approximation calculation of Ref. [122], where useis made of a model spectral function based on the realisticAv18 potential to describe the nuclear structure and of theGoloskokov-Kroll model to parametrize the nucleonic GPDs(older calculations can be found in [123, 124]), are showntogether with the data of Ref. [119] in Fig. 20. Big statisti-cal errors are seen everywhere in the data but, in particular,the extracted < e ( H A ) is less precise than = m ( H A ) , due tothe small coefficient α in Eq. (39). Forthcoming data fromJLab with the upgraded 12 GeV electron beams, using also arecoiling detector developed by the ALERT run-group [125],will improve the statistical precisions. Together with refinedrealistic theoretical calculations, in progress for light nuclei,the new data will help to unveil a possible exotic behavior ofthe real and imaginary part of H A . Nonetheless, the extracted < e ( H A ) will be always less precise than = m ( H A ) , intrinsi-cally, due to the small coefficient α in Eq. (39). A preciseknowledge of < e ( H A ) for light nuclei would be instead cru-cial. Positron beams would guarantee this achievement: asa matter of fact, combining data for properly defined asym-metries measured using electrons and positrons, the role of < e H A would be directly accessed. One should notice that,between the quantities appearing in the above equations andthe cross sections defining the generic photo- e ± productioncross section in the following schematic general expression,previously given in this White Paper, σ eλ = σ BH + σ DV CS + λ ˜ σ DV CS + eσ INT + eλ ˜ σ INT , (40) the following relations hold: σ BH ∝ α ( φ ) ,σ DV CS ∝ α ( φ ) (cid:0) < e ( H A ) + = m ( H A ) (cid:1) ,σ INT ∝ α ( φ ) < e ( H A ) , ˜ σ INT ∝ α ( φ ) = m ( H A ) , (41) He-DVCS e + @JLab White Paper | 27 R e H A x B I m H A x B Fig. 20.
The real (left) and imaginary (right) parts of the CFF measured in coherent DVCS off He: data are from Ref. [119] and calculations (red crosses) from Ref. [122]. while ˜ σ DV CS is proportional to a term kinematically sup-pressed at JLab kinematics, which depends on higher twistCFFs. From a combined analysis of data taken with polar-ized electrons and/or positrons, one could access all the fivecross sections in Eq. (40). We stress in particular that, usingjust unpolarized electrons and positrons, < e ( H A ) would bedirectly accessed, building charge beam asymmetries. Let usbriefly analyze why the knowledge of < e H A would be veryimportant for nuclei. Formally one can write, for the quanti-ties < e ( H A ) and = m H A shown in Figs. 20 [115]: < e H A ( ξ, t ) ≡ P Z dxH + ( x, ξ, t ) C + ( x, ξ ) , (42) and = m H A = − πH + ( ξ, ξ, t ) , (43) with: H + = H ( x, ξ, t ) − H ( − x, ξ, t ) , (44) amd C + ( x, ξ ) = 1 x + ξ + 1 x − ξ , (45) with H ( x, ξ, t ) being the chiral-even leading twist GPD.Moreover, it is also known that < e ( H A ) satisfies a once sub-tracted dispersion relation at fixed t and can be therefore re-lated to = m H A , Ref. [92, 93, 126, 127], leading to < e H A ( ξ, t ) ≡ P Z dxH + ( x, x, t ) C + ( x, ξ ) − ∆( t ) . (46) One notices that, in contrast to the convolution integral defin-ing the real part of the CFF in Eq. (42), where the GPD en-ters for unequal values of its first and second arguments, theintegrand in the dispersion relation corresponds to the GPDwhere its first and second arguments are equal. The subtrac-tion term ∆( t ) can be related to the so-called d − term and ac-curate measurements, supplemented by precise calculations,would allow therefore to study this quantity in nuclei, forthe first time. This d − term, introduced initially to recoverthe so-called polinomiality property in DDs approaches toGPDs modelling [95], has been related to the form factor of the QCD energy momentum tensor (see e.g. Ref. [98]). Itencodes information on the distribution of forces and pres-sure between elementary QCD degrees of freedom in the tar-get. For nuclei, it has been predicted to behave as A / in amean field scheme, either in the liquid drop model of nuclearstructure [96] or in the Walecka model [128].None of theseapproaches makes much sense for light nuclei, for which ac-curate realistic calculations are possible. Using light nucleione would therefore explore, at the parton level, the onset andevolution of the mean field behavior across the periodic table,from deuteron to He, whose density and binding are not farfrom those of finite nuclei.In this sense, coherent DVCS off He targets acquire an im-portant role: an intermediate behavior is expected betweenthat of the almost unbound deuteron system and that of thedeeply bound alpha particle. The formal description of co-herent DVCS off He follows that already presented for theproton, a spin one-half target, in terms of CFFs and re-lated GPDs. Properly defining spin dependent asymmetries.Realistic theoretical calculations are available for GPDs inRef. [129–132] and are in progress for the relevant CFFs,cross sections, and asymmetries, representing an importanmtsupport to the planning of measurements. One could ob-ject that the use of He, either longitudinally or transverselypolarized, represents at the moment a challenge, either withelectron or positron beams. Actually beam-charge asymme-tries, built using electron and positron data, would represent,even with unpolarized He targets and unpolarized beams, apossible access to < e H A ( ξ, t ) , as previously described for He, with the same potential to explore the "d-"term for thisrelevant light nucleus.
Incoherent DVCS
A subject aside is represented by the incoherent DVCS offHelium nuclei, i.e., the process where the DVCS occurs ona bound-nucleon, which is ejected from the nucleus. There-fore, the bound-nucleon’s CFFs can be accessed, its GPDs,in principle, extracted and, ultimately, its tomography is ob-tained. This would provide a pictorial representation of the
28 | e + @JLab White Paper S. Fucini et al. ealization of the EMC effect and a great progress towards theunderstanding of its dynamical origin. As already stressed,this channel has been successfully isolated in the EG6 ex-periment of the CLAS collaboration at JLab [120] and a firstglimpse at the parton structure of the bound proton in thetransverse coordinate space is therefore at hand (see the re-cent impulse approximation calculation in Ref. [133] for atheoretical description of the recent data with conventionalrealistic ingredients). The program at JLab 12 includes animprovement of the accuracy of these measurements, in par-ticular, for the first time in DVCS, tagging the struck nucleonusing the detector developed by the ALERT run group [134].This would allow to keep possible final state interactions, rel-evant in principle in this channel, under control. Measure-ments performed with electron and positron beams wouldallow for example the measurement of the d − term for thebound nucleon, either proton in He (tagging 2H from DVCSon He) or in He (tagging H from DVCS on He) or neu-tron in He (tagging He from DVCS on He). Modificationsof the d − term of the nucleon in the nuclear medium, studiede.g. in Ref. [135], would be at hand, as well as a glimpse atthe structure of the neutron in the transverse plane, comple-mentary to that obtained with deuteron targets. Beyond a chiral even GPDs description ofDVCS on He As a last argument, we note that, from the measurement ofbeam spin asymmetries built using cross sections measuredwith polarized electrons and positrons in coherent DVCSoff He, the cross sections ˜ σ DV CS and ˜ σ INT , appearing inEq. (40), could be independently accessed. This would al-low, for the first time, to study the other leading twist CFFof a spinless target, the so called gluon transversity GPD H T , giving a corresponding name to the CFF H T , appear-ing in ˜ σ DV CS . In Ref. [121], it is shown how the contri-bution of H T to the cross section occurs through an inter-ference between twist-two and effective twist-three CFFs. Afirst glimpse at this complicated interrelation would be ob-tained for a spin-less target, in particular for a nuclear tar-get, for the first time. As for any other gluon-sensitive ob-servable, data for the cross section ˜ σ DV CS would be a per-fect tool to study gluon dynamics in nuclei. For example, acomparison with calculations performed in an Impulse Ap-proximation scheme, where the relevant nuclear degrees offreedom are colorless nucleons and mesons, with gluons con-fined within them, would have the potential to expose possi-ble exotic gluon dynamics in nuclei. This would be a prettynew possibility, complementary to that planned at JLab with12 GeV, using exclusive vector meson electroproduction off He [134]. Such an interersting behavior would be veryhardly seen using electrons only, due to the strong kinemati-cal suppression of ˜ σ DV CS with respect to the other contribu-tions in Eq. (40).
Conclusions
The unique possibilities offered by the use of positron beamsin DVCS off three- and four-body nuclear systems have beenreviewed. Summarizing, we can conclude that the main ad-vantages will be:• in coherent DVCS off He and He, using polarizedelectrons and unpolarized positrons, the real part of thechiral even unpolarized CFF would be measured witha precision comparable to that of the imaginary part,providing a tool for the study of the so called d termand to the distribution of pressure and forces betweenthe partons in nuclei, a new way to look at the nuclearmedium modifications of nucleon structure;• in incoherent DVCS off He and He, possibly taggingslow recoiling nuclear systems, the same programmecould be run for the bound proton and neutron;• using polarized He targets, a more complicated setupfor the moment, spin dependent and parton helicity flipCFFs would be accessed for the first time for a nucleus,in both their real and imaginary parts;• coherent DVCS off He, initiated with polarizedpositrons, would allow a first analysis of nuclear chiralodd CFFs and GPDs, with higher twist contaminationssuitable to tenptatively explore gluon dynamics in nu-clei.To conclude, a program of nuclear measurements withpositron beams would represent therefore an exciting com-plement to the experiments planned with nucleon targets, andto those planned with nuclear targets and electron beams.
He-DVCS e + @JLab White Paper | 290 | e + @JLab White Paper S. Fucini et al. ouble deeply virtual Compton scattering withpositrons at SoLID S. Zhao, A. Camsonne, E. Voutier, Z.W. Zhao
Positron beams, both polarized and unpolarized, are an impor-tant tool to study the partonic structure of the nucleon usingthe Generalized Parton Distributions (GPDs) framework. TheDouble Deeply Virtual Compton Scattering (DDVCS) processprovides the only experimental way to measure the GPDs de-pendence on both the average and transferred momentum in-dependently. The SoLID DDVCS experiment combining highluminosity and large acceptance will usher in an era of preci-sion measurements of DDVCS. Its positron program will bringbrand new physics observables that will provide access to thereal parts of Compton form factors and higher twist effects. Wediscuss the feasibility of such a program and demonstrate itspower with projections based on pseudo-data.
Introduction
The description of the partonic structure of hadronic mattervia the Generalized Parton Distributions (GPDs) has beenprofoundly extended the understanding of the structure anddynamics of the nucleon. The electroproduction of a leptonpair eN → eN l ¯ l , which is sensitive to the Double Deeply Vir-tual Compton Scattering (DDVCS) amplitude, provides theonly experimental framework for a decoupled measurementof GPDs( x, ξ, t ) as a function of both the average momentumfraction x and the transferred one ξ [107, 136–138].For instance, cross section or asymmetry experiments can ac-cess the Compton form factor (CFF) H . It is associated withthe GPD H can be written H ( ξ , ξ, t ) = P Z − H ( x, ξ, t ) (cid:20) x − ξ + 1 x + ξ (cid:21) dx − iπ [ H ( ξ , ξ, t ) − H ( − ξ , ξ, t )] (47) where P indicates the Cauchy principal value of the integral.The imaginary part accesses the GPD values at x = ± ξ . TheDeeply Virtual Compton Scattering (DVCS) and Time-likeCompton Scattering (TCS) processes has the limitation of ξ = ξ and ξ = − ξ respectively. Because of the virtuality offinal state photons, DDVCS with electron or positron beamsprovides a way to circumvent this limitation, allowing accessto decoupled information at ξ = ξ . For the complex quan-tity of the real part of the CFF, it involves the convolutionof parton propagators and the GPD values over x . One thenneeds DDVCS with positron beams to access it by brand newobservables.The DDVCS process is very challenging from the experimen-tal point of view due to the small magnitude of the cross sec-tion, and requires high luminosity and full exclusivity of thefinal state. Taking advantage of the energy upgrade of the Jefferson Lab CEBAF accelerator and next generation de-vice like SoLID with high luminosity and large acceptance,it is finally possible to investigate the electroproduction of µ + µ − di-muon pairs (avoiding complex antisymmetrizationissues with electron and postrion pair) and measure the exclu-sive ep → e p γ ∗ → e p µ + µ − reaction in the hard scatteringregime [139–142]. Physics Observable
Fig. 21. the handbag diagram symbolizing the DDVCS direct term with di-muon finalstates (there is also a crossed diagram where the final time-like photon is emittedfrom the initial quark).
At sufficiently high virtuality of the initial space-like pho-ton and small enough four-momentum transfer to the nucleonwith respect to the photon virtuality ( − t (cid:28) Q ), DDVCS canbe seen as the absorption of a space-like photon by a parton ofthe nucleon, followed by the quasi-instantaneous emission ofa time-like photon by the same parton, which finally decaysinto a di-muon pair as shown in Fig. 21. And the 7-fold dif-ferential crosssection has complicated kinematic dependencesuggested by Fig. 22Among them, Q and Q represent the virtuality of the in-coming space-like and outgoing time-like photons, respec-tively. The scaling variables ξ and ξ are ξ = Q − Q + t/ Q /x B − Q − Q + t , (48) ξ = Q + Q Q /x B − Q − Q + t (49) from which one obtains ξ = ξ Q − Q + t/ Q + Q . This relationindicates that ξ , and consequently the CFF imaginary part,changes sign around Q = Q . This present a strong testingground of the universality of the GPD formalism. DDVCS e + @JLab White Paper | 31 ig. 22. Reference frame of the DDVCS reaction. p p'* g e e'*' g + m - m p p'*' g e e'* g + m - m Fig. 23. two kinds of Bethe-Heitler processes contributing to electroproduction of adi-muon pair besides DDVCS , i.e. BH (left) and BH (right). A further complexity in studying GPDs via DDVCS is thatthere is an additional significant mechanism contributing tothe same final states, the Bethe-Heitler (BH) processes, asshown in figure 23. In the BH process the time-like pho-ton is radiated by the incoming or scattered electron, and inthe BH process it is produced within the nuclear field. TheBH and DDVCS mechanisms interfere at the amplitude level.However, the BH amplitudes are precisely calculable theoret-ically at small momentum transfers t . Thus the lepton-pairelectroproduction process consists of two other interferingBH terms with implied crossed contributions. The 7-fold dif-ferential cross section is proportional to the square of the totalamplitude that is the coherent sum of the three processes, i.e. d σ/ ( dQ dx B dtdQ dφd Ω µ ) ∝ |T DDVCS + T BH + T BH | .We consider in this study the 5-fold cross section, integrat-ing over the muon solid angle. The integration leads to thevanishing of the interference contributions originated fromthe BH amplitude: d σ/ ( dQ dx B dtdQ dφ ) ∝ |T DDVCS + T BH | + |T BH | [137, 138]. Though partial information issacrificed, this simplification offers an easier understandingof this totally unexplored reaction. Thus the cross section canbe described in terms of different contributions after integrat-ing over the final lepton angle, as the 5-fold differential crosssection d σ , whose decomposition in terms of beam chargeand polarization at leading order are shown below: d σ = d σ BH1UU + d σ BH2UU + d σ DDVCSUU + P l d σ DDVCSLU + ( − e l ) d σ INT1UU + P l ( − e l ) d σ INT1LU . (50) where the helicity-dependent DDVCS contribution d σ DDVCSLU rises at the twist-3 level. For experimentalobservables below, we use symbol ± for beam charge and → , ← for beam helicity.About cross section, one can easily obtain unpolarized andpolarized quantities for both electron and positron beams. σ − UU ( φ ) = 12 (cid:0) d σ −→ + d σ −← (cid:1) (51) = d σ BH1UU + d σ BH2UU + d σ DDVCSUU + d σ INT1UU , ∆ σ − LU ( φ ) = 12 (cid:0) d σ −→ − d σ −← (cid:1) (52) = P l d σ DDVCSLU + d σ INT1LU σ + UU ( φ ) = 12 (cid:0) d σ + → + d σ + ← (cid:1) (53) = d σ BH1UU + d σ BH2UU + d σ DDVCSUU − d σ INT1UU , ∆ σ + LU ( φ ) = 12 (cid:0) d σ + → − d σ + ← (cid:1) (54) = P l d σ DDVCSLU − d σ INT1LU
Therefore, it is possible to have two standalone Beam SpinAsymmetries (BSA) from polarized electron and positronbeams, and three correlated asymmetries, unpolarized andpolarized Beam Charge Asymmetry (BCA) and averagecharge spin asymmetry as follows. Each of them has uniquesensitivity to different component of DDCVS reactions andGPD. A − LU ( φ ) = (cid:0) d σ −→ − d σ −← (cid:1) ( d σ −→ + d σ −← ) (55) = P l d σ DDVCSLU + d σ INT1LU d σ BH1UU + d σ BH2UU + d σ DDVCSUU + d σ INT1UU ,A + LU ( φ ) = (cid:0) d σ + → − d σ + ← (cid:1) ( d σ + → + d σ + ← ) (56) = P l d σ DDVCSLU − d σ INT1LU d σ BH1UU + d σ BH2UU + d σ DDVCSUU − d σ INT1UU ,A CUU ( φ ) = (cid:0) d σ −→ + d σ −← (cid:1) − (cid:0) d σ + → + d σ + ← (cid:1) ( d σ −→ + d σ −← ) + ( d σ + → + d σ + ← ) (57) = d σ INT1UU d σ BH1UU + d σ BH2UU + d σ DDVCSUU ,A CLU ( φ ) = (cid:0) d σ −→ − d σ −← (cid:1) − (cid:0) d σ + → − d σ + ← (cid:1) ( d σ −→ + d σ −← ) + ( d σ + → + d σ + ← ) (58) = d σ INT1LU d σ BH1UU + d σ BH2UU + d σ DDVCSUU ,A ( φ ) = (cid:0) d σ −→ − d σ −← (cid:1) + (cid:0) d σ + → − d σ + ← (cid:1) ( d σ −→ + d σ −← ) + ( d σ + → + d σ + ← ) (59) = P l d σ DDVCSLU d σ BH1UU + d σ BH2UU + d σ DDVCSUU ,
32 | e + @JLab White Paper S. Zhao et al. M Calorimeter(large angle) EM Calorimeter(forward angle)Target GEM Light GasCherenkov Heavy GasCherenkovIron Yoke Scint
SoLID DDVCS
MRPCScint
Beamline
Muon Detector(forward angle)
Coil e - /e + μ μ Muon Detector(large angle)
Fig. 24.
SoLID DDVCS setup in Hall A of JLab.
Experimental Setup
SoLID, shown in Fig. 24, will be an all-new detector in HallA at JLab during the 12 GeV era [143]. It is designed to use asolenoid field to sweep away low-energy background chargedparticles. With custom designed high rate and high radiationtolerant detectors, it can carry out experiments using high in-tensity electron beams incident on unpolarized or polarizedtargets in an open geometry with full azimuthal coverage.There are two groups of sub-detectors. The forward angledetector group covers a polar angle range from ◦ to ◦ andconsist of several planes of Gas Electron Multipliers (GEM)for tracking, a light gas Cherenkov (LGC) for e/ π separation,a heavy gas Cherenkov (HGC) for π /K separation, a Multi-gap Resistive Plate Chamber (MRPC) for time-of-flight, aScintillator Pad (SPD) for photon rejection and a ForwardAngle Electromagnetic Calorimeter (FAEC). The large angledetector group covers a polar angle range from ◦ to ◦ andconsist of several planes of GEM for tracking, a SPD and aLarge Angle Electromagnetic Calorimeter (LAEC).Electrons and positrons will be detected and identified bymeasuring their momenta, time-of-flight, photons producedin the threshold Cherenkov detectors, and energy losses in thecalorimeters. However, we would need dedicated detectorsfor muons. At the large angle, there are enough material fromboth LAEC and iron flux return can work as shielding and acouple thin layers detectors like GEM at the outer radius ofthe downstream encap can detect muon effectively. However,the existing materials at the forward angle,including LAECand the downstream endcap backend iron, are not enough.Fortunately, when SoLID adopted the CLEO II soelnoid forits magnet from Cornell University, its massive iron flux re-turn was also transferred over to JLab. We plan to reconfigurethose layered iron slabs to form shielding at the forward anglebehind the downstream endcap and add thin layer detectorslike GEM as the forward angle muon detector.The acceptance of muons, electrons and positrons accordingto SoLID Geant4 detector simulation with energy loss in ma-terials, is shown in Fig. 25. The design of various detectorsare still being optimized as SoLID project moving forward μ - / μ + e - /e + Forward Angle Large Angle
Fig. 25.
The acceptance of muon (top) and e − /e + (bottom) at the SoLID forwardangle (left) and large large (right) detectors quickly.The 1st phase of SoLID DDVCS experiment is planned as aparallel run of the approved SOLID J/ψ experiment with a15 cm long unpolarized liquid hydrogen target and 3 µ A 85%polarized electron beam. With an instantaneous luminosityat L = 1 . e cm − s − and 50 days of running, unprece-dent amount of data will be collected and can be used forcross section and asymmetry study with electron beam spinasymmetry ( A − LU ). The 2nd phase would be dedicated run-ning with a unpolarized positron beam at the same luminosityfor 50 days. In addition to the cross section, the unpolarizedbeam charge asymmetry ( A C UU ) study can be carried out bycombining the electron beam data from the 1st phase. Thepotential 3rd phase is to use polarized positron beam to studythe positron beam spin asymmetry ( A + LU ) and polarized beamcharge asymmetry ( A CLU ) and charge average spin asymmetry( A ). Projections
A DDVCS event generator based on VGG model [144–146]at leading-twist has been developed for this study. Currentlyit has the twist-3 d σ DDVCSLU term as 0 and more of its de-tails can be obtained from the reference [142]. With elec-tron/positron and both muons are detected, we take SoLIDDDVCS acceptance and the overall detector efficiency ( ≈ ) into account to obtain the BH and DDVCS event countsfor both 1st and 2nd phase of the experiment.Figure 26 depicts the count number distribution on the( Q , − t ) and ( ξ , ξ ) planes. The experiment covers verybroad kinematic range within the factorization regime ( − t (cid:28) Q ) and between the DVCS correlation ( ξ = ξ ) and the TCScorrelation ( ξ = − ξ ). With unprecedented statistics, we canstudy DDVCS in all 5 independent kinematic variables of ξ , ξ, Q , t, φ .The projection of the electron beam spin asymmetry A − LU over φ with statistic errors from the 1st phase is shown in the DDVCS e + @JLab White Paper | 33 (GeV Q0 1 2 3 4 5 6 7 ) t ( G e V - x - - - - x Fig. 26.
The distribution of DDVCS and BH event count number on ( Q , − t ) plane(top) and on ( ξ ,ξ ) plane (bottom). The kinematic coverage indicate the DDVCSevents are in the factorization regime ( − t (cid:28) Q ) and between the DVCS ( ξ = ξ )and the TCS limitation ( ξ = − ξ ). (deg) f - L U A - = 1.25 GeV Q 0.06 - ' = x = 1.25 GeV Q' = 0.075 x = 1.875 GeV Q' = 0.075 x t = 0.25 GeV - = 0.135, x (deg) f C UU A - = 1.25 GeV Q 0.06 - ' = x = 1.25 GeV Q' = 0.075 x = 1.875 GeV Q' = 0.075 x t = 0.25 GeV - = 0.135, x Fig. 27.
The electron beam spin asymmetry A − LU (upper panel) and the unpolarizedbeam charge asymmetry ( A C UU ) (lower panel) for the three kinematic bins where ξ changes its sign. top plot of Fig. 27. 3 kinematic bins of ξ , ξ, Q , t are chosento demonstrate the data would allow explore how the asym-metry distribution changes its sign when ξ cross over fromnegative to positive values. When the unpolarized positronbeam data at the 2nd phase is added, we can obtain the unpo-larized beam charge asymmetry ( A C UU ) over φ with statisticerrors as shown in bottom plot of Fig. 27. The same 3 kine-matic bins of ξ , ξ, Q , t are chosen. Similar data points withgood precision will be obtained across the broad kinematiccoverage of the experiment. They can be used in a global fit-ting to extract CFFs and GPDs where no other measurementcan provide. Conclusions
The SoLID DDVCS experiment at its 1st phase can provideimportant information about imaginary part of CFFs. Withunpolarized positron beam added at the 2nd phase, it wouldstudy real part of CFFs with extraordinary coverage and pre-cision. Finally polarized positron beam at the 3nd phasemakes it even possible to explore GPD at the twist-3 level.Positron beams, both polarized and unpolarized, when com-bined with the power of SoLID’s high luminosity and largeacceptance capabilities, make the DDVCS reaction reach itsfull potential to study nucleon structure through GPDs.
ACKNOWLEDGEMENTS
S. Zhao is supported by the China Scholarship Council (CSC) and the French Cen-tre National de la Recherche Scientifique (CNRS).34 | e + @JLab White Paper S. Zhao et al. etermination of two-Photon exchange via e + p/e − p scattering with CLAS12 J.C. Bernauer, V. Burkert, E. Cline, A. Schmidt
The proton elastic form factor ratio shows a discrepancy be-tween measurements using the Rosenbluth technique in unpo-larized beam and target experiment and measurements usingpolarization degrees of freedom. The proposed explanationof this discrepancy are uncorrected hard two-photon exchange(TPE) effects, a type of radiative corrections. Their size andagreement with theoretical predictions has been tested recentlyby three experiments. While the results support the existence ofa small two-photon exchange effect, they cannot establish thattheoretical treatments are valid. At larger momentum trans-fers, theory remains untested. This proposal aims to measuretwo-photon exchange over a so far largely untested, extended Q and ε range with high precision using the CLAS12 experi-ment. Such data are crucial to clearly identify or rule out TPEas the driver for the discrepancy and test several theoretical ap-proaches, believed valid in different parts of the tested Q range. Introduction
Over more than half a century, proton elastic form factorshave been extracted from electron-proton scattering exper-iments with unpolarized beams over a large range of four-momentum transfer squared, Q , via the so-called Rosen-bluth separation. The data indicate that the form factor ratio µG E /G M is in agreement with scaling, i.e., that the ratio isclose to 1. This ratio is also accessible via polarized beamswith fundamentally different kinematics, and, especially atlarge Q , improved precision. In contrast to the unpolarizedresult, the data indicate a roughly linearly fall-off of the ra-tio. Some result of the different experimental methods, aswell as recent fits, are compiled in Fig. 28. The two data setsare clearly inconsistent with each other, indicating that onemethod (or both) are failing to extract the proton’s true formfactors. The resolution of this "form factor ratio puzzle" iscrucial to advance our knowledge of the proton form factors.The differences observed by the two methods have been at-tributed to two-photon exchange (TPE) effects [19, 104, 147,148], poised to affect especially the Rosenbluth method data.Two-photon exchange corresponds to the group of diagramsin the second order Born approximation of lepton scatteringwhere two photon lines connect the lepton and proton. Thecase where on of these photons has negligible moment, theso-called “soft” case, is included in the standard radiativecorrections, like Ref. [62, 63]. The “hard” part, where bothphotons can carry considerable momentum, however, is not,but has been the focus of ongoing theoretical work.To evaluate the theoretical prescriptions and test if TPE is in-deed the solution of the puzzle, precise measurements over awide Q range are required. The most straightforward accessto TPE is via measurement of the ratio of elastic e + p/e − p . .
52 0 2 4 6 8 10
OLYMPUSVEPP-3JLABCLAS12 µ G E / G M Q [(GeV/ c ) ] Rosenbluth
Litt ’70Bartel ’73Andivahis ’94Walker ’94Christy ’04Qattan ’05
Polarization
Gayou ’01Punjabi ’05Jones ’06Puckett ’10Paolone ’10Puckett ’12
Fits Bernauer ’13
Fit RosenbluthFit all + phen. TPE
Fig. 28.
The proton form factor ratio µG E /G M , as determined via Rosenbluth-type (black points, from [54, 56–60]) and polarization-type (gray points, from [3, 40,41, 45, 48]) experiments. While the former indicate a ratio close to 1, the latter showa distinct linear fall-off. Curves are from a phenomenological fit [149], to either theRosenbluth-type world data set alone (dark curves) or to all data, then including aphenomenological two-photon-exchange model. We also indicate the coverage ofearlier experiments as well as of the experiment described below. scattering, R γ = σ e + σ e − ≈ δ T P E . (60) We propose a new definitive measurement of the TPE ef-fect that would be possible with a positron source at CEBAF.By alternately scattering positron and electron beams froma liquid hydrogen target and detecting the scattered leptonand recoiling proton in coincidence with the large acceptanceCLAS-12 spectrometer, the magnitude of the TPE contribu-tion between Q values of 2 and 10 GeV could be signifi-cantly constrained. With such a measurement, the question ofwhether or not TPE is at the heart of the “proton form factorpuzzle” could be answered definitively. Previous work.
One significant challenge is that hard TPEcannot be calculated in a model-independent way. There areseveral model-dependent approaches. A full description ofthe available theoretical calculations are outside of the scopeof this letter. Suffice it to say that they can be roughly di-vided into two groups: hadronic calculations, e.g. [69], whichshould be valid for Q from 0 up to a couple of GeV , andGPDs based calculations, e.g. [71]. The latter give a gooddescription of nucleon form factors and wide-angle Comptonscattering at JLAB kinematics and should become valid for Q > , where the early onset of scaling is observed in DIS.At these scales, point-like quarks start to be resolved and theemissions of quarks from and re-absorption into a nucleon aredescribed by GPDs, the overlap of light cone wave functions.Three contemporary experiments measured the size of TPE,based at VEPP-3 [64], Jefferson Lab (CLAS, [65, 66, 150])and DESY (OLYMPUS, [67]). These experiments measuredthe ratio of positron-proton to electron-proton elastic crosssections. The kinematic reach of the three experiments isshown in Fig. 29. The kinematic coverage in these experi- TPE@CLAS12 e + @JLab White Paper | 35 . . . . Q [ G e V / c ] (cid:15) CLASOLYMPUS VEPP-3 Run IVEPP-3 Run II . . . . Fig. 29.
Kinematics covered by the three recent experiments to measure the two-photon exchange contribution to the elastic ep cross section. ments is limited to Q < GeV , and ε > . , where the two-photon effects are expected to be small, and systematics ofthe measurements must be extremely well controlled. Com-parisons of the data with theoretical predictions find overallpoor agreement, an indication that TPE is not fully under-stood from theory. Compared to phenomenological predic-tions [149], the agreement in good, indicating that TPE canindeed explain the majority of the discrepancy at the testedkinematics. However, at the highest Q points, the predic-tions over-shoot the data considerably, pointing towards thepossibility that TPE might not sufficiently explain the dis-crepancy at higher Q .We refer to [104] for a more in-depth review. The uncertaintyin the resolution of the ratio puzzle jeopardizes the extractionof reliable form factor information, especially at high Q , ascovered by the Jefferson Lab 12 GeV program. Clearly, newdata are needed. Proposed experiment
Theories and phenomenological extractions predict a roughlyproportional relationship of the TPE effect with − ε anda sub-linear increase with Q . However, interaction ratesdrop sharply with smaller ε and higher Q , correspondingto higher beam energies and larger electron scattering an-gles. This puts the interesting kinematic region out of reachfor storage-ring experiments, and handicaps external beamexperiments with classic spectrometers with comparativelysmall acceptance.With the large acceptance of CLAS12 , combined with an al-most ideal coverage of the kinematics, measurements of TPEacross a wide kinematic range are possible, complementingthe precision form factor program of Jefferson Lab, and test-ing both hadronic (valid at the low Q end) as well as GPD-based (valid at the high Q -end) theoretical approaches. Fig-ure 30 shows the angle correlation between the lepton and theproton for different beam momenta. There is a one-to-onecorrelation between the lepton scattering angle and the pro-ton recoil angle. For the kinematics of interest, say ε < . and Q > GeV for the chosen beam energies from 2.2 to6.6 GeV, nearly all of the lepton scattering angles falls into ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ε < . P r o t o n s c a tt e r i n g a n g l e θ p Lepton scattering angle θ l ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ . . . . . . . . . ε Fig. 30.
Polar angle correlation and ε coverage for lepton and proton. a polar angle range from ◦ to ◦ , and corresponding tothe proton polar angle range from ◦ to ◦ . These kine-matics are most suitable for accessing the TPE contributions.The setup will also be able to measure the reversed kine-matics with the electrons at forward angle and the protonsat large polar angles, i.e. the standard CLAS12 configura-tion of DVCS and most other experiments. While the two-photon exchange is expected to be small in this range, thesign change in TPE seen in the experiments, but not predictedby current theories, can be studied.Figure 31 shows the expected elastic scattering rates cover-ing the ranges of highest interest, with ε < . and Q =2 − GeV . Sufficiently high statistics can be achievedwithin 10 hrs for the lowest energy and within 1000 hrs forthe highest energy, to cover the full range in kinematics. Notethat all kinematic bins will be measured simultaneously at agiven energy, and the shown rates are for the individual binsin ( Q , ε ) phase-space. In order to achieve the desired kine-matics reach in Q and ε the CLAS12 detection system has tobe used with reversed detection capabilities for leptons. Themain modification will involve replacing the current CentralNeutron Detector with a central electromagnetic calorimeter(CEC). The CEC will not need very good resolution, whichis provided by the tracking detectors, but will only be usedfor trigger purposes and for electron/pion separation. Thestrict kinematic correlation of the scattered electron and therecoil proton will be sufficient to select the elastic events. The
CLAS12 configuration suitable for this experiment is shownin Fig. 32.
Central Electromagnetic Calorimeter.
The Central Elec-tromagnetic Calorimeter (CEC) will be used for trigger pur-poses to detect electrons elastically scattered under largeangles and for the separation of electrons (positrons) andcharged pions. The CEC will be built based on a novelJLab Tungsten Powder/Scintillating Fiber Calorimetry tech-nology proposed in 1999. This original proposal was todevelop a compact, high-density fast calorimeter with goodenergy resolution at polar angles greater than 35 ◦ for the CLAS12 spectrometer [151], and occupy the radial space
36 | e + @JLab White Paper J.C. Bernauer et al. . . . . Q [ G e V ] (cid:15) Proton not detected Lepton not detected . . . . . G e V . G e V . G e V . G e V
10 10 . . . . Q [ G e V ] (cid:15) Proton not detected Lepton not detected . . . . . G e V . G e V . G e V . G e V Fig. 31.
Expected elastic event rates per hour for energies 2.2, 3.3, 4.4, 6.6 GeVin the ε - Q plane. Shaded areas are excluded by the detector acceptance. Top:proposed experiment; Bottom: standard setup Fig. 32.
CLAS12 configuration for the elastic e − p/e + p scattering experiment(generic). The central detector will detect the electron/positrons, and the bending inthe solenoid magnetic field will be identical for the same kinematics. The proton willbe detected in the forward detector part. The torus field direction will be the samein both cases. The deflection in φ due to the solenoid fringe field will be of samein magnitude of ∆ φ but opposite in direction. The systematic of this shift can becontrolled by doing the same experiment with reversed solenoid field direction. of ≈
10 cm to fit inside the Central Solenoid. For the pro-posed elastic scattering experiment, the CEC would replace the current Central Neutron Detector, which occupies ap-proximately the same radial space and polar angle range. Thepowder calorimeter’s essential features are compactness, ho-mogeneity, simplicity, and unique readout capabilities. Fromthe original proposal there exists a prototype calorimeter de-signed, built, and cosmic-ray tested. The dimensions of theactive volume filled with tungsten powder are approximatelylength × width × height = 0.1 × × in volume andwith 5,488 fibers (Bicron BCF-12) with 0.75 mm diame-ter, uniformly distributed inside the tungsten powder volume.These fibers make up 35% of the volume and the tungstenpowder is filled into the remaining volume. The final den-sity of the tungsten powder radiator is 12 g/cm , or about 5%higher as compared with the density of bulk lead. The overalltotal density of the prototype active volume is ≈ .There is the possibility of increasing the density of the radi-ator to ≈ , which will lead to an increase of thedetector absorption power. Also an additional increase canbe obtained by simply decreasing sampling ratio, since hav-ing higher energy resolution is not a critical requirement. Ithas to be mentioned that due to the cylindrical shape of theCEC there will be no side wall effects. The estimated sig-nal strength is about 75 photoelectrons per MeV. The pro-totype can be tested and calibrated with electrons of knownenergy. Utilizing the unique Tungsten Powder Calorimetryexpertise developed at JLab we propose to build a CEC withparameters close the the existing prototype calorimeter. Thecalorimeter will need to cover polar angles in a range of 40 ◦ to 130 ◦ , and the full 2 π range in azimuth. Projected measurements.
For the rate estimates and thekinematical coverage we have made a number of assumptionsthat are not overly stringent: i) Positron beam currents (unpolarized), I e + ≈ nA; ii) Beam profile, σ x , σ y < . mm; iii) Polarization not required, so phase space at the sourcecan be optimized for yield and beam parameters; iv)
Operate experiment with 5 cm liquid H target and lu-minosity of . × cm − · sec − ; v) Use the
CLAS12
Central Detector for lepton ( e + /e − )detection at Θ l = ◦ - ◦ ; vi) Use
CLAS12
Forward Detector for proton detection at Θ p = ◦ - ◦ .We propose to take data at beam energies of 2.2, 3.3, 4.4 and6.6 GeV, for 10 h, 50 h, 200 h and 1000 h respectively, split1:1 in electron and positron running. The expected statisticalerrors, together with the expected effect size (phenomeno-logical extraction from [149]) are shown in Fig. 33. Thequality of the measured data will quantify hard two-photon-exchange over the whole region of precisely measured andto-be-measured cross section data, enabling a model-free ex-traction of the form factors from those. It will test if TPE TPE@CLAS12 e + @JLab White Paper | 37 . . . . . . . . . . . R γ (cid:15) E beam = 2 . GeV, 10h E beam = 3 . GeV, 50h E beam = 4 . GeV, 200h E beam = 6 . GeV, 1000h
Fig. 33.
Predicted effect size and estimated errors for the proposed measurementprogram at
CLAS12 . We assume bins of constant ∆ Q = . GeV . can reconcile the form factor ratio data where the discrep-ancy is most significantly seen, and test, for the first time,GPD-based calculations. Systematics of the comparison between electron andpositron measurements.
The main benefit to measure bothlepton species in the same setup closely together in time is thecancellation of many systematics which would affect the re-sult if data of a new positron scattering measurement is com-pared to existing electron scattering data. For example, onecan put tighter limits on the change of detector efficiency andacceptance changes between the two measurements if theyare close in time, or optimally, interleaved.For the ratio, only relative effects between the species typesare relevant; the absolute luminosity, detector efficiency, etc.cancel. Compared to classic small acceptance spectrometers,even the requirements on the relative luminosity determina-tion are somewhat relaxed, as all data points of one speciesshare the same luminosity, that is, even without any knowl-edge of the relative normalization between species, the evo-lution of TPE as a function of ε for constant beam momentacould be extracted. To achieve then an absolute normaliza-tion of the ratio, the relative luminosity must be controlled.The primary means of normalization for low current exper-iments in Hall B is the totally absorbing Faraday cup (FC)in the Hall B beam line. The absolute accuracy of the FC isbetter than 0.5% for currents of 5 nA or greater. The FC canbe used in e + / e − beams with up to 500 W, which should notbe a limitation for experiments in Hall B with CLAS12 . Therelative accuracy for the ratio of electrons to positrons shouldbe at least as good as the absolute accuracy. The only knowndifference between electrons and positrons is the interactionof e + and e − with the vacuum window at the entrance tothe FC, which is a source of Møller scattering for electronsand a source of Bhabha scattering for positrons. The FC de-sign contains a strong permanent magnet inside the vacuumvolume and just after the window. This magnet is meant totrap (most of) the low-energy Møller electrons to avoid over-counting the electric charge. It will also trap (most of) theBhabha scattered electrons from the positron beam to avoid under-counting (for positrons) the electric charge. However,there may be a remaining, likely small charge asymmetry forMøller and Bhabha scattered electrons in the response of theFC to the different charged beams. This effect will be fur-ther studied in detail with a GEANT4 simulation. In anycase, they relative efficiency of the FC can be calibrated witha measurement of R at small scattering angles, i.e. ε → ,where TPE effects become negligible. This calibration couldbe performed with the Forward Tagger Calorimeter whichcovers down to 2.5 degrees. The high counting rates makethis a simple and fast calibration. Summary
Despite recent measurements of the e + p/e − p cross sectionratio, the proton’s form factor discrepancy has not been con-clusively resolved, and new measurements at higher momen-tum transfer are needed. CLAS12 , in combination with apositron beam at CEBAF, would be the definitive measure-ment of TPE over a wide and highly significant kinematicrange. Only one major detector configuration change wouldbe necessary to support such a measurement, the installationof the central electromagnetic calorimeter. In designing theJLab positron source, it will be crucial for this and severalother experiments to keep to a minimum the time necessaryto switch between electron and positron modes, in order toreduce systematic effects.
38 | e + @JLab White Paper J.C. Bernauer et al. irect two-photon exchange measurement via e + p/e − p scattering at low ε in Hall A E. Cline, J.C. Bernauer, A. Schmidt
The proton elastic form factor ratio can be measured eithervia Rosenbluth separation in an unpolarized beam and targetexperiment, or via the use of polarization degrees of freedom.However, data produced by these two approaches show a dis-crepancy, increasing with Q . The proposed explanation of thisdiscrepancy – two-photon exchange – has been tested recentlyby three experiments. The results support the existence of asmall two-photon exchange effect but cannot establish that the-oretical treatments at the measured momentum transfers arevalid. At larger momentum transfers, theory remains untested,and without further data, it is impossible to resolve the discrep-ancy. A positron beam at Jefferson Lab allows us to directlymeasure two-photon exchange over an extended Q and (cid:15) rangewith high precision. With this, we can validate whether the ef-fect reconciles the form factor ratio measurements, and test sev-eral theoretical approaches, valid in different parts of the tested Q range. We propose a measurement program in Hall A thatmakes use of Super BigBite, BigBite, and one High ResolutionSpectrometer to directly measure the two-photon effect specifi-cally at low (cid:15) , where the magnitude of the effect is expected tobe largest. The higher luminosity possible in Hall A will allowa high-precision determination from a relatively short measure-ment to serve a robust cross check of a longer measurement pro-gram in Hall B. Introduction
Over more than half a century, proton elastic form factorshave been studied in electron-proton scattering with unpolar-ized beams. These experiments have yielded data over a largerange of four-momentum transfer squared, Q . The form fac-tors were extracted from the cross sections via the so-calledRosenbluth separation. Among other things, they found thatthe form factor ratio µG E /G M is in agreement with scal-ing, i.e., that the ratio is constant. Somewhat more recently,the ratio of the form factors was measured using polarizedbeams, with different systematics and increased precision es-pecially at large Q . However, the results indicate a roughlylinearly fall-off of the ratio. The result of the different ex-perimental methods, as well as some recent fits, are compiledin Fig. 34. The two data sets are clearly inconsistent witheach other, indicating that one method (or both) are failing toextract the proton’s true form factors. The resolution of this“form factor ratio puzzle" is crucial to advance our knowl-edge of the proton form factors, and with that, of the distri-bution of charge and magnetization inside the proton.The differences observed by the two methods have been at-tributed to two-photon exchange (TPE) effects [19, 104, 147,148], which are much more important in the Rosenbluthmethod than in the polarization transfer method, where in theratio they partially cancel out. TPE corresponds to a group of . .
52 0 2 4 6 8 10
OLYMPUSVEPP-3JLABCLAS12 µ G E / G M Q [(GeV/ c ) ] Rosenbluth
Litt ’70Bartel ’73Andivahis ’94Walker ’94Christy ’04Qattan ’05
Polarization
Gayou ’01Punjabi ’05Jones ’06Puckett ’10Paolone ’10Puckett ’12
Fits Bernauer ’13
Fit RosenbluthFit all + phen. TPE
Fig. 34.
The proton form factor ratio µG E /G M , as determined via Rosenbluth-type (black points, from [54, 56–60]) and polarization-type (gray points, from [3, 40,41, 43, 45, 48]) experiments. While the former indicate a ratio close to 1, the lattershow a distinct linear fall-off. Curves are from a phenomenological fit [149], to eitherthe Rosenbluth-type world data set alone (dark curves) or to all data, then includinga phenomenological two-photon-exchange model. We also indicate the coverageof earlier experiments as well as of the experiment described below. diagrams in the second order Born approximation of leptonscattering, namely those where two photon lines connect thelepton and proton. The so-called “soft” case, when one of thephotons has negligible momentum, is included in the stan-dard radiative corrections, like ref. [62, 63], to cancel infrareddivergences from other diagrams. The “hard” part, whereboth photons can carry considerable momentum, is not. Itis important to note here that the division between soft andhard part is arbitrary, and different calculations use differentprescriptions.It is obviously important to study this proposed solution tothe discrepancy with experiments that have sensitivity to two-photon contributions. The most straightforward process toevaluate two-photon contribution is the measurement of theratio of elastic e + p/e − p scattering, which in leading orderis given by the expression: R γ = 1 − δ γγ . Several experi-ments have recently been carried out to measure the 2-photonexchange contribution in elastic scattering: the VEPP-3 ex-periment at Novosibirsk [64], the CLAS experiment at Jef-ferson Lab [65, 66, 150], and the OLYMPUS experiment atDESY [67]. The kinematic reach of these experiments waslimited, however, as seen in Fig. 35.The current status can be summarized as such:• TPE exists, but is small in the covered region.• Hadronic theoretical calculations, supposed to be validin this kinematic regime, might not be good enoughyet.• Calculations based on GPDs, valid at higher Q , are sofar not tested at all by experiment.• A comparison with the phenomenological extractionallows for the possibility that the discrepancy might notstem from TPE alone. Direct e + p/e − p e + @JLab White Paper | 39 . . . . Q [ G e V / c ] (cid:15) CLASOLYMPUS VEPP-3 Run IVEPP-3 Run II . . . . Fig. 35.
Kinematics covered by the three recent experiments to measure the TPEcontribution to the elastic ep cross section.
We refer to [104] for a more in-depth review. The uncertaintyin the resolution of the ratio puzzle jeopardizes the extractionof reliable form factor information, especially at high Q , ascovered by the Jefferson Lab 12 GeV program. Clearly, newdata are needed.Both theories and phenomenological extractions predomi-nantly predict a roughly proportional relationship of the TPEeffect with − ε and a sub-linear increase with Q . How-ever, interaction rates drop sharply with smaller ε and higher Q , corresponding to higher beam energies and larger elec-tron scattering angles. This puts the interesting kinematicregion out of reach for storage-ring experiments, and hand-icaps external beam experiments with classic spectrometerswith comparatively small acceptance. Constraints on thenon-linearities in the TPE effect are given in [152]. Proposed Measurement
In this proposal, we advance a new definitive measurement ofthe TPE effect that would be possible with a positron sourceat CEBAF. By alternately scattering positron and electronbeams from a liquid hydrogen target and detecting the scat-tered lepton in the spectrometers available in Hall A, the mag-nitude of the TPE contribution between Q values of 2 and6 GeV , and at low ε could be significantly constrained. Withsuch a measurement, the question of whether or not TPE isat the heart of the “proton form factor puzzle” could be an-swered.Hall A would provide a quick (<2 weeks) measurement of theTPE effect. Utilizing the spectrometers in the Hall, we wouldbe able to make the measurement at very specific kinematicsin the region of interest for the TPE effect. With the proposedSBS detector and the existing BB spectrometer we would beable to extend the measurement to a previously inaccessiblekinematic region, ε < . . The speed and precision of thesemeasurements would be instrumental to addressing the “formfactor puzzle".In addition to a standard ep Rosenbluth measurement, wewould make use of a proton detection measurement. Thisapproach is less sensitive to the difference between electronand positron beam runs, allowing for a precise study of TPE
20 40 60 80 100 120 ) (cid:176)
Lepton Scattering Angle (0.00.10.20.30.40.50.60.70.80.91.0 E p s il on Beam EnergyE = 2.2 GeVE = 4.4 GeV
10 20 30 40 50 ) (cid:176)
Proton Scattering Angle (0.00.10.20.30.40.50.60.70.80.91.0 E p s il on Beam EnergyE = 2.2 GeVE = 4.4 GeV
Fig. 36.
Polar angle and ε coverage for electron detection (left) and for protondetection (right). effects with a positron-only measurement (combined with ex-isting electron data). The Q range is comparable to that ofthe standard Rosenbluth measurements, from 3 GeV to 6GeV , and the measurement extracts the TPE contribution tothe ε dependence of the cross section, rather than the crosssection at a fixed value of Q and ε . However, it does not re-quire frequent changes between electron and positron beams,and is less sensitive to beam quality issues.A similar proton-only measurement technique was used byJLab experiments E01-001 and E05-017 to provide a moreprecise Rosenbluth extraction of the ratio G E /G M for com-parison to precise polarization measurements [59, 60]. Theimproved precision comes from the fact that G E /G M is in-dependent of systematic effects that yield an overall renor-malization of the measurements at a fixed Q , combined withthe fact that many of the experimental conditions are un-changed when detecting e − p scattering at fixed Q over arange of ε values. The proton momentum is fixed, and somomentum-dependent corrections drop out in the extractionof G E /G M . In addition, the cross section dependence on ε is dramatically reduced when detecting the proton, while thesensitivity to knowledge of the beam energy, spectrometermomentum, and spectrometer angle is also reduced. Finally,the large, ε -dependent radiative corrections also have reduced ε dependence for proton detection.Figure 36 shows the angle coverage for both the electron(left) and for the proton (right). There is a one-to-one cor-relation between the electron scattering angle and the pro-ton recoil angle. For the kinematics of interest, ε < . and Q > GeV for the chosen beam energies from 2.2 & 4.4GeV, nearly all of the electron scattering angles falls into apolar angle range from ◦ to ◦ , and corresponding to theproton polar angle range from ◦ to ◦ . These kinematicsare most suitable for accessing the TPE contributions.It has been shown [61] that the extraction of the high- Q form factors is not limited by our understanding of the TPEcontributions, as long as the assumption that the Rosenbluth-Polarization discrepancy is explained entirely by TPE contri-butions. The proposed measurement would test this assump-tion, and also provide improved sensitivity to the overall sizeof the linear TPE contribution that appears as a false contribu-
40 | e + @JLab White Paper E. Cline et al. ig. 37. A not-to-scale schematic of the detector configuration for the proposedexperiment. The particle type in parentheses indicate what will be detected by thatspectrometer. tion to G E when TPE contributions are neglected. The mea-surement is also sensitive to non-linear contributions [152]coming from TPE, and would provide improved sensitivitycompared to existing electron measurements. More detailsare provided in Ref. [153]. Experimental Set-Up
Here we discuss the setup for our measurement to be per-formed in Hall A. The main kinematic considerations arethe limited momentum reach of the spectrometers in Hall A.However, the large acceptance of BigBite and Super BigBiteallows measurements at very low values of ε with excellentprecision.For the rate estimates and the kinematical coverage we havemade a number of assumptions that are not overly stringent:• Positron beam currents (unpolarized): I e + ≈ µ A.• Beam profile: σ x , σ y < . mm.• Polarization: not required, so phase space at the sourcemaybe chosen for optimized yield and beam parame-ters.• Operate with a
10 cm liquid H target and luminosityof . − s − • Use the HRS and BigBite for lepton ( e + /e − ) detectionat θ l = 40 − ◦ .• Use the SBS for proton detection at θ p = 6 − ◦ .The Hall A configuration suitable for this experiment isshown in Fig. 37.The proposed measurement program for Hall A is listed inTab. 1. While these measurements could provide precisemeasurements over a range of ε values in a short run pe-riod, they cover a limited range of beam energies. Because the Rosenbluth measurements suffer from the same beam-related systematics, they would benefit from rapid change-over between positrons and electrons, as well as an indepen-dent small-angle luminosity monitor to provide checks on theluminosity of the electron and positron beams.Proton detection scattering is also beneficial in making pre-cise comparisons of electron and positron scattering. Becausemost of the systematic uncertainties cancel when looking atthe ε dependence with electrons (or positrons), the measure-ment does not rely on rapid change of the beam polarity, oron a precise cross normalization or comparison of conditionsfor electron and positron running.This approach with proton detection scattering can give asensitive comparison of electron- and positron-proton scat-tering, with minimal systematic uncertainties and no need tocross-normalize electron and proton measurements. It doesnot provide direct comparisons of the e + p/e − p cross sectionratio, but does provide a direct and precise comparison of the ε dependence of the elastic cross section, for which the G E contribution is identical for positrons and electrons, and theTPE contribution changes sign. The general measurementswould be similar to the E05-017 experiment, with the excep-tion of using a low intensity positron beam and alternatingwith a similar electron beam. Assuming a 1 µ A positronbeam and the 10 cm LH2 target used in E05-017, a 12 dayrun could provide measurements with sub-percent statisticaluncertainties from 2.2 & 4.4 GeV , yielding total uncertain-ties comparable to the electron beam measurements. . . . . . . . . . . . . . . . a) R γ (cid:15) E beam = 2 . GeV E beam = 4 . GeV
Fig. 38.
Predicted effect size from the Bernauer phenomenological TPE parame-terization and estimated statistical errors in the region of interest in Hall A.
Figure 38 show the estimated errors and predicted effect sizefor Hall A. A high-impact measurement is possible with acomparatively small amount of beam time. Even in the casethe final positron beam current is lower than assumed here,the experiment remains feasible.
Systematics of the comparison between elec-tron and positron measurements
The main benefit to measure both lepton species in thesame setup closely together in time is the cancellation ofmany systematics which would affect the result if data of a
Direct e + p/e − p e + @JLab White Paper | 41 able 1. The second proposed Measurement plan in Hall A. Again note that SBS is used to detect protons, the corresponding lepton angle is given in parentheses. The totalproposed measurement time is 12 days. E beam ◦ ) * 50 70 12 (110) 80 120 6.2 (140) 40 80 15 (70) Q [( GeV /c ) ] (cid:15) * Central angles of the HRS, BigBite, and SBS new positron scattering measurement is compared to exist-ing electron scattering data. For example, one can put tighterlimits on the change of detector efficiency and acceptancechanges between the two measurements if they are close to-gether in time, or optimally, interleaved.To make use of these cancellations, it is paramount that thespecies switch-over can happen in a reasonable short timeframe ( < day) to keep the accelerator and detector setupstable. For the higher beam energies, where the measure-ment time is longer, it would be ideal if the species could beswitched several times during the data taking period.For the ratio, only relative effects between the species typesare relevant; the absolute luminosity, detector efficiency, etc.cancel. Of special concern here is the luminosity. While anabsolute luminosity is not needed, a precise determinationof the species-relative luminosity is crucial. Fortunately, theluminosity can easily be monitored to sub-percent accuracybased on beam current measurements and monitoring the tar-get density. The standard Hall A cryotarget is designed towithstand a 100 µ A beam with no more than 1% reductionin density, vastly more strenuous conditions than in this pro-posal. The beam current monitors in Hall A are conserva-tively estimated to have 1% accuracy. This system wouldlikely need to be upgraded to cope with beam currents below1 µ A.To keep the beam properties as similar as possible, the elec-tron beam should not be generated by the usual high qualitysource, but employ the same process as the positrons. Thiswill help minimize any differences in effects such as beampower on the target, beam dispersion, etc.
Conclusion
Despite recent measurements of the e + p/e − p cross sectionratio, the proton’s form factor discrepancy has not been con-clusively resolved, and new measurements at higher momen-tum transfer are needed. With a positron source at CEBAF,the enormous capabilities of the Hall A spectrometers couldbe brought to bear on this problem and provide a wealth ofnew data over a widely important kinematic range.Using the existing and in-development spectrometers in HallA, our proposed measurement could be completed with a typ-ical spectrometer configuration following the construction ofa positron source. The measurement using standard Rosen-bluth separation allows for a comparison with existing elec-tron scattering data, while extending the search for TPE con-tributions to the proton form factors.Utilizing proton-only detection in SBS allows for a sensi- tive test of TPE contributions that does not require the rapidchangeover between positrons end electrons. It does not di-rectly compare positron and electron scattering at fixed kine-matics. Instead, it measures the impact of TPE on the Rosen-bluth extraction of µ p G E /G M with high precision.The data that the proposed experiments could provide will beable to map out the transition between the regions of valid-ity for hadronic and partonic models of hard TPE, and makedefinitive statements about the nature of the proton form fac-tor discrepancy.
42 | e + @JLab White Paper E. Cline et al. measurement of two-photon exchange in e + p / e − p super-Rosenbluth separations J. Arrington, M. Yurov
While two-photon exchange (TPE) contributions are believed toresolve the discrepancy between proton form factor extractionsbased on polarized and unpolarized electron scattering, therehave been no direct measurements confirming the presence ofsufficient TPE in the kinematics needed to explain the discrep-ancy. Comparisons of positron and electrons scattering from theproton can directly measure the impact of TPE on the extrac-tion of the form factors, and we present here a method to extendsuch measurements to momentum transfer values directly rele-vant to the form factor discrepancy. This method allows for anextraction of the form factor ratio G E /G M that is independentof TPE effects and directly measures the impact of TPE on theform factor extraction. Introduction
The first precision measurements of the proton charge-to-magnetic form factor ratio G E /G M [1] using polarizationdegrees of freedom demonstrated a significant disagreementwith previous extraction utilizing the (unpolarized) Rosen-bluth technique, e.g. [58]. Careful examinations of thedata [154, 155], along with additional polarization [2, 49]and Rosenbluth [59, 60] measurements confirmed this dis-crepancy and showed that it grew with increasing momentumtransfer [4, 156], as seen in Figure 39 Fig. 39.
Comparison of Rosenbluth measurements (red circles and crosses) andpolarization extractions (blue triangles) of µ p G E /G M . Adapted from Ref. [60] .Two-photon exchange corrections are generally believed tobe responsible for the discrepancy between Rosenbluth andPolarization measurements [104, 147, 148]. Several calcu-lations of TPE, e.g. [20, 157, 158], demonstrated that TPEcontributions could resolve some or all of the discrepancy and suggest that the TPE contributions are roughly linear in ε at low-to-modest Q values and vanish at ε = 1 . A globalanalysis of Rosenbluth separation data sets significant limitson non-linear contributions up to Q ≈ GeV [152].A combined analysis of cross section and polarizationdata [61] demonstrated that the extraction of the form fac-tors is not currently limited by uncertainties associated withTPE corrections under the assumptions that TPE are respon-sible for the entire discrepancy and that TPE are linear in ε .However, next generation measurements of the form factorsat Jefferson Lab will reach Q values where the assumptionof linearity is not strongly supported by theory or experiment,and where TPE uncertainties may again become a limitingfactor in extraction of the form factors.Direct measurements of TPE contributions can be made viathe comparison of e + p and e − p scattering, as the TPE con-tribution depends on the charge of the lepton. An analysisof older measurements [159] and a series of new measure-ments [64–67, 150] have observed TPE contributions up to Q ≈ GeV that are qualitatively in agreement with calcu-lations that can largely explain the observed discrepancy atlarger Q values. The kinematics covered by these measure-ments do not directly overlap with the region where there is aclear discrepancy between Rosenbluth and polarization data,although some phenomenological extractions [149, 160] sug-gest that the discrepancy is significant down to Q = 1 GeV or below. As such, direct confirmation that TPE correc-tions explain the discrepancy at the same kinematics, plusimproved constraints on the ε dependence at large Q val-ues, are necessary for precise and reliable extraction of thenucleon form factors at large Q .The “Super-Rosenbluth” technique has been shown [60] toprovide precise extractions of the ratio of the proton’s chargeto magnetic form factor ratio. This technique, which re-lies on detection of only the struck proton, has the advan-tages of minimizing systematic corrections and uncertain-ties [153, 161, 162] between measurements at different val-ues of the virtual photon parameter, ε . By combining theadvantages of the Super-Rosenbluth approach with measure-ments of positrons, we can extend measurements of TPE tohigh Q values and large scattering angles (small ε ) wherethe contributions are expected to be large. Because G E /G M is extracted separately for positron and electron scattering,we can measure the impact of TPE on the Rosenbluth sep-arations without knowing the relative luminosities of thepositron and electron beams. We can also combine thepositron and electron data to extract G E /G M free from TPEcontributions. In addition, given a precise measurements ofthe relative luminosities, TPE contributions can be directlyextracted as a function of Q and ε over the full kinematicrange of the experiment. Super-Ros e + @JLab White Paper | 43 Figure 22. Parameterizations of R = µ p G E /G M (left) and R (right) from LT andpolarization data, along with the results expected for positrons assuming that TPEcorrections fully explain the LT-Polarization discrepancy. The right figure indicates the Q range that could be covered under the assumptions provided in the text, and thepoint for the electron and positron R LT results indicate the uncertainties from theprevious Hall A Super-Rosenbluth extraction [Qat05]. " dependence for proton detection.These advantages are also beneficial in making precise comparisons of electronand positron scattering. Because most of the systematic uncertainties cancelwhen looking at the " dependence with electrons (or positrons), the measure-ment does not rely on rapid change of the beam polarity, or on a precise crossnormalization or comparison of conditions for electron and positron running.Because extensive data were taken using this technique with electrons duringthe 6 GeV era, we would propose to use only positrons and extract G E /G M which depends only on the relative positron cross sections as a function of " .If rapid changes in the beam polarity are possible, then this approach wouldallow direct comparison of the cross sections with the advantage that the ac-ceptance is unchanged, while electron detection would require a change ofpolarity for the Hall A/C measurements, and the overall coincidence accep-tance is modified for the CLAS12 measurements. However, for this letter weassume that we would take only positron data for comparison to the existingE01-001 and E05-017 data sets. This approach can give a sensitive comparisonof electron- and positron-proton scattering, with minimal systematic uncer-tainties and no need to cross-normalize electron and proton measurements. Itdoes not provide direct comparisons of the e + p/e p cross section ratio, butdoes provide a direct and precise comparison of the " dependence of the elas-tic cross section, for which the G E contribution is identical for positrons andelectrons, and the TPE contribution changes sign.The general measurements would be identical to the E05-017 experiment, withthe exception of using a low intensity positron beam rather than the 30-80 µ Aelectron beam. Assuming a 1 µ A positron beam and the 4 cm LH target usedin E05-017, an 18 days run could provide measurements with sub-percent sta-tistical uncertainties from 0.4-4.2 GeV , yielding total uncertainties compara-ble to the electron beam measurements. This could be extended to > with the use of a 10 cm target, or if higher beam currents are available. Fig-44 Fig. 40.
Curves for ( µ p G E /G M ) (left) and ( µ p G E /G M ) (right) for existing polarization transfer (PT) data, and for projected Super-Rosenbluth measurements withpositrons and electrons. The black line indicates the region where precision comparisons can be made for positrons and electrons. The red uncertainties indicate theuncertainties of PT measurements in this region (placed on the curve), while the projected uncertainties for the LT separations are assumed to be identical to those from theE01-001 [60] measurement. Figure taken from Ref. [153]. See text for details. Proposed measurement
The Super-Rosenbluth measurement involves detection of thestruck proton, rather than the scattered electron. This has sev-eral advantages in controlling corrections and uncertainties inextracting the ε dependence (angle dependence) of the crosssection at fixed Q , as detailed in Refs. [60, 153, 161]. Thismeans that many of the issues associated with conventionalRosenbluth separations are under much better control:• The proton momentum is fixed for a given Q value,eliminating any corrections associated with the mo-mentum dependence of the detector response.• The low- ε cross section, which limits electron-basedmeasurements, is typically a factor of 10 or morehigher for proton detection.• The cross section for proton detection is roughly con-stant as a function of ε , while the cross section for elec-tron detection can vary by 2-3 orders of magnitude.This dramatically reduces rate-dependent systematicsand allows measurements to be performed a at fixedbeam current, minimizing the uncertainties in the rel-ative beam current measurement and density fluctua-tions due to target heating.• The proton detection cross section is typically muchless sensitive to offsets in the beam energy.We propose to perform Super-Rosenbluth measurementswith positrons (and electrons) in Hall C, detecting protonsin the High Momentum Spectrometer (HMS), with beam en-ergies from 2.2 to 6.6 GeV. The Super High MomentumSpectrometer (SHMS) would be used to measure electronsin coincidence for some settings to confirm that the pro-ton detection has clean isolation of elastic scattering events.The measurement is similar to the electron Super-RosenbluthMeasurements E01-001 in Hall A [60] and E05-017 in Hall C [163]. We take the configuration to be identical to the E05-017 experiment, but using a positron beam current of 1 µ Aas opposed to the 30–80 µ A electron beam used in E05-017;details are provided in Ref. [153]. With this setup, we canmake precision LT separations for both positron and electronbeams up to Q = 4 . GeV . An increased luminosity, fromeither a higher positron beam current or a longer liquid hy-drogen target, would allow an extension to Q values above5 GeV [153]. Note that the minimum Q achievable withhigh precision is 1-1.5 GeV with a minimum beam energyof 2.2 GeV; measurements down to 0.4 GeV are straightfor-ward with measurements at lower beam energies.Figure 40 shows projections for three Q points from 2.6-4.1 GeV , using the published results from E01-001 [60]as an estimate of the achievable systematic uncertainties.The left plot shows µ p G E /G M for polarization measure-ments (red points and lines), and for electron (blue) andpositron (green) Super-Rosenbluth measurements. TheBosted fit [164] is used for the electron Super-Rosenbluthprojection, and the positron curve is based on the electronmeasurements, applying TPE corrections to the slope takenfrom the difference between the Bosted fit and the fit topolarization-based extractions. Note that for Q > GeV ,the Rosenbluth slope is negative, and the curve in this re-gion is the square root of the absolute value of the Rosen-bluth slope. The right figure shows ( µ p G E /G M ) , propor-tional to the Rosenbluth slope, indicating more clearly theexpected difference between the electron and positron Super-Rosenbluth extractions.In addition to providing precise extractions of G E /G M , theSuper-Rosenbluth data also provide the most precise con-straints on non-linearity in elastic e − p scattering [60, 152].The experiment presented here can expand the Q range ofsuch tests, while providing enhanced sensitivity by directlycomparing electron and positron measurements of the ε de-pendence. In addition, with reliable measurements of the rel-ative electron and positron beam luminosities, using either
44 | e + @JLab White Paper J. Arrington et al. luminosity monitor or the SHMS spectrometer measuringelastic scattering at fixed angle where TPE are small, a directextraction of TPE contributions can be performed at each ε , Q point measured in the experiment. Conclusions
In conclusion, new Super-Rosenbluth measurements utiliz-ing a 1 µ A positron beam and the spectrometers in Hall C atJefferson Lab could make a precise extraction of the impactof TPE on Rosenbluth separations from 0.4-4.2 GeV . Thesedata would also provide new information on the ε dependenceof the TPE contributions at large Q , where no such data ex-ist so far, and where calculations yield significantly differentpredictions. Such a measurement could confirm TPE as thesource of the form factor discrepancy up to high Q valuesand measure deviations from linearity in the ε dependence ofthe TPE corrections. ACKNOWLEDGEMENTS
This work was supported by the U.S. Department of Energy, Office of Science,Office of Nuclear Physics, under contract DC-AC02-06CH11357Super-Ros e + @JLab White Paper | 456 | e + @JLab White Paper J. Arrington et al. olarization transfer in ~e + p → e + ~p scattering us-ing the Super BigBite Spectrometer A.J.R. Puckett, J.C. Bernauer, A. Schmidt
The effects of multi-photon-exchange and other higher-orderQED corrections on observables of elastic electron-proton orpositron-proton scattering have been a subject of high experi-mental and theoretical interest and investigation since the po-larization transfer measurements of the proton electromagneticform factor ratio G pE /G pM at large momentum transfer Q con-clusively established the strong decrease of this ratio with Q for Q (cid:38) GeV , a result incompatible with previous extractions ofthis quantity from cross section measurements using the Rosen-bluth Separation technique. Much experimental attention hasbeen focused on extracting the two-photon exchange (TPE) ef-fect through the unpolarized e + p/e − p cross section ratio, butpolarization transfer in polarized elastic scattering can also re-veal evidence of hard two-photon exchange. Furthermore, ithas a different sensitivity to the generalized TPE form fac-tors, meaning that measurements provide new information thatcannot be gleaned from unpolarized scattering alone. Both (cid:15) -dependence of polarization transfer at fixed Q , and deviationsbetween electron-proton and positron-proton scattering are keysignatures of hard TPE. A polarized positron beam at Jeffer-son Lab would present a unique opportunity to make the firstmeasurement of positron polarization transfer, and comparisonwith electron-scattering data would place valuable constraintson hard TPE. Here, we propose a measurement program in HallA that combines the Super BigBite Spectrometer for measuringrecoil proton polarization, with a non-magnetic calorimetric de-tector for triggering on elastically scattered positrons. Thoughthe reduced beam current of the positron beam will restrict thekinematic reach, this measurement will have very small system-atic uncertainties, making it a clean probe of TPE. Introduction
The discrepancy between the ratio µ p G E /G M of the the pro-ton’s electromagnetic form factors extracted from polariza-tion asymmetry measurements, and the ratio extracted fromunpolarized cross section measurements, leaves the field ofform factor physics in an uncomfortable state (see [104] fora recent review). On the one hand, there is a consistentand viable hypothesis that the discrepancy is caused by non-negligible hard two-photon exchange (TPE) [19, 20], the oneradiative correction omitted from the standard radiative cor-rection prescriptions [62, 63]. On the other hand, three re-cent measurements of hard TPE (at VEPP-3, at CLAS, andwith OLYMPUS) found that the effect of TPE is small in theregion of Q < GeV /c [64–67]. The TPE hypothesisis still viable; it is possible that hard TPE contributes moresubstantially at higher momentum transfers, and can fully re-solve the form factor discrepancy. But the lack of a definitiveconclusion from this recent set of measurements is an indica-tion that alternative approaches are needed to illuminate the situation, and it may be prudent to concentrate experimentaleffort on constraining and validating model-dependent the-oretical calculations of TPE. There are multiple theoreticalapproaches, with different assumptions and different regimesof validity [68–71, 165]. If new experimental data could val-idate and solidify confidence in one or more theoretical ap-proaches, then hard TPE could be treated in the future likeany of the other standard radiative corrections, i.e., a correc-tion that is calculated, applied, and trusted.VEPP-3, CLAS, and OLYMPUS all looked for hard TPEthrough measurements of the e + p to e − p elastic scatteringcross section ratio. After applying radiative corrections, anydeviation in this ratio from unity indicates a contribution fromhard TPE. However, this is not the only experimental signa-ture one could use. Hard TPE can also appear in a numberof polarization asymmetries. Having constraints from manyorthogonal directions, i.e., from both cross section ratios andvarious polarization asymmetries would be valuable for test-ing and validating theories of hard TPE. As with unpolar-ized cross sections, seeing an opposite effect for electronsand positrons is a clear signature of TPE.Here, we propose one such polarization measurement thatcould both be feasibly accomplished with a positron beamat Jefferson Lab, and contribute new information about twophoton exchange that could be used to constrain theoreticalmodels. We propose to measure the polarization transfer (PT)from a polarized positron beam scattering elastically from aproton target, for which no data currently exist. The proposedexperiment uses a combination of the Hall A Super Big-BiteSpectrometer (SBS) to measure the polarization of recoilingprotons and a lead-glass calorimeter for detecting scatteredpositrons in coincidence. In the following sections, we re-view polarization transfer, sketch the proposed measurement,and discuss possible systematic uncertainties. Polarization Transfer
In the Born approximation (i.e. one-photon exchange), thepolarization transferred from a polarized lepton to the recoil-ing proton is P t = − hP e q (cid:15) (1 − (cid:15) ) τ G E G M G M + (cid:15)τ G E ,P l = hP e √ − (cid:15) G M G M + (cid:15)τ G E , (61) where P t is the polarization transverse to the momentumtransfer 3-vector (in the reaction plane), P l is the longitudi-nal polarization, P e is the initial lepton polarization, h is thelepton helicity, τ ≡ Q M is the dimensionless 4-momentumtransfer squared, (cid:15) ≡ h τ ) tan (cid:16) θ e (cid:17)i − , with θ e e + p recoil polarization e + @JLab White Paper | 47 he electron scattering angle in the nucleon rest (laboratory)frame, is the virtual photon polarization parameter, and G E and G M are the proton’s electromagnetic form factors. Thestrength of the polarization transfer technique is to measure P t /P l , thereby cancelling some systematics associated withpolarimetry, and isolating the ratio of the proton’s form fac-tors: P t P l = − s (cid:15)τ (1 + (cid:15) ) G E G M . (62) This technique has several advantages over the traditionalRosenbluth separation technique for determining form fac-tors. This polarization ratio can be measured at a single kine-matic setting, avoiding the systematics associated with com-paring data taken from different spectrometer settings. Thistechnique allows the relative sign of the form factors to be de-termined, rather than simply their magnitudes. And further-more, whereas the sensitivity of Rosenbluth separation to G E diminishes at large momentum transfer, polarization trans-fer retains sensitivity to G E even when Q becomes large.When used in combination at high Q , Rosenbluth separa-tion can determine G M , while polarization transfer can de-termine G E /G M , allowing the form factors to be separatelydetermined.Polarization transfer using electron scattering has been usedextensively to map out the proton’s form factor ratio overa wide-range of Q , with experiments conducted at MITBates [50], Mainz [51], and Jefferson Lab [40, 44–47], in-cluding three experiments, GEp-I [1, 41], GEp-II [2, 48],and GEp-III [3, 49] that pushed to high momentum trans-fer. Another experiment, GEp-2 γ , looked for hints of TPEin the (cid:15) -dependence in polarization transfer [48, 166]. Twoother experiments made equivalent measurements by polariz-ing the proton target instead of measuring recoil polarization[43, 52].While polarization transfer is less sensitive to the effects ofhard TPE, it is not immune. Following the formalism ofRef. [147], one finds that P t P l = − s (cid:15)τ (1 + (cid:15) ) G E G M × " Re δ e G M G M ! + 1 G E Re (cid:16) δ e G E + νM e F (cid:17) − G M Re (cid:18) δ e G M + (cid:15)ν (1 + (cid:15) ) M e F (cid:19) + O ( α ) , (63) with ν ≡ ( p e + p e ) µ ( p p + p p ) µ , and where δ e G E , δ e G M , and δ e F are additional form factors that become non-zero whenmoving beyond the one-photon exchange approximation and,crucially, depend on both Q and (cid:15) , whereas the one-photon-exchange form factors depend only on Q . This particulardependence on new form factors is slightly different thanwhat one finds when taking a positron to electron cross sec- tion ratio: σ e + p σ e − p = 1 + 4 G M Re (cid:16) δ e G M + (cid:15)νM e F (cid:17) − (cid:15)τ G E Re (cid:16) δ e G E + νM e F (cid:17) + O ( α ) . (64) A measurement of the difference in polarization transfer be-tween electron and positron scattering therefore adds infor-mation about TPE in addition to what can be learned fromcross section ratios alone.The GEp-2 γ experiment looked for the effects of TPE in po-larization transfer by making measurements at three kine-matic points with varying values of (cid:15) , but with Q fixed at2.5 GeV /c [166]. Since in the absence of hard TPE theratio G E /G M has no (cid:15) -dependence, any variation with (cid:15) is asign of hard TPE. The GEp-2 γ measurement was statisticallyconsistent with no (cid:15) -dependence, though its measurement ofthe relative variation with (cid:15) of the longitudinal component P ‘ showed deviations from the one-photon exchange expec-tation at the level of 1.4%, with a statistical significance ofroughly 2 σ .A measurement with positron scattering for several Q valueswhere the discrepancy between cross section and polarizationdata is large, and where the e − p polarization transfer observ-ables have already been measured precisely, will be useful forconstraining TPE effects, because deviations from the Born-approximation should have the opposite sign from those inelectron scattering. This will help determine if deviations aretruly caused by TPE, or if they arise from systematic effects.As the largest systematic uncertainties in polarization trans-fer are associated with proton polarimetry, a measurementwith positrons would have largely the same systematics as anexperiment with electrons. Proposed Measurement
We propose a measurement of e + p polarization transfer ob-servables at two distinct values of Q in the region wherethe Rosenbluth-polarization discrepancy is large, using thenewly constructed Super BigBite Spectrometer (SBS), thatwas designed to measure G pE /G pM to Q ≈ GeV usingthe polarization transfer technique. Despite the lower ex-pected figure-of-merit P I of polarized positron beams com-pared to polarized electron beams, these measurements canbe accomplished in a reasonable time frame owing to thelarge solid-angle acceptance of the new SBS apparatus. Fig-ure 41 shows the layout of the proposed experiment in g4sbs ,the SBS GEANT4-based Monte Carlo simulation package.Polarized positrons are elastically scattered from free protonsat rest in a 40-cm liquid hydrogen target. Scattered positronsare detected in a lead-glass calorimeter (ECAL) and a “coor-dinate detector” (CDET), consisting of two planes of scintil-lator strips with high segmentation in the vertical direction.The combination of CDET and ECAL provides a highly ef-ficient and selective trigger for elastically scattered positronsand precise measurement of the positron’s scattering angles,for a clean selection of the elastic e + p channel in the presence
48 | e + @JLab White Paper A. J. R. Puckett et al. ig. 41. Screenshot from the GEANT4-based Monte Carlo simulation of the SBS-GEP apparatus, illustrating one elastic e + p event generated within the 40-cm liquidhydrogen target, with the electron detected in the lead-glass calorimeter (located on beam left) and the outgoing polarized proton detected in the SBS on beam right. of higher-rate inelastic background processes, predominantly π photoproduction.Elastically scattered protons are detected in the SBS, whichconsists of a large dipole magnet with a transverse field inte-gral along the direction of particle motion of up to 2.5 T · m,a proton polarimeter with Gas Electron Multiplier (GEM)-based tracking and CH as analyzer material, and a largehadron calorimeter. The role of the dipole magnet is formomentum analysis and to precess the longitudinal polar-ization of the recoiling proton into a transverse componentthat can be measured by the secondary analyzing scatter-ing in the CH . The tracking in SBS relies on the rela-tively recently invented technology of Gas Electron Multi-pliers (GEMs) [167], which can operate with stable gainat very high charged particle fluxes. The SBS front tracker,made of six GEM layers of area × cm , is used forreconstruction of the proton’s momentum, scattering angles,and interaction vertex, and also to define the proton’s inci-dent trajectory on the polarimeter, for subsequent measure-ment of the angular distribution of the secondary scattering.The spin-orbit coupling in the ~p + CH → ~p + X scatteringgives rise to an azimuthal asymmetry in the distribution ofscattered protons that is proportional to their initial trans-verse polarization. Each of the two CH analyzer blocks hasa thickness of approximately one nuclear interaction length,and is followed by a tracker assembled from five GEM lay-ers of area × cm , to measure the angular distributionof the polarization-analyzing scattering. Finally, a large iron-scintillator sampling hadronic calorimeter (HCAL), absorbsthe energy of the protons and provides for efficient triggeringon the events of interest, which are those in which the protonundergoes forward-angle elastic scattering in either (or both)of the two analyzers [168].To design an optimized measurement of R e + p ≡− µ p P t P ‘ q τ (1+ (cid:15) )2 (cid:15) , which equals µ p G pE /G pM in the one-photon approximation, requires a choice of Q and beamenergy that maximizes the product of the asymmetry mag-nitude squared and the event rate. Merely maximizing the electron differential cross section dσ/d Ω e by choosing thehighest available beam energy does not always lead to thehighest figure of merit (FOM) at a given Q , due to the (cid:15) dependence of P t and P ‘ , which both vanish in the limit (cid:15) → (see equations Eq. (61)), and also the diminishingreaction Jacobian at forward angles of the electron, wherethe solid angle ∆Ω e corresponding to the fixed proton solidangle ∆Ω p becomes small. The uncertainty of the ratio R is typically dominated by the uncertainty of the trans-verse component P t of the transferred polarization, whichreaches a maximum at (cid:15) ≈ . , which usually occurs around θ e ≈ ◦ . On the other hand, event rate considerationsgenerally favor somewhat more forward angles. Generallyspeaking, for a fixed proton solid angle acceptance ∆Ω p ,the FOM at a constant Q has a broad central maximum inthe region . ≤ (cid:15) ≤ . , in which it does not vary strongly.A simple rule of thumb is that the optimal FOM for apolarization transfer measurement occurs when the electronand proton scattering angles θ e and θ p are approximatelyequal, typically around (cid:15) ≈ . − . .To design an exploratory measurement of R e + p , Q shouldbe chosen large enough that significant TPE corrections tothis observable might reasonably be expected, but smallenough that useful precision can be achieved in a “reason-able” amount of beam time. It is also desirable to choose a Q for which R e − p is already precisely known. Q ≈ . GeV is an obvious choice, being close to the most preciseexisting measurements [49] in the Q region where the dis-crepancy is significant. A second measurement at a meaning-fully larger Q ≈ . GeV also seems attractive, as it wouldbe very close to two existing measurements from the GEp-I [41] and GEp-II [2] experiments which, however, are sig-nificantly less precise. Going significantly higher in Q than3.5 GeV would most likely require prohibitive beam time toreach a precision goal of 2%, given the low maximum currentfor polarized positrons.Table 2 shows the basic parameters of a plausible R e + p mea-surement using the SBS GEP apparatus. To estimate the pre-cision of these measurements, elastic e + p scattering events e + p recoil polarization e + @JLab White Paper | 49 able 2. Summary of proposed measurements. E e is the incident lepton energy, (cid:10) Q (cid:11) is the acceptance averaged Q , θ e is the central lepton scattering angle, h (cid:15) i is theacceptance averaged (cid:15) value, θ p is the central proton scattering angle, and p p is the central proton momentum. The expected event rate is based on the assumption of a 200nA (30 µ A) positron (electron) beam, and ∆ R is the projected absolute statistical uncertainty for the indicated number of beam days in the ratio R ≡ − µ p PtP‘ p τ (1+ (cid:15) )2 (cid:15) ,which equals µ p G pE /G pM in the one-photon approximation, assuming 60% (85%) positron (electron) polarization. On the third line, we depict an ancillary e − p measurementat kinematics identical to the higher Q e + p measurement, that could achieve 1% statistical precision in 24 hours (not including any time required to change CEBAF from e + to e − running). Lepton E e (cid:10) Q (cid:11) θ e h (cid:15) i θ p p p Event rate Days ∆ R GeV GeV deg. deg. GeV Hz (absolute) e + e + e − e + beam ona 40-cm liquid hydrogen target. For an initial, exploratorymeasurement, we choose a goal of ≈ absolute statisticaluncertainty in R e + p at each Q point. Since the precision ofthe existing data at the higher Q is only about 4% (absolute),it would be desirable to include an additional measurement of e − p scattering in identical kinematics. This could be accom-plished in a tiny fraction of the total beam time, as shown inTab. 2, plus any time that would be required to change CE-BAF from positron mode to electron mode and back again.The systematic uncertainties of the polarization transfermethod are typically extremely small. Because both P t and P ‘ are measured simultaneously in a single kinematic config-uration, a number of sources of systematic uncertainty, suchas beam polarization and analyzing power, cancel in the ra-tio P t /P ‘ . The luminosity also doesn’t need to be knownprecisely. Moreover, the ep reaction is self-calibrating withrespect to the analyzing power, and the rapid beam helicityreversal cancels the effects of false or instrumental asym-metries in the polarimeter. In previous experiments of thistype, a dominant source of systematics was the calculation ofthe proton spin precession in focusing magnetic spectrome-ters with several quadrupole magnets in addition to the main,momentum-analyzing dipole. In the SBS case, the spin pre-cession calculation is much simpler, as the SBS is a single,simple dipole magnet which is non-focusing. It is thereforeanticipated that any measurement of e + p polarization trans-fer observables will be statistics-limited in terms of accuracy.In addition, the relatively low luminosity of the proposed e + p measurements means that the event reconstruction in theSBS detectors will be extremely clean, and far less challeng-ing than in the approved high- Q measurements of E12-07-109 [73].Figure 42 shows what could be accomplished in a 90-dayexperiment at a constant beam energy of 4.4 GeV, underthe perhaps-somewhat-optimistic assumption that a positronbeam of 200 nA current and 60% polarization could be re-alized at CEBAF. This would be the first measurement of (GeV Q0.00.51.0 p M / G p E G p m Diehl05 (GPD)Segovia14 (DSE)Lomon06 (VMD)Gross08 (GCS) ) p Cloet12 (Diquark-Miller05 (RCQM)Cross section dataPolarization dataSBS GEP projectedp projected + SBS e
Fig. 42.
Projected results of the proposed future 90-day measurement of R e + p using the polarization transfer method with the SBS GEP apparatus, compared toexisting data, selected theoretical predictions, and the projected results of E12-07-109 [73]. Theory curves are Refs. [169] (Diehl05), [170] (Segovia14), [171, 172](Lomon06), [173] (Gross08), [174] (Cloet12), and [175] (Miller05). Projections of fu-ture experiments are shown at values of R from the global fits described in Ref. [49] polarization transfer in e + p scattering, reaching very re-spectable precision in the Q regime where the discrepancybetween cross sections and polarization observables is large,and where R p is falling most rapidly as a function of Q .Such data would provide important model-independent con-straints on hard TPEX amplitudes, toward the goal of find-ing a conclusive explanation of the discrepancy and a model-independent, data-constrained theoretical prescription for ap-plying hard TPEX corrections to elastic e ± p scattering ob-servables. Acknowledgements
This work was supported in part by the US Department ofEnergy Office of Science, Office of Nuclear Physics, AwardID DE-SC0014230.
50 | e + @JLab White Paper A.J.R. Puckett et al. arget-normal single spin asymmetries mea-sured with positrons A. Schmidt, T. Kutz
The two-photon exchange and the larger class of hadronic boxdiagrams are difficult to calculate without a large degree ofmodel-dependence. At the same time, these processes are sig-nificant radiative corrections in parity-violating electron scat-tering, in neutron decay, and may even be responsible for theproton’s form factor ratio discrepancy. New kinds of experi-mental data are needed to help constrain models and guide fu-ture box-diagram calculations. The target-normal single spinasymmetry, A n , formed with an unpolarized beam scatteringfrom a target that is polarized normal to the scattering plane, issensitive to the imaginary part of the two-photon exchange am-plitude, and can provide a valuable constraint. A measurementwith both electrons and positrons can reduce sources of exper-imental error, and distinguish between the effects of TPE andthose of T -violation. This note describes a proposed experimentin Hall A, using the new Super Big-Bite Spectrometer that cancover a momentum transfer range in the critical zone of uncer-tainty, between where hadronic calculations and those based onGeneralized Parton Distributions are expected to be accurate. Introduction
Hadronic box diagrams in elastic electron scattering are diffi-cult to calculate without significant model-dependence. Un-fortunately, they are also lead to significant radiative cor-rections in a number of measurements, for example, γZ -exchange in parity-violating electron scattering) and γW ± -exchange in measurements of beta-decay widths. Two-photon exchange in elastic electron-proton scattering is hy-pothesized to be responsible for discrepancy between unpo-larized and polarized extractions of the proton’s form factorratio. All of these applications require a better understandingof box-diagram processes, and new experimental constraintsare needed to help improve theoretical calculations. Thereare several experimental observables that are directly sensi-tive to box-diagrams contributions, and because they provideorthogonal constraints, it is advantageous to pursue a variety.One such observable is a target-normal single-spin asymme-try (SSA), denoted by A n . This asymmetry is measured byscattering an unpolarized electron (or positron) beam on atarget polarized in a direction perpendicular to the scatter-ing plane, and comparing cross sections for “up” and “down”target polarizations. In the limit of one-photon exchange,single-spin asymmetries are forbidden, so A n is a direct mea-sure of multi-photon exchange.Following the formalism of Ref. [147], A n for a proton targetcan be related to the proton’s higher-order form factors, δ ˜ G E , δ ˜ G M , and δ ˜ F , by A n = p (cid:15) (1 + (cid:15) ) √ τ (cid:0) G M + (cid:15)τ G E (cid:1) × " − G M Im (cid:16) ˜ G E + νM ˜ F (cid:17) + G E Im (cid:18) ˜ G M + 2 (cid:15)νM (1 + (cid:15) ) ˜ F (cid:19) + O ( α ) , (65) G E and G M are the proton’s standard electric and magneticform factors, M is the mass of the proton, τ ≡ Q / M , (cid:15) − ≡ τ ) tan θ , and ν ≡ ( p e + p e ) µ ( p p + p p ) µ .Eq. 65 shows that A n is sensitive to the imaginary partsof the higher-order form factors, meaning that it providesa completely different constraint than measurements of theunpolarized positron-proton/electron-proton cross section ra-tio, which probes the real parts. Any process that violatestime-reversal symmetry (i.e., T-violating) will also lead to anon-zero A n . This means that a combined measurement withboth electrons and positrons can unambiguously distinguishbetween the TPE amplitude and T-violation.There are several different theoretical approaches for calcu-lating hard two-photon exchange, but they most fall into twoclasses: hadronic (for example, [68, 69] and others) and par-tonic (for example, [70, 71] and others). The hadronic cal-culations are expected to be most valid at lower momen-tum transfer, i.e., Q < GeV /c , while the partonic cal-culations are applicable for very high momentum transfer,i.e., Q > GeV /c . The zone in between, i.e., from 3–5 GeV /c is a region where new experimental constraintsare especially useful. Previous Measurements
Previous measurements of A n with electron scattering haveeither been made with inelastic scattering [176–180] search-ing for T -violation, or in quasielastic scattering from po-larized He [181]. There are currently no published re-sults from elastic electron scattering from polarized hydro-gen. Ref. [181] measured an asymmetry of a few parts perthousand in He, which corresponds to an asymmetry of afew percent from polarized neutrons. It would be reasonableto expect an asymmetry of similar size from polarized pro-tons.The measurement of Ref. [181] used the two high-resolutionspectrometers in Hall A to simultaneously measure at 17 ◦ both left and right of the beam direction. The target asym-metry was measured as a left/right asymmetry. The targetpolarization was additionally flipped to reduce systematics.This left-right approach has the advantage of being a simul-taneous measurement; both the left and right arms experiencethe same time-varying beam conditions. Target-Normal SSAs e + @JLab White Paper | 51 able 3. Proposed Measurement Plan
SBS/Big-Bite HRSBeam Energy [GeV] Q [GeV /c ] (cid:15) θ e [ ◦ ] Days Q [GeV /c ] (cid:15) θ p [ ◦ ] Days6.6 4.0 0.8696 21.22 8 0.5 0.9932 66.25 106.6 3.0 0.9207 17.34 24.4 3.0 0.8065 28.56 6 0.5 0.9844 64.67 74.4 2.0 0.9004 21.28 12.2 2.0 0.5600 53.18 6 0.1 0.9892 76.29 72.2 1.0 0.8419 30.27 0.52.2 0.5 0.9353 19.74 0.5Overhead 6 6 Totals 30 30
Proposed Measurement
We propose a measurement of A n in both electron- andpositron scattering from polarized protons. This measure-ment would provide the first A n data on protons, and wouldcover a range of Q , extending up to 4 GeV /c , in betweenthe regions where hadronic calculations are partonic calcula-tions are expected to be most accurate. This is a more am-bitious proposal than that first suggested in Ref. [182], andthis is made possible by the new Super BigBite Spectrometer(SBS), paired with the upgraded BigBite Spectrometer (BS)to add acceptance.The factor that limits the luminosity is not the available beamcurrent, but the polarized target. Several different polarizedproton targets have been used at Jefferson Lab [183–186],with the target from the g p and G pE Experiments [186]demonstrating the best performance under high-luminosityconditions. This target dynamically polarized protons infrozen beads of ammonia (NH ), within a 2.5–5 T holdingfield, and achieved approximately 70% average polarizationwith a beam current of up to 100 nA. This corresponds to aluminosity of roughly cm s − , given a 3 cm long tar-get, and a rough estimate of a 60% packing fraction for theammonia beads. For this proposal, it is assumed that a sim-ilar target could be designed and deliver 66% polarization ata luminosity of cm s − .Elastically scattered leptons would be detected either by SBSor BS. The two spectrometers would be paired to measureidentical angles on either side of the beam line, and the mea-surement of A n could be made from the left-right asymmetryalone. Target polarization flips (relatively easy with a dynam-ically polarized target) could be used to reduce systematicscoming from the target or from acceptance differences be-tween the two spectrometers. A top-view schematic of themeasurement layout is shown in Fig. 43.SBS and BS are not the only spectrometers in Hall A. If theleft high-resolution spectrometer is still operational, it can beused to cover additional kinematic points. Its small accep-tance will mean that its only useful at lower Q where ratesare higher. And it’s lack of a partner on the opposite side ofthe beam (assuming the right HRS will have been decommis-sioned) will require a measurement of A n through target spinflips, rather than a simultaneous left/right asymmetry mea-surement. However, we see no reason to omit it from the S B S ( e ± ) B i g B i t e ( e ± ) HRS ( p )NH Target e ± beam Fig. 43.
Layout of the proposed measurement in Hall A. SBS and BigBite will look atthe same scattering angle, allowing a simultaneous left/right asymmetry measure-ment. If available an HRS can be used to simultaneously measure the asymmetrybetween the two target polarization directions at low Q by detecting recoil protons. proposed measurement plan. To avoid any interference withthe SBS, the HRS will be positioned at more backward an-gles, where it can detect recoiling protons. Given a minimumcentral momentum of 300 MeV /c , the HRS has a minimum Q of approximately 0.1 GeV /c .The proposed measurement plan is shown in Table 3, andconsists of a total of 30 days (24 running, 6 overhead). TheSBS and BS will cover simultaneously Q values of 0.5, 1,2, 3, and 4 GeV /c . The use of three different beam ener-gies will allow measurements of Q = 2 and 3 GeV /c tobe made at multiple values of (cid:15) . The number of days listed in-clude both electron and positron running, i.e., 8 days means 4days with an electron beam and 4 days with a positron beam.To minimized any time-varying systematics, it would be de-sirable to be able to switch between electrons and positronsfrequently. Similarly, the target polarization direction shouldbe flipped frequently. Since the target would likely need tobe re-annealed every few hours to restore polarization, thiswould be the sensible timescale for target spin flips.The HRS will be used to detect protons from elastic scatteringat Q = 0 . GeV /c during the 6.6 and 4.4 GeV running,and positioned to cover Q = 0 . GeV /c during 2.2 GeVrunning, to avoid interference with the SBS.Fig. 44 shows an estimate of the statistical precision of the
52 | e + @JLab White Paper A. Schmidt et al. − . . . . . Proposed e + runningProposed e − runningHall A (2015, n ) A n Q [GeV /c ] Fig. 44.
Anticipated statistical precision of the proposed measurement. The Hallresults for the neutron using a polarized He target are from Ref. [181]. proposed measurement. The statistical precision was esti-mated as: δA n = 12 P D q dσd Ω Ω L T ε , (66) where P is the target polarization (assumed 66.7%), D isthe target dilution factor (assumed 15% for NH ), dσd Ω is theelastic scattering cross section, Ω is the spectrometer accep-tance, L is the luminosity ( cm − s − ), T is the run timeper target polarization setting, and ε is the running efficiency(assumed 50%). For these estimates, SBS and BS were as-sumed to use a common 70 msr angular acceptance, whilethe HRS was assumed to cover 4 msr. The proposed mea-surement would have approximately 1% statistical precisionor smaller on A n . The results of [181] indicate that, at leastfor the neutron, A n is a percent-level asymmetry. Systematics
The proposed measurement would have several sources ofsystmatic uncertainty to overcome. The dominant sourcewould be the time-variation of the target polarization. Thetarget polarization is one of the multiplicative factors that isneeded to extract A n from the measured count-rate asym-metry, and uncertainty in this polarization goes directly intouncertainty in A n . For the target described in Ref. [186],polarization was monitored continuously through NMR, anda similar procedure would be vital for the proposed mea-surement. The stability of the NMR system would be crit-ical in order to ascertain the charge-weighted target polar-ization for every measurement setting. Ref. [186] observedthat in between annealings, the target polarization degradedsignificantly with accumulated dose: though peak polariza-tions of 90% were achieved, this would degrade steadily,and the average polarization obtained was only 70%. The g p -Experiment claimed an uncertainty of 2–4.5% on the tar-get polarization [187]. For the proposed measurement, thiswould translate to a relative uncertainty on the asymmetry,i.e. a 5% target polarization uncertainty would produce anuncertainty of 0.05% on a 1% asymmetry. Note that the time-dependence would be somewhat mitigated in the SBS/BSmeasurements, which would make a simultaneous left/rightmeasurement. The systematics for the single HRS would bemuch worse. Another systematic uncertainty would come from the knowl-edge of the dilution factor of the NH target. This uncertaintywould be common to both positron and electron measure-ments, i.e., it would have no effect on T-violation, but wouldbias the measurement of TPE. The dilution factor calculationcan be made easier by enriching the target material with N,which is only one proton-hole shy of doubly-magic O. Bycontrast N has both an unpaired proton and an unpairedneutron.Other systematics would include differences in spectrome-ter efficiencies, spectrometer alignment, and beam currentmonitoring would be mitigated by making a simultaneousleft/right asymmetry, and by flipping the target polarization.
Summary
The target-normal single spin asymmetry A n is sensitive tothe imaginary part of the two-photon exchange amplitude,and has never been measured on a polarized proton target.By using both a positron and an electron beam, some exper-imental systematics can be reduced. Using the new SBS inHall A, a 30-day measurement would allow a comprehensivescan of Q at modest (cid:15) , and push up to Q = 4 GeV /c ,in-between the region of validity for hadronic calculationsand those using GPDs. These data would be a valuable con-straint on models of two-photon exchange of other hadronicbox processes. Target-Normal SSAs e + @JLab White Paper | 534 | e + @JLab White Paper A. Schmidt et al. ow momentum transfer elastic scattering D.W. Higinbotham, D. Dutta
Due to an apparent discrepancy between muonic and atomicdeterminations of the proton’s charge radius, there has beena renewed interest in the topic of lepton universality. As theproton’s radius is of course fixed, a difference in the appar-ent size of the proton when determined from ordinary versusmuonic hydrogen, could point to new physics. While recentmeasurements seem to now be in agreement, there is to dateno high precision elastic scattering data with both electrons andpositrons. A high precision proton radius measurement could beperformed in Hall B at Jefferson Lab with a positron beam andthe calorimeter based setup of the PRad experiment. This mea-surement could also be extended to deuterons where a similardiscrepancy has been observed between the muonic and atomicdetermination of deuteron charge radius.
Introduction
Elastic lepton scattering, electron or positron, at low four-momentum transfer can be used to determine the charge andmagnetic radii of light nuclei by by determining the slope ofthe charge form factor, G E , or the magnetic form factor, G M in the limit of four momentum transferred square, Q , of zerovia the following equation: r pE = − G pE ( Q )d Q (cid:12)(cid:12)(cid:12)(cid:12) Q =0 ! / ,r pM = − µ p d G pM ( Q )d Q (cid:12)(cid:12)(cid:12)(cid:12) Q =0 ! / (67) where r pE is the charge radius of the proton, r pM is the mag-netic radius of the proton, and µ p is the magnetic momentof the proton. This definition of the proton’s radius is con-sistent with the definition of the radius as extracted by bothatomic and muonic lamb shift measurements [188]. In elec-tron scattering the data do not extend to Q of zero, thus it de-sirable for experiments to measure at Q as low as as achiev-able. In 2010, Lamb shift measurements in muonic hydrogen( µ H) [189, 190] with their unprecedented, < r pE that was a combined eight-standard deviationssmaller than the average value from all previous experimentstriggering the "proton radius puzzle" [191, 192]. The puzzleprompted new scattering experiments [149, 193, 194] and nu-merous reanalysis of the electron scattering data [195–206]The most recent electron scattering [207] and atomic hydro-gen spectroscopy [208] results seem to have brought themback in agreement with the µ H results [209]. Nonetheless,the new results do not rule out one of the original expla-nations for the proton radius puzzle [191], a fundamentaldifference between electrons and muons that violates lep-ton universality. Previous experiment done in the 70’s and80’s showed that at the 10% level lepton universality, but whether this is absolutely true is yet to be experimentallyshown though it is often theoretically accepted in the stan-dard model as being true. The MUSE experiment [210, 211]which has started running at PSI may be able to determine ifuniversality holds and if the puzzle is truly solved. But, it ishighly desirable to verify the results from MUSE with highprecision measurements with electrons and positrons.The PRad experiment [207] has credibly demonstrated theadvantages of the calorimetric method in e − p scattering ex-periments to measure r pE with high accuracy. An upgradedexperiment (PRad-II), which will reduce the overall experi-mental uncertainties by a factor of 2.5 compared to PRad hasrecently been proposed. The PRad setup can also be usedwith a positron beam to measure r pE with high precision andthereby help verify lepton universality in the electron sectorwith sub-percent precision. In addition, it will allow us tovalidate the radiative correction calculations for electron scat-tering that account for internal and external Bremsstarahlungsuffered by the incident and scattered electrons and contribu-tions from two-photon exchange (TPE) processes. Proposed Experiment
Jefferson Lab, with a positron beam, would be ideal for per-forming a high precision follow-up experiment to MUSE.The setup used for the PRad experiment is Hall B could bereused to measure the cross sections and extract the proton ra-dius and thereby verify whether the proton radius is identicalwhen measured with electrons and positrons.The PRad experiment was designed to use a magnetic-spectrometer-free, calorimeter based method [207]. The in-novative design of the PRad experiment enabled three majorimprovements over previous e − p experiments: (i) The largeangular acceptance ( . ◦ − . ◦ ) of the hybrid calorimeter(HyCal) allowed for a large Q coverage spanning two ordersof magnitude ( . × − − × − ) (GeV / c) , in thelow Q range. The single fixed location of HyCal eliminatedthe multitude of normalization parameters that plague mag-netic spectrometer based experiments, where the spectrom-eter must be physically moved to many different angles tocover the desired range in Q . In addition, the PRad experi-ment reached extreme forward scattering angles down to . ◦ achieving the lowest Q ( . × − (GeV / c) ) in e − p experiments, an order of magnitude lower than previouslyachieved. Reaching a lower Q range is critically importantsince r p is extracted as the slope of the measured G pE ( Q )at Q = 0. (ii) The extracted e − p cross sections were nor-malized to the well known quantum electrodynamics process- e − e − → e − e − Møller scattering from the atomic electrons( e − e ) - which was measured simultaneously with the e − p within the same detector acceptance. This leads to a signif-icant reduction in the systematic uncertainties of measuringthe e − p cross sections. (iii) The background generated fromthe target windows, one of the dominant sources of system- Low Q elastic e + @JLab White Paper | 55 tic uncertainty for all previous e − p experiments, is highlysuppressed in the PRad experiment.The PRad experimental apparatus consisted of the followingfour main elements (Figure 45): (i) a 4 cm long, window-less, cryo-cooled hydrogen (H ) gas flow target with a den-sity of × atoms/cm . It eliminated the beam back-ground from the target windows and was the first such targetused in e − p experiments; (ii) the high resolution, large ac-ceptance HyCal electromagnetic calorimeter [212, 213]. Thecomplete azimuthal coverage of HyCal for the forward scat-tering angles allowed simultaneous detection of the pair ofelectrons from e − e scattering, for the first time in thesetypes of measurements; (iii) one plane made of two high res-olution X − Y gas electron multiplier (GEM) coordinate de-tectors located in front of HyCal; and (iv) a two-section vac-uum chamber spanning the 5.5 m distance from the target tothe detectors.The PRad experiment was the first electron scattering exper-iment to utilize a new technique with completely differentsystematics compared to all previous magnetic-spectrometerbased e − p experiments. The first generation PRad exper-iment was able to determine the proton radius to ± Q range of 10 − GeV allowing a more accurate and robust extraction of the protonradius. This new experiments will push the precision of theproton radius extraction to 0.003 fm, allowing it to addresspossible systematic difference between e − p and the µ H ex-periments.Additionally, a proposal for a high precision elastic ed scat-tering cross section measurement ((DRad) at very low scat-tering angles, θ e = 0 . ◦ − . ◦ ( Q = × − to × − (GeV / c) ), using the PRad-II experimental setup has alsobeen submitted to the 2020 PAC. This experiment has onemajor modification to the PRad-II setup. To ensure the elas-ticity of the ed scattering process a low energy Si-based cylin-drical recoil detector will be included within the windowlessgas flow target cell(See Fig. 46. As in the PRad experiment,to control the systematic uncertainties associated with mea-suring the absolute ed cross section, a well known QED pro-cess, the ee Møller scattering will be simultaneously mea-sured in this experiment. The DRad experiment will providea new measurement of the deuteron radius with a precisionof 0.4%.As the PRad type measurements in Hall B do not requirepolarization thus is should be relatively easy to achieve thefull planned luminosity; thus, the projected precision radiusextraction for protons and deuteron should be able to beachieved.
Summary
Using the PRad setup in Hall B would allow for an extremelyprecise comparison of the proton radius as extracted frompositrons and electrons. While currently the initial protonradius puzzle seems to be solved, there is still a hint at a dif-ference been muonic and atomic results which can only beresolved with precision experiments. In addition, even if theproton radius puzzle is solved, our understanding of radia-tive corrections can also be improved by studying differencebetween electrons and positrons.
56 | e + @JLab White Paper D. W. Higinbotham ig. 45. A schematic layout of the PRad experimental setup in Hall B at Jefferson Lab, with the electron beam incident from the left. The key beam line elements are shownalong with the window-less hydrogen gas target, the two-segment vacuum chamber and the two detector systems.
Fig. 46.
A schematic of the cylindrical recoil detector consisting of 20 silicon stripdetector modules, held inside the target cell. All solids are shown as transparent forease of viewing. Q [fm ] G E Pseudo DataRational Function
Fig. 47.
Shown are the expected precision of elastic scattering in Hall B using thePRad experimental setup. Data of this quality, would allow the proton radius to beextracted using a low order rational function and would achieve a precision approx-imately ± Q [fm ] G E Pseudo DataRational Function
Fig. 48.
Log scale version of the figure to highlight the low Q data.Low Q elastic e + @JLab White Paper | 578 | e + @JLab White Paper D.W. Higinbotham onstraining hadronic uncertainties in nuclear β -decay with elastic e + /e − scattering at JLab T. Kutz, A. Schmidt
Introduction
The Cabibbo–Kobayashi–Maskawa (CKM) matrix describesthe mixing of quark flavors by the weak interaction. TheStandard Model predicts first-row unitarity of the CKM ma-trix, that is: | V ud | + | V us | + | V ub | = 1 (68) Precision tests of CKM unitarity can be used to search fornew physics, or place constraints on new physics.The CKM matrix elements can be extracted by normalizingreaction rates of (semi)-leptonic reactions, such as nuclear β -decay, by the muon lifetime (or equivalently, by the Fermiconstant G F ) [215]. Super-allowed β decays ( + → + ) areespecially useful, as at tree level such reactions include onlythe weak vector current and are proportional to the weak vec-tor coupling G V . By conserved vector current (CVC), G V isnot renormalized in the nuclear medium. However, higher-order electroweak radiative corrections (EWRC) can includethe weak axial current, which is sensitive to hadronic renor-malization. Currently, the largest uncertainties in CKM ma-trix elements arise from hadronic uncertainties in the calcu-lation of EWRC [216].Of particular interest is the largest first-row element, V ud .The most precise determinations of V ud have come from re-action rates of super-allowed β -decays: | V ud | = G V G F = 2984 . s F t (1 + ∆ VR ) (69) Here, F t is a corrected value of the experimentally observed f t value, where f and t are the statistical rate function andpartial half-life of the observed process, respectively. F t in-cludes all nucleus-dependent corrections, and should be inde-pendent of nucleus if CVC holds. The nuclear independenceof F t has been observed in nuclei from A =
10 to 74 [216]. ∆ VR are the nucleus-independent EWRC.Currently, precision extractions of V ud are limited by uncer-tainties in the calculation of ∆ VR . These uncertainties aredominated by hadronic uncertainties in the γW box diagramdepicted in Figure 49. Unlike other possible radiative pro-cesses, the γW box contains an intermediate state sensitiveto the hadronic structure of the nucleus.The γW box belongs to class of two-boson exchange boxdiagrams, including γZ and γγ (two-photon exchange, orTPE). While these individual diagrams are only relevant tospecific processes (e.g., γW in β -decay), any theoretical ν e − A γ W A ′ Fig. 49.
The γW box diagram in nuclear β -decay. framework for EWRC should be able to calculate each di-agram. Currently, TPE offers the best possibility of clean ex-perimental measurement, making it an ideal benchmark forvarious theoretical approaches to EWRC.A number of experimental observables are directly sensitiveto the magnitude of TPE. One such observable is the chargeasymmetry, the ratio of the positron to electron elastic crosssections. As TPE contributes to the elastic scattering of elec-trons and positrons with opposite sign, the charge asymmetryis sensitive to TPE in a given nucleus: R = σ ( e + ) σ ( e − ) ≈ − δ γ δ even (70) In this expression, the ratio R has been corrected for the inter-ference term between electron and nuclear bremsstrahlung. δ even is the charge-even correction factor to the ratio. δ γ isthe correction factor arising from TPE. Previous measurements
Early measurements of the ratio of positron-proton andelectron-proton elastic cross sections have were performedas early as the 1960s [217–223]. More recent, high-precisionmeasurements have been performed by CLAS [65, 66],VEPP-3 [64], and OLYMPUS [67]. The data is highly con-centrated in regions of low momentum transfer Q and large (cid:15) ( > (cid:47)
1% to thecross section. A goal of future experiments will be to ex-tend the kinematics of charge asymmetry measurements intohigher Q and lower (cid:15) , where TPE contributions are pre-dicted to reach up to 10%. Similar measurements of thecharge asymmetry in nuclei do not exist. Proposed measurement
We propose a measurement of the elastic e + /e − chargeasymmetry from various nuclei. This measurement wouldrequire the use of either the high-resolution spectrometer Nuclear β -decay e + @JLab White Paper | 59 HRS) in Hall A, or the high-momentum and super-high-momentum spectrometers (HMS, SHMS) in Hall C, in orderto separate the elastic scattering peak from inelastic events.However, the specifications of these spectrometers, shown inTable 4, will dictate which are adequate given the choice oftargets and kinematics.Spectrometer Resolution( δp/p ) Minimummomentum (GeV)HRS (Hall A) × − × − × − Table 4.
Spetrometers.
In the following, the maximum electron/positron current isassumed to be 1 µ A. As this measurement is fully unpolar-ized, limitations on the maximum polarization of the positronbeam or target are not considered.
Nuclear targets.
For the purposes of constraining EWRCto V ud , the most useful charge asymmetry measurementsare on the daughter nuclei of super-allowed β -decays usedfor V ud extraction. The daughter nucleus for twelve of thebest known super-allowed transitions are shown in Table 5[216], along with the natural abundance and first excitedstate energy of each nucleus. The latter quantity will de-termine which nuclei would allow feasible elastic measure-ments given the resolution of available spectrometers.Of these nuclei, N, Mg, S, Ar, Ca, and Fe arenotable for their natural abundance and/or relatively largefirst excited state energy. The ability of the spectrometersto resolve the elastic peak is dependent on the initial beamenergy. At 2 GeV, the minimum central momentum allowedby the SHMS, the resolution of the Hall C spectrometers onlyallow measurements of N, S, and Ar. At a lower beamenergy of 1 GeV, measurements of all 6 nuclei would be pos-sible with both the HRS and HMS.The most convenient approach would be to design a targetladder capable of holding a variety of gas and solid targets.For nitrogen and argon, a pressurized 25 cm long aluminumNucleus Abundance (%) E ∗ (keV) B 19.9 718.380 N 99.6 2312.798 Na trace 583.05 Mg 11.01 1808.74 S 4.25 2127.564 Cl N/A 146.36 Ar 0.0629 2167.472 Ca 0.647 1524.71 Ti 8.25 889.286 Cr 4.345 783.31 Fe 5.845 1408.19 Kr N/A 455.61
Table 5.
Daughter nuclei for twelve of the best-known super-allowed β -decays, withthe isotopic abundance and first excited state energy listed for each. cell with thin entrance and exit windows could be used tocontain the target gas. Similar gas targets have been suc-cessfully implemented for electron scattering in the past, no-tably the argon gas target for experiment E12-14-012 at Jef-ferson Lab [224]. For magnesium, sulfur, calcium, and iron,solid targets with thicknesses of 6 mm or less could be im-plemented. Similar solid targets were used for PREX andCREX, which measured elastic scattering from lead and cal-cium. As is standard for such target ladders, additional targetsfor optics and background measurements could be included.Based on previous implementations of gas and solid targetsat JLab, a nominal target density of 1 g cm − is assumed.Combined with the previously mentioned maximum positronbeam current of 1 µA, the achievable luminosities range from10 -10 cm − s − , depending on nuclear species. Runplan.
Given the discussion in the previous section, wepropose a measurement of the charge asymmetry on sixisotopically-enriched nuclear targets: N, Mg, S, Ar, Ca, and Fe. The runplan is shown in Table 6. Measure-ments are proposed at three different kinematic settings, allof which have Q ≤ . GeV and (cid:15) ≥ . . This experi-mental program prioritizes measurements of multiple nucleartargets over covering large regions of phase space.To perform estimates of the expected experimental rates,a Monte Carlo simulation of a high-resolution, small-acceptance spectrometer was used. The simulation employedcross sections calculated from I. Sick’s parameterization ofnuclear form factors [225]. As global data fit parameters[226] were not available for all nuclei, rates were linearlyinterpolated to intermediate Z values. The form factors forthree of the six proposed nuclei are shown in Figure 50. Alsoshown are the kinematic settings proposed in Table 6.For each nucleus and kinematic setting, the beam time hasbeen estimated to achieve better than 1% statistical uncer-tainty on the e + /e − ratio. It is anticipated that in this eraof JLab physics, Hall A will only have one operational HRS.Further, the kinematic settings listed in Table 6 are incompat-ible with the SHMS in Hall C. Therefore, the required beam- Q (GeV ) − − − − − − | F ( q ) | (cid:15) = 0.95 (cid:15) = 0.896 (cid:15) = 0.973 Mg S Ca Fig. 50.
Form factors used for rate estimates. Indicated in red are the proposedkinematic settings.60 | e + @JLab White Paper T. Kutz et al. (GeV) θ e ± ( ◦ ) Q (GeV ) (cid:15) Nucleus Days1.1 18.12 0.120 0.950 N 0.5 Mg 0.5 S 0.5 Ar 0.5 Ca 0.5 Fe 0.51.1 26.27 0.250 0.896 N 0.5 Mg 7.0 S 3.5 Ar 2.0 Ca 1.5 Fe 3.52.2 13.05 0.250 0.973 N 0.5 Mg 0.5 S 1.5 Ar 0.5 Ca 0.5 Fe 0.5
TOTAL Table 6.
Proposed run plan for charge asymmetry measurements on various nuclei. time has been calculated based on the rate for a single spec-trometer. A factor of 2 has been included in the beamtime toaccount for approximately 50% beam efficiency.
Systematics.
As the effect of TPE on the charge asymme-try at the proposed kinematics is expected to be (cid:47) (cid:47)
Summary
Extractions of the CKM matrix element V ud from nuclear β -decay measurements are currently limited by uncertaintyin the theoretical calculation of EWRC. This hinders the useof CKM unitarity as a precision test of the Standard Model.The uncertainties are dominated by the calculation of the γW box diagram, which is sensitive the hadronic structureof the nucleus. Two-photon exchange is an experimentallyaccessible process that can provide a critical benchmark forthe theoretical calculation of EWRC. The charge asymmetry R = σ ( e + ) /σ ( e − ) is sensitive to the real contribution of TPEto the elastic cross section. This proposed 30 day programwould complete measurements of the charge asymmetry ona variety of nuclei used for β -decay extractions of V ud . Thiswould provide a constraint on the EWRC to these processesthat could improve the precision of CKM unitarity tests. Nuclear β -decay e + @JLab White Paper | 612 | e + @JLab White Paper T. Kutz et al. ccessing neutral weak coupling C q usingpositron and electron beams at Jefferson Lab X. Zheng, J. Erler, Q. Liu
Electroweak neutral weak couplings are important parametersof the Standard Model of particle physics. The product of leptonand quark couplings, C q , C q and C q , or g eqAV , g eqV A and g eqAA ,can be accessed in lepton scattering off a nucleon or nuclear tar-get. Recent parity violation electron scattering experiments atJefferson Lab have improved the precision of the C q, q cou-plings. On the other hand, the C q couplings can only be mea-sured by comparing scattering cross sections between a leptonand an anti-lepton beam, and have been measured only once atCERN. In this document, we present the definitions and currentknowledge of the C q, q, q and how to access them in chargedlepton scattering. We found the DIS cross section asymme-try between an electron and a positron beam scattering off anisoscalar target arise purely from C q . We present at the endexploratory calculations for possible measurements of C q us-ing the planned SoLID spectrometer at Jefferson Lab. Weak Neutral Couplings in the StandardModel
In the Standard Model, electroweak interactions are de-scribed by the gauge group SU(2) L × U(1) Y . Here theSU(2) L group describes an interaction that couples to onlyleft-handed fermions and is described by the weak isospin T . The U(1) Y group describes an interaction that couplesboth to left- and right-handed fermions, and is described bythe weak hypercharge Y . The two quantum numbers are re-lated to each other by T + Y / Q where Q is the elec-tric charge of the fermion and T is the 3 rd component ofthe weak isospin. While the observed weak charged currents,carried by the W ± bosons, is described by the SU(2) L group,the observed neutral weak and the electromagnetic currents,carried by the Z boson and the photon, respectively, are de-scribed by linear combinations of the neutral current J µ ofthe SU(2) L and the J Yµ current of the U(1) Y group, J emµ = J µ + 12 J Yµ , J NCµ = J µ − sin θ W J emµ , (71) where θ W is the Weinberg or the weak mixing angle whichcan be determined by experiments.The weak neutral currents of fermions have different left- andright-handed components. This causes the parity symmetryto be violated in weak interactions. The weak neutral currentsfor neutrinos, leptons, and quarks are, J ν = 12 ¯ νγ µ (1 − γ ) ν , (72) J l = 12 ¯ lγ µ ( c lV − c lA γ ) l , (73) J q = 12 ¯ qγ µ ( c qV − c qA γ ) q , (74) respectively, where ν , l and q are Dirac spinors. c fV = T f − θ W Q f and c fA = T f are the vector and the axialcouplings of the corresponding fermion f , respectively [228].The coupling for antifermion ¯ f can be found by applyingcharge conjugation to the current, giving c ¯ fV = − c fV and c ¯ fA = c fA .Experimentally, parity violating observables can be used toaccess lepton or quark weak neutral couplings, and further-more the weak mixing angle. Whether they provide a singlevalue of sin θ W tests the consistency of the Standard Model.Furthermore, it is believed that the current Standard Model isnot the ultimate theory, but instead is only an effective theoryof a larger theoretical framework. From this point of view,measurements of the different neutral weak couplings willshed light on possible Beyond the Standard Model (BSM)physics. Accessing Weak Neutral Couplings inCharged Lepton Scattering
The Lagrangian of weak neutral interaction involved in elec-tron deep inelastic scattering (DIS) off quarks inside the nu-cleon is [229] L e − qNC = G F √ X q [ C q ¯ eγ µ γ e ¯ qγ µ q + C q ¯ eγ µ e ¯ qγ µ γ q + C q ¯ eγ µ γ e ¯ qγ µ γ q ] , (75) where G F is the Fermi constant, C q = 2 c eA c qV , C q =2 c eV c qA and C q = − c eA c qA are products of the lepton andquark neutral couplings. The Standard Model predictions forthese couplings for u and d quarks are C u = −
12 + 43 sin θ W , C d = 12 −
23 sin θ W , (76) C u = −
12 + 2 sin θ W , C d = 12 − θ W , (77) C u = 12 , C d = − . (78) In recent years, a different set of quantities – g eqAV , g eqV A and g eqAA – has been introduced [230] into which some higher-order process-specific corrections have been absorbed.Among the three terms on the RHS of Eq. (75), the termsinvolving the C q, q are parity violating and induce a crosssection asymmetry between left- and right-handed electronsscattering off unpolarized nuclear or nucleon targets. The C q, q can be further separated by measuring parity violationasymmetries of different processes: the C q have been mea-sured primarily in atomic parity violation and electron elasticscattering off nuclear targets, while electron DIS off nuclear C q e + @JLab White Paper | 63 argets access a linear combination of the C q and C q . Theterm involving the C q does not violate parity, but can be ac-cessed by comparing cross sections of lepton to anti-leptonscattering.Measurements have been carried out for C q and C q througha variety of observables, see Figs. 51 and 52, with the lat-est results on C q and C q from the 6 GeV Qweak [17] andPVDIS [231, 232] experiments at Jefferson Lab (JLab), re-spectively. −0.72 −0.715 −0.71 −0.705 [2 g eu − g ed ] AV [ g e u + g e d ] A V P2 (expected 1.7% H asym)P2 (expected 0.3% C asym)2018 (all data)2018 + P2 (H target)2018 + P2 (H + C targets)Standard Model prediction
Fig. 51.
From Ref. [233]: Current experimental knowledge of the couplings C q or g eqAV . The latest measurement is from the 6 GeV Qweak experiment [17] at JLab.Also shown are expected results from the planned P2 experiment at Mainz. −1 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0[2 g eu − g ed ] AV −0.5−0.4−0.3−0.2−0.100.10.20.30.40.5 [ g e u − g e d ] V A Qweak + APVSLAC−E122JLab−Hall A all publishedSMSoLID (expected)−0.76−0.74−0.72−0.70−0.68−0.20−0.18−0.16−0.14−0.12−0.10−0.08−0.06
Fig. 52.
Current experimental knowledge [234] of the couplings C q or g eqV A . Be-cause all observables sensitive to the C q depend on linear combinations involvingthe C q , our knowledge of the C q is best plotted together with the C q , as shownhere. The latest measurement is from the 6 GeV PVDIS experiment [231, 232] atJLab. Also shown are expected results from the planned SoLID project [235] atJLab. Compared to the C q, q , experimental data on the C q are sparse. There exist only one set of measurements of the C q from comparing (polarized) muon vs. anti-muon DIS crosssections off a carbon target at CERN [236]. The asymmetrymeasured there is, B ≡ σ + ( −| λ | ) − σ − (+ | λ | ) σ + ( −| λ | ) + σ − (+ | λ | )= − G F Q √ πα − (1 − y ) − y ) × [(2 C u − C d ) + | λ | (2 C u − C d )] (79) where the superscript in σ ± indicates the muon charge in thebeam, | λ | is the beam polarization, and ±| λ | represents thehelicity of the incident beam. Nominally, the results for thetwo beam energies of 200 GeV and 120 GeV were, C u − C d + 0 . C u − C d ) = 1 . ± . , (80) C u − C d + 0 . C u − C d ) = 1 . ± . , (81) compared to the SM tree level predictions of . and . ,respectively. Note that these results were previously summa-rized in [237] but the calculations are updated here. Using theSM values for C u − C d , which are in good agreement withthe PVDIS experiment [231, 232], we find the constraint, C u − C d = 1 . ± . , (82) where we assumed that the (smaller) systematic error of the200 GeV data, was common to both beam energies.Assuming lepton universality, one may compare this preci-sion with those shown in Fig. 51 and Fig. 52. However,we note that there is so far no experimental data on C q forelectron-quark interactions.From Eq. (79), one can see that our knowledge on the lepton C q can be improved by comparing electron vs. positron DIScross sections if and when a high luminosity positron beambecomes available. Additionally, since the sensitivity to the C q is independent of the beam polarization, it is not nec-essary to use polarized beams and the asymmetry betweenunpolarized electron and positron scattering cross sections isproportional to C u − C d . On the other hand, the unpolar-ized DIS cross section difference between e − and e + scat-terings is subject to processes such as two photon exchange(TPE) and other higher-order electromagnetic effects. Sep-arating these effects from the C q contribution may be pos-sible using their different Q dependence, but is beyond thescope of this short write-up and will not be discussed here. Inthe following we will perform an exploratory calculation forthe C q sensitivity assuming other competing processes canbe separated in principle. Accessing the C q in e − and e + Scattering
To derive the asymmetry between electron and positron DIScross sections, we first followed the formalism in Ref. [238]that provided two observables sensitive to the C q , A l − − l + = σ (cid:0) l − + N → l − + X (cid:1) − σ (cid:0) l + + N → l + + X (cid:1) σ ( l − + N → l − + X ) + σ ( l + + N → l + + X ) , (83)
64 | e + @JLab White Paper X. Zheng et al. nd A l − L − l + R = σ (cid:0) l − L + N → l − + X (cid:1) − σ (cid:0) l + R + N → l + + X (cid:1) σ (cid:0) l − L + N → l − + X (cid:1) + σ (cid:0) l + R + N → l + + X (cid:1) , (84) where for the purpose of this document, l − and l + are elec-trons and positrons, respectively, and the subscript L, R de-notes their helicities. These two asymmetries are related toeach other by A l − L − l + R = c eV + c eA c eA A l − − l + , (85) which implies they are similar in size as | c eV | (cid:28) | c eA | for elec-trons. In practice, the asymmetry A l − − l + should be pursuedfirst because the luminosity that can be achieved with an un-polarized beam is often higher than that of a polarized beam.The parity-violating electron DIS (PVDIS) asymmetry,which has been measured first at SLAC [239, 240] and then atJLab [231, 232], was derived in Ref. [238] as the observable, A l − L − l − R = σ (cid:0) l − L + N → l − + X (cid:1) − σ (cid:0) l − R + N → l − + X (cid:1) σ (cid:0) l − L + N → l − + X (cid:1) + σ (cid:0) l − R + N → l − + X (cid:1) . (86) We derived our asymmetries by comparing Eqs (84)-(86)with the PVDIS asymmetry in Ref. [241], and also directlyfrom the Standard Model. Both methods arrived at the re-sult that the asymmetries accessible in electron vs. positronscattering off a proton target can be written as, A e + − e − p = − G F Q √ πα − (1 − y ) − y ) C u u V − C d d V u + + d + , (87) and, A e + L − e − R p = − G F Q √ πα − (1 − y ) − y ) × (2 C u u V − C d d V ) + | λ | (2 C u u V − C d d V )4 u + + d + , (88) where u + ≡ u + ¯ u , d + ≡ d + ¯ d , u V ≡ u − ¯ u and d V ≡ d − ¯ d are parton distribution functions (PDF). The factor | λ | (beampolarization) can either be added by hand or derived fromthe Standard Model as it is not explicit in the derivation ofRef. [238].Similarly, the two asymmetries for the deuteron are, A e + − e − d = − G F Q √ πα − (1 − y ) − y ) [2 C u − C d ] R V , (89) and, A e + L − e − R d = − (cid:18) G F Q √ πα (cid:19) − (1 − y ) − y ) × [(2 C u − C d ) + | λ | (2 C u − C d )] R V , (90) where R V ≡ ( u V + d V ) / ( u + ¯ u + d + ¯ d ) . Note that contribu-tions from s and c quarks have been neglected. Plugging in the value of G F one obtains for the deuteron, A e + − e − d = − − (1 − y ) − y ) Q (108 ppm) R V (2 C u − C d ) , (91) where Q is in GeV . Isoscalar targets are preferred in or-der to reduce the uncertainty from PDFs. This asymme-try is comparable in size to the PVDIS asymmetry that hasbeen measured at JLab to (2-3)% precision [231, 232]. Wenote that unlike the PVDIS asymmetry where the contribu-tion from the C u − C d is quite small, the asymmetry inEq. (91) arises fully from the couplings we wish to measure. Feasibility of Measurements at JLab 11 GeV
We considered the setting of Ref. [242] as our starting point.Ref. [242] is a PVDIS proposal using a 11 GeV, 85 µ Aelectron beam, a 40-cm long liquid deuterium target andboth HMS and SHMS in Hall C. At this setting one has A e + − e − d ≈ − ppm. Scaling the rates of Ref. [242] to theforseeable 1 µ A for the unpolarized positron beam, the ratesin HMS and SHMS combined are approximately 3.8 kHz and A e + − e − d can be measured to a 3% statistical precision within60 days if one can be provided a 1 µ A positron beam inter-changeably with a 1 µ A electron beam. However, measure-ment at a single kinematic point will not allow us to separate C q from higher order electromagnetic effects.Next, we consider the planned Solenoid Large Intensity De-vice, or SoLID [235]. SoLID will be used in Hall A of JLabfor measurements of PVDIS and semi-inclusive DIS (SIDIS).With the PVDIS configuration one must reverse the polarityof the solenoid magnet when the charge of the beam is re-versed, while for the SIDIS configuration the reversal is op-tional. Because the effective acceptance of SoLID is nearlytwo orders of magnitude higher than that of HMS and SHMScombined, it is possible to perform a 3% measurement on A e + − e − d within days. At this point, it looks promising to di-vide the data into multiple bins in order to isolate C q fromother competing effects to the asymmetry.We studied the feasibility of a C q measurement using thesimulated PVDIS rate used in the SoLID pre-Conceptual De-sign Report [243]. In Ref. [243], the PVDIS measurementon the deuteron assumed a 40 cm liquid deuterium targetand a 50 µ A electron beam. Scaling to a 1 µ A unpolarizedpositron or electron beam and keeping the target length un-changed, we estimated the statistical uncertainty of the asym-metry measurement assuming 20 PAC beam days. Next, wefit the asymmetry using A e + − e − d ( Q ) = a + bR V (cid:20) − (1 − y ) − y ) (cid:21) Q (92) where a and b are parameters to be fitted, see Fig. 53. Weobtained δb = ± . ppm. This will provide a statistical un-certainty of ∆(2 C u − C d )(stat . ) = ± . .The use of Eq. (92) will allow one to add additional termsto separate higher order electromagnetic effects from C q .Assuming the systematic uncertainty in the asymmetry, both C q e + @JLab White Paper | 65 A ( e − e )( pp m ) Rv g(y) Q (GeV ) −2000 +− Fig. 53.
Expected size and statistical uncertainty for a measurement of A e + − e − d ( Q ) using 20 PAC days of 1 µ A unpolarized beam, interchanging be-tween positrons and electrons, and a 40 cm long liquid deuterium target. The SoLIDdetector with its PVDIS configuration is assumed to detect scattered positrons orelectrons. The polarity of the solenoid magnet of SoLID must be reversed betweenpositron and electron runs. The straight line shows the fit of Eq. (92), with thehorizontal axis being R V g ( y ) Q where g ( y ) = [1 − (1 − y ) ] / [1 + (1 − y ) ] . from higher order electromagnetic effects and from exper-imental factors, can be controlled at a level comparableto the statistical uncertainty, the total uncertainty will be ∆(2 C u − C d ) = ± . , a factor of seven compared to theCERN µ ± experiment.From the above estimate one can see that a measurementof C q is possible using SoLID provided we can switch be-tween a positron and an electron beam. On the other hand,the difference between the electron and the positron beams,such as intensity, position, direction and spot size, need tobe controlled to the level of helicity-correlated beam differ-ences maintained during the 6 GeV PVDIS experiment atJLab. One must also require that the difference in the spec-trometer response to electrons and positrons is well below theplanned statistical uncertainty. We note that while these re-quirements look daunting to reach in practice, they had beenachieved in the 96-day long CERN measurement [236]: thebeam switched between µ + and µ − twice for each of the 12-day run period; care was taken to ensure the µ ± data weretaken at the same intensity such that many systematic effectscancel; and the spectrometer magnet was operating at a fullysaturated state such that the field can be reproduced to a highprecision with each polarity reversal. Additionally, a 40-mlong carbon target was used to achieve the luminosity neededfor the measurement. New Physics Mass Limit
The strong coupling mass limit on BSM physics that can beimposed by the C q is Λ = v s √ π ∆(2 C u − C d ) , (93) where v = q / ( √ G F ) = 246 . GeV is the Higgs vacuumexpectation value setting the electroweak scale, and the √ is a normalization factor taking into account the coefficientsof the C u, d in the denominator. Thus, a determination of C u − C d with ± . total uncertainty implies a sensitiv-ity up to scales Λ = 8 . TeV. Any model predicting a signif-icant effect in the C q (AA), while leaving the C q, q (AVand VA) unaltered, is presumably contrived or tuned; how-ever, the C q are couplings independent of the C q, q andtheir mass limits on BSM physics are complementary. Con-versely, if new physics is seen in the C q or C q , it would beof paramount importance to measure the C q , as well. Summary
We have reviewed the current knowledge on the electron-quark effective couplings C q , C q and C q . All three setsof couplings are accessible in charged lepton scattering. The C q couplings can be extracted from A e + − e − d , the DIS crosssection asymmetry between an electron and a positron beamon a deuterium target, assuming that other contributions canbe reliably separated and that all experimental systematic un-certainties are under control. Exploratory calculations wereperformed to study the possibility of measuring A e + − e − d us-ing the planned SoLID spectrometer at JLab. We found themeasurement to be promising, and it is possible to improvethe current knowledge in the C q by a factor of seven within avery reasonable amount of beam time. Such improvement iscomparable to or better than what the Qweak and the 6 GeVPVDIS experiments had achieved on the C q and C q , re-spectively. The precision of the measurement and the masslimit it will impose on BSM physics can be improved furtherif a higher beam current is possible or if more beam time thanwhat is assumed is invested in the measurement. ACKNOWLEDGEMENTS
The early stage of this work by X.Z. was supported by U.S. Department of Energy(DOE) Early Career Award SC0003885. The work of X.Z. is current supported byU.S. DOE under Award number DE-SC0014434. The work of J.E. is supported bythe German-Mexican research collaboration grant SP 778/4–1 (DFG) and 278017(CONACyT).66 | e + @JLab White Paper X. Zheng et al. ight dark matter searches with positrons L. Marsicano, M. Battaglieri, A. Celentano, M. Raggi
We present two complementary measurements to search forlight dark matter at Jefferson Laboratory, exploiting a possiblepositron beam available in the future at this facility. Light darkmatter is the new compelling hypothesis that identifies darkmatter with new sub-GeV “Hidden Sector” states, neutral un-der Standard Model interactions and interacting with our worldthrough a new force. Accelerator-based searches at the intensityfrontier are uniquely suited to explore it.Thanks to the unique properties of the CEBAF (ContinuousElectron Beam Accelerator Facility) beam – the high intensityand the high energy – and exploiting a novel light dark mat-ter production mechanism, the positron annihilation on atomicelectrons, the proposed experiments will be able to explore newregions in the light dark matter parameters space, confirmingor ruling out this hypothesis.
Introduction
The existence of dark matter (DM) is a “smoking gun” evi-dence of physics beyond the Standard Model (SM). However,all experimental evidence is based on gravitational effects,and so far we know nothing about the particle contentof DM: uncovering this puzzle is thus a top priority infundamental physics.
Since its formulation, this compellingquestion motivated a large number of experiments aimed atDM detection. So far the theoretical and experimental ef-forts have focused on the WIMPs (Weakly Interacting Mas-sive Particles) scenario, assuming new high mass particlesinteracting via the known SM weak force [244]. However,null results in direct detection experiments of galactic haloDM and in high-energy accelerator searches at the LHC callfor an alternative explanation to the current paradigm [245].In recent years a new, alternative hypothesis for the DM na-ture has been introduced. This predicts the existence of sub-GeV light dark matter (LDM) particles, interacting withSM states through a new interaction. The simplest modelpredicts LDM particles (denoted as χ ) with masses below1 GeV/c , charged under a new force and interacting with theSM particles via the exchange of a light spin-1 boson, usuallyreferred to as “heavy photon” or “dark photon” ( A ) [246–248]. This picture allows the existence of an entire new“Dark Sector”, with its own particles and interactions, and iscompatible with the well-motivated hypothesis of DM ther-mal origin [249]. It assumes that, in the early Universe, DMreached the thermal equilibrium with SM particles throughan interaction mechanism such as the one described above.The present DM density, deduced from astrophysics mea-surements, is thus a relic “remnant” of its primordial abun-dance [249]. The thermal origin hypothesis provides a rela-tion between the observed DM density and the model param-eters, resulting in a clear, predictive target for discovery orfalsification [250]. A ′ γ γe −e + e − e + Z Ze − e + A ′ A ′ e − e + ( a )( b )( c ) Fig. 54.
Three different A production modes in fixed target lepton beam experi-ments: ( a ) A -strahlung in e − /e + -nucleon scattering; ( b ) A -strahlung in e + e − annihilation; ( c ) resonant A production in e + e − annihilation. Many LDM models have been proposed, with different hy-pothesis for the LDM to A coupling (diagonal or off-diagonal), as well as for the particle nature (scalar orfermion). However, the phenomenology of thermal freeze-out and the consequences on the LDM particle physicsmodel arise solely from the ratio between the mediator andthe LDM mass. In particular, the most relevant scenariofor accelerator-based experiments is the direct annihilationregime in which m χ < m A . In this case, the dominantLDM-to-SM process is the s − channel virtual mediator ex-change, χχ → A → f f , where f is a charged SM fermion.The velocity-averaged cross-section for this process scales as h σv i ’ α D ε m χ /m A , with the χ -to- A mass ratio andthe dark coupling g D = α D π at most O (1) and the parame-ter ε defining the intensity of the mixing between the darkphoton and the SM photon.Since the thermal origin mechanisms implies Ω DM ∝ / h σv i , the minimum SM-LDM coupling compatible withthe observed DM abundance is: Ω DM = 0 . ± . [251]: y ≡ ε α D (cid:18) m χ m A (cid:19) (cid:38) h σv i relic m χ . (94) This constraint, within the simple A model, is valid for everyDM/mediator variation up to order-one factors, provided that m DM < m MED : reaching this benchmark sensitivity is theultimate goal of all light dark matter searches. Dark sector searches with positron beams onfixed targets
The production of LDM particles can be generated in colli-sions of electrons or positrons of several GeV with a fixed tar-
LDM searches with e + e + @JLab White Paper | 67 et by the processes depicted in Fig. 54, with the final state A decaying to a χχ pair. For experiments with electron beams,diagram ( a ) , analogous to ordinary photon bremsstrahlung, isthe dominant process, although it was recently shown that forthick-target setups, where positrons are generated as secon-daries from the developing electromagnetic shower, diagrams ( b ) and ( c ) give non-negligible contributions for selected re-gions of the parameters space [252] – See Ref. [250] for acomprehensive review of past/current experiments and futureproposals.On the other hand, for experiments with positron beams, di-agrams ( b ) and ( c ) play the most important role. In thisdocument, we present two complementary measurements tosearch for light dark matter with positron beams at JeffersonLaboratory, exploiting the unique potential of the proposed e + -beam facility. In the following, we introduce the two ap-proaches, and for each one we briefly discuss the experimen-tal setup, the measurement strategy, the data analysis, and theforeseen results. We underline that Jefferson Laboratory isplaying a leading role in the LDM searches, with differentexperiments already running, HPS [253] and APEX [254],or approved to run in the near future, BDX [255] and Dark-Light [256].
1. Thin-target measurement.
This measurement exploitsthe A -strahlung production in electron-positron annihila-tion described by diagram ( b ) . The primary positron beamimpinges on a thin target, where a photon- A is produced.By detecting the final-state photon in an electromagneticcalorimeter, the missing mass kinematic variable M miss canbe computed event-by-event: M miss = ( P beam + P target − P γ ) . (95) The signal would show up as a peak in the missing mass dis-tribution, centered at the A mass, on top of a smooth back-ground due to SM processes resulting from events with a sin-gle photon measured in the calorimeter. The peak width ismainly determined by the energy and angular resolution ofthe calorimeter. Several experiments searching for A withthis approach have been proposed. PADME (Positron Anni-hilation into Dark Matter Experiment) at LNF [257] is one ofthe first e + on thin target experiment searching for A . It usesthe 550 MeV positron beam provided by the DA Φ N E linacat INFN LNF (Laboratori Nazionali di Frascati) impingingon a thin diamond target.
2. Active thick-target measurement.
This measurementexploits the resonant A production by positrons annihila-tion on atomic electrons described by diagram ( c ) . The pri-mary positron beam impinges on a thick active target, andthe missing energy signature of produced and undetected χ is used to identify the signal [258]. The active target mea-sures the energy deposited by the individual beam particles:when an energetic A is produced, its invisible decay prod-ucts – the χχ pair – will carry away a significant fractionof the primary beam energy, thus resulting in measurable re-duction in the expected deposited energy. Signal events are identified when the missing energy E miss , defined as the dif-ference between the beam energy and the detected energy,exceeds a minimum threshold value. The signal has a verydistinct dependence on the missing energy through the rela-tion m A = √ m e E miss . This results in a specific experi-mental signature for the signal, that would appear as a peak inthe missing energy distribution, at a value depending solelyon the dark photon mass. Thanks to the emission of softBremmsthralung photons, the thick target provides an almostcontinuous energy loss for the impinging positrons. Eventhough the positron energy loss is a quantized process, thefinite intrinsic width of the dark photon – much larger thanthe positron energies differences – and the electrons energyand momentum spread induced by atomic motions [259] willindeed compensate this effect. This allows the primary beamto “scan” the full range of dark photon masses from the maxi-mum value (corresponding to the loss of all the beam energy),to the minimum value fixed by the missing energy thresh-old [260], exploiting the presence of secondary positrons pro-duced by the developing electromagnetic shower.
1. Positron annihilation on a thin target
Signal signature and yield.
The differential cross-sectionfor dark photon production via the positron annihilation onthe atomic electron of the target e + e − → A γ , is given by: dσdz = 4 πα ε s (cid:18) s − m A s z − β z + m A s − m A − β z (cid:19) . Here s is the e + e − system invariant mass squared, z is thecosine of the A emission angle in the CM frame, measuredwith respect to the positron beam axis, and β = q − m e s .This result has been derived at tree level, keeping the lead-ing m e dependence to avoid non-physical divergences when | z | → . The emission of the annihilation products in theCM frame is concentrated in the e + e − direction. This resultsin an angular distribution for the emitted γ peaked in the for-ward direction in the laboratory frame. In the case of invisibledecays, the A escapes detection, while the γ can be detectedin the downstream electromagnetic calorimeter (ECAL). Themeasurement of the photon energy and emission angle, to-gether with the precise knowledge of the primary positronmomentum, allows computing the missing mass kinematicvariable from Eq. 95. The mass range that can be spannedis constrained by the available energy in the center of massframe: using an 11 GeV positron beam at JLab, A massesup to ∼ MeV /c can be explored.The signal yield has been evaluated using CALCHEP [261];the widths σ ( m A ) of the missing mass distributions of themeasured recoil photon has been computed for six differ-ent values of the A mass value in the 1–103 MeV range.CALCHEP provides the total cross section of the process,for ε = 1 ; the cross section value as a function of ε has beenobtained multiplying it by ε . Figure 55 shows results for m A is the dark photon mass and m e = 0 . MeV/c is the electronmass.
68 | e + @JLab White Paper L. Marsicano et al. ig. 55. Computed missing mass spectrum for signal events for 4 different valuesof m A . e + e − → γA process kinematics,the missing mass resolution for the signal is best for large A masses and degraded for a “light” A ( m A < MeV).
Expected background.
All processes resulting in a single γ hitting the calorimeter represent the background for theexperiment, the most relevant being bremsstrahung andthe e + e − annihilation processes in two and three photons.In order to reduce the bremsstrahlung background, the pro-posed detector features an active veto system composed ofplastic scintillating bars: positrons losing energy via bremm-strahlung in the target are detected in the vetos, rejectingthe event. However the high bremsstrahlung rate is an is-sue for this class of experiments, limiting the maximumviable beam current. To evaluate this background, a fullGEANT4 [262] simulation of the positron beam impingingon the target, based on the PadmeMC simulation program[263], has been performed. For all bremsstrahlung photonsreaching the ECAL, the missing mass has been computed,accounting for the assumed detector angular and momentumresolution.The e + e − → γγ and e + e − → γγγ annihilation processescan produce background events whenever only one of theproduced photons is detected in the ECAL. This contribu-tion to background has been calculated as follows. Eventshave been generated directly using CALCHEP, which pro-vided also the total cross sections for the processes. As inthe case of bremsstrahlung, the missing mass spectrum wascomputed for events with a single photon hit in the ECAL.This study proved that, if one requires the measured energyto be greater than 600 MeV, the two photon annihilation back-ground becomes negligible. This is due to momentum con-servation: asking for only one photon to fall within the ECALgeometrical acceptance translates in a strong constraint on itsenergy. This argument does not apply to the three photon an-nihilation: this process generates an irreducible backgroundfor the experiment (see Fig. 56 for the missing mass spectrumproduced by the three-photons annihilation). Fig. 56. . Computed missing mass spectrum from positron annihilation into threephotons events.
Fig. 57.
Layout of the proposed thin target setup.
Experimental Setup.
The experimental setup of the pro-posed measurement is shown in Fig. 57. The 11 GeV positronbeam impinges on a 100 µm thick carbon target, this ma-terial being a good compromise between density and a lowZ/A ratio allowing to reduce bremsstrahlung rate. A mag-net capable of generating a field of 1 T over a region of 2m downstream the target bends the charged particles (includ-ing non-interacting positrons) away from the ECAL, placeda few meters downstream. The ECAL is composed of highdensity scintillating crystals, arranged in a cylindrical shape.High segmentation is necessary to obtain a good angular res-olution, critical for a precise missing mass computation, butshould however be matched with the Moliére radius of thechosen material.Crystals of PbWO , LSO(Ce) and BGO, represent optimalchoices, given the fast scintillating time, high-density andshort radiation length. Energy resolution, as well as angularresolution, plays a crucial role in the missing mass computa-tion; a value of σ ( E ) E = √ E has been assumed for this study,consistent with the performance of the 23 cm long PADMEBGO detector, corresponding to 20 radiation lengths. Sucha depth is indeed needed for achieving this performance, dueto longitudinal shower containment.Since the small-angle bremsstrahlung high rate would blindthe central crystals of the calorimeter, the simplest solutionis to foresee a hole at the center of the cylinder. Assuming aradius of 30 cm and a distance from the target of 6 m, a ge-ometrical acceptance of ∼ mrad is achieved. In PADME,with a crystal front-face of 20 ×
20 mm , a spatial resolution LDM searches with e + e + @JLab White Paper | 69 f ∼ . mm has been measured (significantly better than 20mm / √ ). At 6 m distance this corresponds to an angularresolution of . mrad .Besides the ECAL, the experimental setup includes a vetosystem to reduce the bremsstrahlung background. Follow-ing the layout of the PADME experiment, the vetos are com-posed of plastic scintillator bars. Whenever the primary e + loses energy via bremsstrahlung in the target, its trajectory isbent by the magnetic field and it impinges on the veto bars,rejecting the event. For the sake of this study, a . vetoefficiency has been considered. This assumption is provenrealistic by the performance of the existing PADME experi-ment veto system [257].Further suppression of the background can be achievedby placing a photon detector, much faster than the maincalorimeter, covering its central hole. Such a fast calorimeterwould also help in the reduction of γγ and γ events withone or two photons lost. In the case of PADME a 5 × × PbF crystals is used. The Cherenkov light fromshowers is readout by fast photo-multipliers, providing a ∼ ∼
300 nsdecay time of the BGO).
Positron beam requirements.
As already mentioned, the A mass range that the proposed thin target experiment canexplore is strictly constrained by the available energy in thecenter of mass frame. In this respect, a 11 GeV positron beamwould allow extending significantly the A mass range withrespect to other similar experiments, up to ∼ MeV /c .Being the e + e − → γA annihilation a rare process, the sen-sitivity of the proposed search depends on the number ofpositron on target (POT) collected. In this setup, the max-imum current is constrained by the bremsstrahlung rate onthe ECAL innermost crystals. Therefore, a continuous beamstructure is preferable. In this study, a continuous nA beam has been considered, resulting in a manageable ∼ KHz rate per crystal in the inner ECAL. In this con-figuration, POT can be collected in days, coveringa new region in the A parameter space. In the event that theavailable beam current is lower than nA , a similar resultcan be obtained increasing the target thickness, at the priceof a higher background due to multiple scattering.The computation of the missing mass requires a preciseknowledge of the primary positron momentum; this trans-lates to certain requirements in terms of the quality of thebeam. Here, a energy dispersion σ EBeam E Beam < and an an-gular dispersion θ Beam < . mrad of the beam have beenconsidered. With these assumptions, the missing mass reso-lution is dominated by the ECAL performance, with a negli-gible contribution from the beam dispersion. Reuse of the PADME components.
It’s also interesting toinvestigate the possibility of reusing the existing PADME ex-perimental apparatus as the starting point for the new thintarget experiment at the CEBAF accelerator. In this paperwe try to shortly review which part of the apparatus couldbe directly reused, and which will need to be adapted to thedifferent beam conditions. The PADME target can be easily transferred and installed inthe CEBAF accelerator, while the option of a ticker targetwill simplify the design and its easily achievable.The PADME electromagnetic calorimeter performance is ad-equate with the requirements for the thin target experiment:in addition to the excellent energy resolution, < √ E [264],and spatial resolution, ∼ ∼ X .The small angle calorimeter will also profit by the muchhigher energy of the impinging photons, but will suffer morethe longitudinal leakage, being only 15 X long. This willnot compromise its use as photon veto, while performance ascalorimeter, for improving γ and γ acceptance, needs to beevaluated.The charged veto system will certainly require a different ge-ometrical assembly, both due to the need of a longer mag-net and the different boost, but the technology and front-endelectronics can be reused.The trigger and DAQ system of the PADME experiment[265] was built to operate at a rate of 50 Hz as imposed by therepetition rate of the DA Φ NE LINAC. Currently, PADME isoperated in trigger-less mode, i.e. digitizing all channels ofthe detectors every single beam bunch, typically in a 1 µ swindow (1024 samples at 1 Gsample/s). Of course such asystem cannot be used with a continuous beam structure, sothat a new trigger and DAQ system need to be designed andbuilt.
2. Positron annihilation on a thick active tar-get
Signal signature and yield.
The cross-section for LDMproduction through positron annihilation on atomic elec-trons, e + e − → A → χχ , is characterized by a resonantshape [266]: σ = 4 πα EM α D ε √ s q ( s − / q )( s − m A ) + Γ A m A , (96) where s is the e + e − system invariant mass squared, q is the χ − χ momentum in the CM frame, and Γ A is the A width.The kinematics of the e + e − → χχ reaction in the on-shellscenario ( m A > m χ ) is strongly constrained by the under-ling dynamics. Since the A decays invisibly, its energy isnot deposited in the active target, and the corresponding ex-perimental signature is the presence of a peak in the missingenergy ( E miss ) distribution, whose position depends solelyon the A mass through the kinematic relation m A = p m e E miss . (97)
70 | e + @JLab White Paper L. Marsicano et al. (GeV) e E - -
10 110 ) - T r a ck l eng t h / X ( G e V Positrons
Electrons
Fig. 58.
Differential positrons track length distribution, normalized to the radiationlength, for a 11 GeV e + beam impinging on a thick target. For comparison, thesame distribution in case of an impinging electron beam is reported. For a given A mass, the expected signal yield is: N s = n P OT N A A Zρ Z E E CUTmiss dE e T + ( E e ) σ ( E e ) , (98) where A , Z , ρ , are, respectively, the target material atomicmass, atomic number, and mass density, E is the primarybeam energy, N A is Avogadro’s number, σ ( E e ) is the energy-dependent production cross-section, n P OT is the number ofimpinging positrons, and E CUTmiss is the missing energy cut.Finally, T + ( E e ) is the positrons differential track-length dis-tribution [267], reported in Fig. 58 for a 11 GeV positronbeam. Positron beam requirements.
A missing energy measure-ment requires that the intensity of the primary positron beamis low enough so that individual e + impinging on the activetarget can be distinguished. At the same time, the beam cur-rent has to be large enough to accumulate a sizeable numberof positrons on target (POT). For example, a positron beamwith a time structure corresponding to 1 e + /µ s can accumu-late more than POT/year, with an average time intervalbetween positrons of 1 µ s.This specific time structure is challenging for the proposedCEBAF e + operations. In particular, the low beam current, ∼ . pA, is incompatible with the standard beam diagnos-tic tools that are employed to properly steer and control theCEBAF beam. Therefore, the following “mixed operationmode” is currently being considered for the experiment (seealso Fig. 59) [268]. A 10– µ s long 100 nA diagnostic macro-pulse is injected in the CEBAF accelerator with a 60 Hz fre-quency. This results to an average current of 60 pA, with apeak current large enough to enable proper operation of thebeam diagnostic systems. In between every pulse, low inten-sity physics pulses , populated on average by less than 1 e + ,are injected at higher frequency.This challenging operation scheme can be realized using anad-hoc laser system at the injector. With dedicated R & D, it
Typ. 10 us . � +-+
250 MHz = 4 ns
Diagnostic macro pulse I
60 Hz = 16.666 us
31 MHz = 32 ns
I I
Physics macro pulse I Fig. 59.
Simplified scheme of the e + beam time structure for the thick-targetmeasurements, see text for details. would be possible to design and construct a system capableof injecting fast bunches at 31.25 MHz - i.e. one bunch ev-ery 32 ns. Since the (discrete) number of positrons per bunchfollows a Poissonian statistical distribution, the time intervalbetween e + can be further increased by reducing the averagebunch population, by adjusting the laser intensity. A ∼ e + /bunch. The experiment willacquire data only during low-intensity pulses, ignoring the 10 µ s long high current periods. However, if all these positronswould impact on the detector, the average rate of ∼ . e + /s would result in a very large radiation dose deposited inthe active target. To avoid this, we plan to install in frontof the detector a fast magnetic deflector, synchronized to thebeam 60 Hz frequency, in order to transport the positrons be-longing to the high-current pulses to a suitable beam-dump,avoiding their impact on the detector.In summary, the proposed CEBAF operation mode would al-low to obtain a positron beam with particles impinging on thedetector on average every ∼ ns, compatible with the ac-celerator control and diagnostic system. It should be pointedout that this technical solutions requires R & D activities, thatare already (partially) planned in the contest of EIC accelera-tor development. In the following, we will present the sensi-tivity to DM considering POT accumulated in one yearof run.
Experimental setup.
The layout of the proposed measure-ment is schematically reported in Fig. 60. It includes ahomogeneous electromagnetic calorimeter (ECAL) actingas a thick target to measure the energy of each impingingpositron, and a hadron detection system (HCAL) installedaround and downstream the active target to measure long-lived (neutrons/ K L ) or highly penetration (muons/chargedpions) particles escaping from the ECAL.The preliminary ECAL design foresees a 28 radiation lengthsdetector, made as a 10x10 matrix of 20x20x250 mm PbWO crystals. Three layers of crystals are added in front, withthe long axis oriented perpendicular to the beam direction,to act as a pre-shower, resulting in a total calorimeter length LDM searches with e + e + @JLab White Paper | 71 ig. 60. Schematic layout of the active thick-target experimental setup, with theECAL (white) followed and surrounded by the HCAL (gray). The semi-transparentportion of the HCAL in front is that installed all around the ECAL. of 35 X . The choice of PbWO material is motivated byits fast scintillating time ( τ ’ ns), well matched to theexpected hit rate, its high-density, resumlting in a compactdetector, and its high radiation hardness. The total calorime-ter length was selected to limit below ∼ − per POT theprobability that any particle from the developing cascade, inparticularly photons, escape the detector faking a signal. Thetransverse size, was chosen to provide measurements of theshower transverse profile and to optimize the optical match-ing with the light sensor. The total front face size (20x20cm ) is large enough to avoid transverse energy leakage af-fecting the detector resolution. Silicon Photomultipliers willbe used to collect scintillation light from the crystals. The useof these sensors has never been adopted so far in high-energyelectromagnetic calorimetry with PbWO crystals, and re-quires a careful selection of the corresponding parameters.First measurements on PbWO crystals with 6x6 mm de-vices having a 25 µ m pixel size show a light yield of ∼ % is, at maximum, ∼
350 rad/h, corresponding to thecentral crystals. This large value, comparable to the max-imum dose in the CMS PbWO electromagnetic calorime-ter [269, 270], calls for a careful calorimeter design and forthe identification of procedures to mitigate any possible radi-ation damage during detector operation. These include vary-ing the beam impact point on the detector to distribute theradiation dose across crystals, as well as annealing crystalsduring no-beam operations, exploiting both thermal anneal-ing and light-induced processes [271, 272].The main requirement for the HCAL is the hermeticity tolong-lived particles exiting from the ECAL. From a Monte-carlo simulation of this setup, the probability of having oneor more high-energy ( (cid:38) GeV) hadron leaving the active tar-get is ∼ − per POT. This calls for a HCAL inefficiencyof − or lower. The preliminary detector design ueses a modular iron/scintillator inhomogeneous calorimeter, witha length corresponding to approximately 25 nuclear interac-tion lengths, partially surrounding the active target to avoidany particle leakage from the calorimeter lateral faces. Measurement and analysis strategy.
The experiment willbe characterized by a very high measurement rate, dominatedby events with full energy deposition in the calorimeter. Tocope with this, the data acquisition system will be configuredto record only events with a significant ( (cid:38) GeV) energy lossin the calorimeter. From a preliminary estimate, the expectedtrigger rate will be ∼ kHz, for a primary beam imping-ing with 2 MHz frequency on the detector. This minimumbias condition will be initially studied with Montecarlo sim-ulations, to evaluate the efficiency and confirm that no dis-tortions to the experiment physics outcome are introduced.In parallel to the main production trigger, prescaled triggerconditions will be implemented to save full-energy events forcalibration and monitoring.A blind approach to data analysis will be followed. First,events in the signal region, based on a preliminary choice ofthe calorimeter and hadron detection system energy cuts, willbe excluded from the analysis. Then, the expected number ofbackgrounds will be evaluated using both Montecarlo simu-lations and events in the neighborhood of the signal region, inorder to identify an optimal set of selection cuts for the signalthat maximize the experiment sensitivity [273]. Finally, thesignal region will be scrutinized. Results
The sensitivity of the two proposed measurements is shownin Fig. 61, compared with current exclusion limits (gray ar-eas) and expected performance of other missing-energy /missing-mass future experiments (dashed curves). On thesame plot, we show the thermal targets for significant vari-ations of the minimal LDM model presented in the introduc-tion: elastic and inelastic scalar LDM (I), Majorana fermionLDM (II), and pseudo-Dirac fermion LDM (III). For thethin-target effort, the red curve reports the sensitivity esti-mate based on the realistic backgrounds that have been dis-cussed before. For the thick-target case, the orange curverefers to the ideal case of a zero-background measurement.This hypothesis, following what was done in similar experi-ments [274, 275], will be investigated with Montecarlo sim-ulations during the future experiment design phase.
Complementarity of the two approaches.
The two mea-surements that we presented in this document are character-ized by a different sensitivities and design complexity. Theycan be considered as two complementary experiments facingthe light dark matter physical problem, and as such we fore-see a comprehensive LDM physical program at JLab withboth of them running, but with different time schedules.With the availability of a 100 nA, 11 GeV positron beamat JLab, the thin-target experiment can start almost imme-diately, since no demanding requirements on the beam arepresent. The conceptual design is already mature, being
72 | e + @JLab White Paper L. Marsicano et al. ig. 61. The expected sensitivity for the thin-target (red) and thick-target (orange)measurements, compared to existing exclusion limits (gray area) and projections forfuture efforts (dotted lines). The black lines are the thermal targets for elastic andinelastic scalar LDM (I), Majorana fermion LDM (II), and pseudo-Dirac fermion LDM(III). based on realistic Montecarlo simulations. Furthermore, thedetector can be based on an already-existing and workingsetup, the PADME experiment at LNF [257]. As discussedbefore, the possibility of installing PADME at JLab, bene-fiting from both the exiting equipment and the experience inoperating it is a compelling possibility, allowing to run suc-cesfully the thin-target measurements from day one.Meanwhile, we propose starting the necessary R & D activ-ity in preparation to the thick-target measurement, exploitingsynergic activities at the laboratory in the context of the EICprogram. The goal is to be ready to start the measurementson a time scale of few years after the beginning of the e + program at JLab. Conclusions and outlook
In this document, we presented two complementary experi-ments to explore the dark sector exploiting a future e + beamat JLab. The unique properties of this facility - the high en-ergy, the large intensity, and the versatile operation mode willallow these two efforts to investigate unexplored, large re-gions in the parameters space, beyond that covered by currentor planned experiments.In summary, the availability of a positron beam will makeJLab the ultimate facility to explore the dark sector, andthe proposed experimental program will allow confirma-tion or rejection of the LDM hypothesis by covering thethermal targets in a wide region of the parameters space. Although not discussed in this document, we envisage acomprehensive experimental program, with dedicated mea-surements to investigate the full LDM scenario, includingthe most important variations of the vanilla model here dis-cussed. Possible efforts include, for example, a beam-dumpexperiment with a positron beam to investigate both the visi-ble and invisible LDM scenario [252, 260], as well as a dedi- cated measurement to scrutiny the recently reported Be and He anomalies [276, 277].
LDM searches with e + e + @JLab White Paper | 734 | e + @JLab White Paper L. Marsicano et al. harged lepton flavor violation Y. Furletova, S. Mantry
A high intensity polarized positron beam at JLAB in the Contin-uous Electron Beam Accelerator Facility (CEBAF) would allowfor a study of Charged Lepton Flavor Violation (CLFV) througha search for the process e + N → µ + X . Many Beyond the Stan-dard Model scenarios, including those based on the tree-levelprocess of Leptoquark exchange, allow for CLFV rates that arewithin reach of current or future planned experiments. Thepositron beam polarization can be used to distinguish betweensetting limits on left-handed and right-handed Leptoquarks.The high luminosity of the CEBAF facility could allow for animprovement by up to two orders of magnitude over existinglimits from searches at HERA and would complement the strin-gent limits obtained from other low energy experiments. Introduction
The discovery of neutrino oscillations gave conclusive evi-dence that lepton flavor is not a conserved quantity. How-ever, so far, there is no experimental observation of leptonflavor violation in the charged lepton sector. The non-zeromass of neutrinos predicts the existence of charged leptonflavor violating (CLFV) processes, such as µ → eγ , throughloop induced mechanisms. However, the smallness of theneutrino masses makes this process highly suppressed with abranching fraction of Br( µ → eγ ) < − [278], far beyondthe reach of any current or planned experiments.However, many beyond the Standard Model (BSM) sce-narios [229] predict significantly higher CLFV rates thatare within reach of current or future planned experiments.A variety of experiments across the energy spectrum havesearched for and set limits on CLFV processes that involvetransitions between the electron and the muon. These in-clude searches for muon decays µ − → e − γ (MEG experi-ment [279]) and µ − → e − e − e + (Mu3e experiment [280]),the µ − e conversion process µ − + A ( Z, N ) → e − + A ( Z, N ) ( SINDRUM [281] and COMET [282] experiments), andthe Deep Inelastic Scattering (DIS) process e ± N → µ ± X [283]. The most stringent limits come from MEG [284],Br ( µ → eγ ) < . × − , and SINDRUM II [285], CR( µ − e, Au ) < . × − . The H1 [286] and ZEUS [283] collab-orations at HERA have also set limits through searches forthe DIS process e ± N → µ ± X . While some of these CLFVlimits are stronger than others, each can provide complemen-tary information since they can probe different CLFV mech-anisms in different types of processes. Charged Lepton Flavor Violation at CEBAF
A high intensity positron beam at the Continuous ElectronBeam Accelerator Facility (CEBAF) at JLAB can search forthe CLFV process e + N → µ + X . The 11 GeV polarizedpositron beam will impinge on a proton target at rest, cor-responding to a center of mass energy, √ s ∼ . GeV. In
Fig. 62.
The e + N −→ µ + X CLFV process mediated by the tree-level exchangeof LQ states in the s and u channels. spite of the relatively small center of mass energy, its highluminosity, L ∼ − cm − s − , will allow for significantimprovement on existing limits from HERA [283, 286].The experiment should be equipped with detectors, whichcould provide a trigger for muons (for example, muon cham-bers or tagger after the hadron-absorber), as well as a goodtracker and, if possible, vertex detector, to minimize a back-ground coming from pion-decays. CLFV events have a sim-ilar topology to DIS events where scattered electron is re-placed by muon. The selection should be based on eventswhich do not have electrons in the final state, but instead havea clear evidence of a muon track pointing to the vertex.It becomes convenient to study CLFV in the Leptoquark (LQ)scenario. LQs are color triplet bosons that mediates transi-tions between quarks and leptons and carry both baryon num-ber and lepton number. As shown schematically in Fig. 62,the LQs mediate CLFV transitions at tree-level, allowing forlarger cross sections compared to other scenarios in whichCLFV processes are loop suppressed. As seen in Fig. 63,according to the Buchmüller, Rückl and Wyler classifica-tion [287], there are 14 different types of LQs characterizedby their spin (scalar or vector), fermion number F=3B+L(0 or ± ), chiral couplings to leptons (left-handed or right-handed), SU (2) L representation (singlet, doublet, triplet),and U (1) Y hypercharge.For LQ masses M LQ (cid:29) √ s , the tree-level processes inFig. 62 are described by a contact interaction. In this ap-proximation, the cross-section for e + N → µ + X via F=0 and | F | =2 LQ exchange takes the form: σ e + pF =0 = X α,β s π " λ α λ β M LQ Z dx Z dy (99) n xq α ( x, xs ) f ( y ) + x ¯ q β ( x, − u ) g ( y ) o ,σ e + p | F | =2 = X α,β s π " λ α λ β M LQ Z dx Z dy (100) n x ¯ q α ( x, xs ) f ( y ) + q β ( x, − u ) g ( y ) o , respectively. Here u = x ( y − s and f ( y ) = 1 / , g ( y ) =(1 − y ) / for a scalar LQ and f ( y ) = 2(1 − y ) , g ( y ) = 2 for a vector LQ. The λ ij couplings are the lepton-quark-LQ CLFV e + @JLab White Paper | 75 ig. 63. The F = 0 and | F | = 2 leptoquarks in the Buchmüller-Rückl-Wyler mode. F=0 leptoquarks could be only be produced using a positron beam. couplings where first and second indices denote the leptonand quark generations respectively. Note, that the first andsecond terms arise from an s -channel and u -channel LQ-exchange respectively. The positron beam polarization can beused to distinguish between contributions from left-handedand right-handed LQs. Comparing limits [288] obtained us-ing a polarized positron with those obtained from a polarizedelectron beam can also help untangle contributions from F=0and | F | =2 LQs. Thus, the positron beam studies can be com-plementary to CLFV studies planned with an electron beamat the SOLID [289] experiment at JLAB and at the proposedElectron-Ion collider (EIC) [290, 291].The HERA [283, 286] collaborations quantified the results ofthe CLFV searches by setting limits on the coupling to massratios χ αβ ≡ λ α λ β M LQ , (101) that appear in the cross sections in Eq. (99). For example, forthe F=0 LQ state S L / , limits of χ < . TeV − and χ < . TeV − were found [286]. A complete listing of HERAlimits on various LQ states can be found in Refs. [283, 286].For the purposes of comparing the reach at CEBAF to HERAlimits, it becomes useful to define the quantity [291] z ≡ χ αβ χ HERA αβ , (102) which gives the ratio of χ αβ to its upper limit, χ HERA αβ , asset by HERA [283, 286]. Thus, the cross sections in Eq. (99)can be written as a function z . The cross section at z = 1 corresponds to using evaluating it at the HERA limit χ αβ = χ HERA αβ . Similarly, z < corresponds to evaluating the crosssection below the HERA limit χ αβ < χ HERA αβ .A positron beam at CEBAF can improve on the HERA lim-its. The HERA collider operated with a center of mass energy √ s = 300 GeV, much bigger than √ s ∼ . GeV for the CE-BAF facility. Thus, for a fixed value of χ αβ , the LQ crosssections in Eq. (99) at CEBAF are expected to be smaller by the factor ∼ (4 . / = 2 . × − compared to HERA.However, compared to HERA, the CEBAF facility will havean instantaneous luminosity that will be larger by a factor of ∼ or . Running the CEBAF experiment with instanta-neous luminosity L ∼ cm − s − for five years will yieldthe integrated luminosity L int . ∼ × fb − . Without tak-ing efficiencies into account, this will allow for sensitivity tocross sections as small as σ ∼ . × − fb which will yielda number of events of order one.In Fig. 64, we show the cross section at CEBAF for e + N → µ + X , via the exchange of the F=0 left-handed scalar LQ, S L / , as a function of z . The cross section is for a non-zerovalue for λ λ with all other couplings set to zero. Thiscorresponds to the χ contribution to the cross section, cor-responding to both first and second generation quarks beinginvolved in Fig. 62. We see that sensitivity to a cross sec-tion σ ∼ . × − fb, will translate to a limit for z ∼ . ,an improvement by two orders of magnitude over the HERAlimit corresponding to z = 1 . In terms of χ , the HERAlimit is χ HERA12 ∼ . TeV − , so that CEBAF would havesensitivity to χ as small as ∼ . TeV − .The expected two orders of magnitude improvement on theHERA limits can also be complementary to the more strin-gent limits coming from other low energy experiments. Forexample, searches [285] of µ − e conversion on gold nucleiyield the constraint: CR ( µ − e, Au ) = Γ( µ − Au → e − Au )Γ capture < . × − . (103) Since this µ − e conversion involves the Au nucleus in theinitial and final state, it only constrains the product of cou-plings λ α λ β that both involve only same quark generation( α = β ). This yields constraints on χ and χ that are muchor stringent than the HERA limits. For example, the cor-responding limits from µ − e conversion are χ µ − e ∼ . × − TeV − and χ µ − e ∼ . × − TeV − . This can becontrasted with the HERA limits for the S L / LQ which are
76 | e + @JLab White Paper Y. Furletova et al. ig. 64. The cross section for e + N → µ + X with center of mass energy √ s =4 . GeV, via exchange of the F=0 scalar LQ, S L / , as a function of the ratio z defined in Eq. (102). The cross section includes only the χ contribution. z =1 corresponds to evaluating the cross section at the HERA limit χ HERA12 ∼ . TeV − . An integrated luminosity of L ∼ × fb − will allow sensitivity to crosssections as small as σ ∼ . × − fb (horizontal dashed line). This translatesto an improvement over the HERA limit by a factor of about 100, corresponding to z ∼ . (red dashed vertical line). χ HERA11 ∼ . TeV − and χ HERA22 ∼ . TeV − . Thus, theexpected two orders of magnitude improvement at CEBAFover the HERA limits is still not enough to compete with theconstraints from µ − e conversion. However, µ − e conversiondoes not constrain χ which involves quarks from both thefirst and second generations and HERA in fact gives the bestlimit for S L / . Thus, CEBAF can yield significant improve-ment in the region of the theory that might not be accessibleto other low energy experiments. Similarly, for some otherLQs, such as ˜ S L / , which differs from S L / in hypercharge,more stringent limits of χ ∼ × − TeV − , come fromsearches of the CLFV kaon decays K → µ − e + [286]. How-ever, once again, while CLFV kaon decays constrain the ˜ S L / which couples to anti-leptons down-type quarks, it does notconstrain S L / which couples to anti-leptons and up-typequarks.Similarly, much stronger constraints are expected fromCLFV searches at the Large Hadron Collider (LHC) [229].However, compared to the LHC evnironment, a polarizedlepton beam in the initial state allows better control in iso-lating effects from different types of LQs. Furthermore, theCLFV studies at CEBAF will complement future studies atthe Electron-Ion Collider (EIC) which will also search for e → τ CLFV transitions [291–293]. In fact, due to its muchlarger luminosity, the CEBAF bounds on CLFV transitionsbetween the first two lepton generations are still expected tobe stronger than at the EIC. Thus, in general, the CEBAFpositron program to explore CLFV processes can providenew insights and be complementary to other searches acrossa wide variety of experiments.
Conclusions
A polarized positron beam at CEBAF can play an importantrole in the search for charged lepton flavor violation, througha search for the process e + N → µ + X , at the intensity fron-tier. The polarization of the positron beam can distinguishbetween different CLFV mechanisms, such as left-handed vs. right-handed Leptoquarks. It’s large luminosity allows forimproving on HERA limits by up to two orders of magnitudeand complementing CLFV searches in other experiments, in-cluding proposed CLFV studies at the Electron-Ion Collider(EIC) via searches for eN → τ X [291–293]. CLFV e + @JLab White Paper | 778 | e + @JLab White Paper Y. Furletova et al. ibliography [1] M K Jones et al. G Ep /G Mp Ratio by Polarization Transfer in ~ep → e~p . Phys. Rev. Lett. , 84:1398–1402, February 2000.[2] O. Gayou et al. Measurement of g(e(p))/g(m(p)) in e(pol.) p –> e p(pol.) to q**2 = 5.6-gev**2.
Phys. Rev. Lett. , 88:092301, 2002.[3] A J R Puckett et al. Recoil Polarization Measurements of the Proton Electromagnetic Form Factor Ratio to Q = 8 . GeV . Phys. Rev. Lett. , 104(24):242301, 2010.[4] V Punjabi, C F Perdrisat, M K Jones, E J Brash, and C E Carlson. The Structure of the Nucleon: Elastic Electromagnetic Form Factors.
EPJ Web of Conferences , A51(7):79–44, 2015.[5] S. Stepanyan et al. First observation of exclusive deeply virtual compton scattering in polarized electron beam asymmetry measurements.
Phys. Rev. Lett. , 87:182002, 2001.[6] D. Müller, D. Robaschik, B. Geyer, F. M. Dittes, and J. Hoˇrejši. Wave functions, evolution equations and evolution kernels from light ray operators of QCD.
Fortsch. Phys. , 42:101–141, 1994. doi: .[7] Xiang-Dong Ji. Gauge invariant decomposition of nucleon spin.
Phys. Rev. Lett. , 78:610–613, 1997.[8] A. V. Radyushkin. Nonforward parton distributions.
Phys. Rev. , D56:5524–5557, 1997.[9] D.S. Armstrong et al. Strange quark contributions to parity-violating asymmetries in the forward G0 electron-proton scattering experiment.
Phys. Rev. Lett. , 95:092001, 2005. doi: .[10] K. A. Aniol et al. Parity-violating electron scattering from He-4 and the strange electric form factor of the nucleon.
Phys. Rev. Lett. , 96:022003, 2006.[11] K. A. Aniol et al. Constraints on the nucleon strange form factors at Q ≈ . . Phys. Lett. , B635:275–279, 2006.[12] A. Acha et al. Precision measurements of the nucleon strange form factors at Q ≈ . . Phys. Rev. Lett. , 98:032301, 2007.[13] D. Androi´c et al. Strange Quark Contributions to Parity-Violating Asymmetries in the Backward Angle G0 Electron Scattering Experiment.
Phys. Rev. Lett. , 104:012001, 2010. doi: .[14] D. Androi´c et al. Measurement of the parity-violating asymmetry in inclusive electroproduction of π − near the ∆ resonance. Phys. Rev. Lett. , 108:122002, 2012. doi: .[15] D. Androic et al. Transverse Beam Spin Asymmetries at Backward Angles in Elastic Electron-Proton and Quasi-elastic Electron-Deuteron Scattering.
Phys. Rev. Lett. , 107:022501, 2011. doi: .[16] D. Androi´c et al. First Determination of the Weak Charge of the Proton.
Phys. Rev. Lett. , 111(14):141803, 2013. doi: .[17] D. Androi´c et al. Precision measurement of the weak charge of the proton.
Nature , 557(7704):207–211, 2018. doi: .[18] Ross Daniel Young, Julie Roche, Roger D. Carlini, and Anthony William Thomas. Extracting nucleon strange and anapole form factors from world data.
Phys. Rev. Lett. , 97:102002, 2006. doi: .[19] Pierre A.M. Guichon and M. Vanderhaeghen. How to reconcile the Rosenbluth and the polarization transfer method in the measurement of the proton form-factors.
Phys.Rev.Lett. , 91:142303,2003. doi: .[20] P.G. Blunden, W. Melnitchouk, and J.A. Tjon. Two-photon exchange and elastic electron-proton scattering.
Phys.Rev.Lett. , 91:142304, 2003. doi: .[21] E. Voutier. Physics potential of polarized positrons at the Jefferson Laboratory.
Nucl. Theor. , 33:142–151, 2014.[22] X. Zheng. Accessing neutral weak coupling C(3q) using polarized positron and electron beams at Jefferson Lab.
AIP Conf. Proc. , 1160(1):160–163, 2009. doi: .[23] B. Wojtsekhowsky. Searching for a U-boson with a positron beam .
AIP Conf. Proc. , 1160(1):149, 2009. doi: .[24] Luca Marsicano. Searching for dark photon with positrons at Jefferson lab.
AIP Conf. Proc. , 1970(1):020008, 2018. doi: .[25] P.A. Adderley, J. Clark, J. Grames, J. Hansknecht, K. Surles-Law, D. Machie, M. Poelker, M.L. Stutzman, and R. Suleiman. Load-locked dc high voltage GaAs photogun with an inverted-geometryceramic insulator.
Phys. Rev. ST Accel. Beams , 13:010101, 2010. doi: .[26] (PEPPo Collaboration) D. Abbott et al.
Phys. Rev. Lett. , 116:214801, 2016.[27] Haakon Olsen and L.C. Maximon. Photon and Electron Polarization in High-Energy Bremsstrahlung and Pair Production with Screening.
Phys. Rev. , 114:887–904, 1959. doi: .[28] E.A. Kuraev, Yu.M. Bystritskiy, M. Shatnev, and E. Tomasi-Gustafsson. Bremsstrahlung and pair production processes at low energies, multi-differential cross section and polarization phenomena.
Phys. Rev. C , 81:055208, 2010. doi: .[29] A.A. Sokolov, I.M. Ternov.
Sov. Phys. Dokl. , 8:1203, 1964.[30] T. Omori et al. . Phys. Rev. Lett. , 96:114801, 2006.[31] G. Alexander et al.
Phys. Rev. Lett. , 100:210801, 2008.[32] M. Burkardt. Impact parameter dependent parton distributions and off- forward parton distributions for zeta –> 0.
Phys. Rev. , D62:071503, 2000.[33] M. Diehl. Generalized parton distributions in impact parameter space.
Eur. Phys. J. , C25:223–232, 2002.[34] A. Airapetian et al. Measurement of the beam spin azimuthal asymmetry associated with deeply-virtual compton scattering.
Phys. Rev. Lett. , 87:182001, 2001.[35] C. Muñoz Camacho et al. Scaling tests of the cross-section for deeply virtual compton scattering.
Phys.Rev.Lett. , 97:262002, 2006. doi: .[36] F.X. Girod et al. Measurement of Deeply virtual Compton scattering beam-spin asymmetries.
Phys.Rev.Lett. , 100:162002, 2008. doi: .[37] H.-S. Jo. Measurement of deeply virtual Compton scattering (DVCS) cross sections with CLAS.
PoS , QNP2012:052, 2012.[38] E. Seder, A. Biselli, S. Pisano, and S. Niccolai. Longitudinal target-spin asymmetries for deeply virtual Compton scattering.
Phys.Rev.Lett. , 114:032001, 2015. doi: .[39] M. Defurne et al. A glimpse of gluons through deeply virtual compton scattering on the proton.
Nature Commun. , 8(1):1408, 2017. doi: .[40] O. Gayou et al. Measurements of the elastic electromagnetic form-factor ratio mu(p) G(Ep) / G(Mp) via polarization transfer.
Phys. Rev. , C64:038202, 2001. doi: .[41] V. Punjabi et al. Proton elastic form-factor ratios to Q**2 = 3.5-GeV**2 by polarization transfer.
Phys. Rev. , C71:055202, 2005. doi: .[Erratum: Phys. Rev.C71,069902(2005)].[42] B Hu et al. Polarization transfer in the H( ~e,e ~p ) n reaction up to Q = 1.61 (GeV /c ) . Phys. Rev. , C73:064004, 2006.[43] M. K. Jones et al. Proton G(E)/G(M) from beam-target asymmetry.
Phys. Rev. , C74:035201, 2006. doi: .[44] G. MacLachlan et al. The ratio of proton electromagnetic form factors via recoil polarimetry at Q = 1 . (GeV /c ) . Nucl. Phys. , A764:261–273, 2006. doi: .[45] M. Paolone et al. Polarization Transfer in the 4He(e,e’p)3H Reaction at Q = 0 . and 1.3 (GeV /c ) . Phys. Rev. Lett. , 105:072001, 2010. doi: .[46] G. Ron et al. Low Q measurements of the proton form factor ratio µ p G E /G M . Phys. Rev. C , 84:055204, 2011. doi: .[47] X. Zhan et al. High-Precision Measurement of the Proton Elastic Form Factor Ratio µ p G E /G M at low Q . Phys. Lett. , B705:59–64, 2011. doi: .[48] A. J. R. Puckett et al. Final Analysis of Proton Form Factor Ratio Data at Q = . , 4.8 and 5.6 GeV . Phys. Rev. , C85:045203, 2012.[49] A. J. R. Puckett et al. Polarization Transfer Observables in Elastic Electron Proton Scattering at Q = . Phys. Rev. , C96(5):055203, 2017. doi: .[50] B. D. Milbrath et al. A Comparison of polarization observables in electron scattering from the proton and deuteron.
Phys. Rev. Lett. , 80:452–455, 1998. doi: . [Erratum: Phys. Rev. Lett.82,2221(1999)].[51] T. Pospischil et al. Measurement of G(E(p))/G(M(p)) via polarization transfer at Q**2 = 0.4-GeV/c**2.
Eur. Phys. J. , A12:125–127, 2001. doi: .[52] Christopher B. Crawford et al. Measurement of the proton electric to magnetic form factor ratio from vector H-1(vector e, e’ p).
Phys. Rev. Lett. , 98:052301, 2007. doi: .[53] T. Janssens, R. Hofstadter, E. B. Hughes, and M. R. Yearian. Proton form factors from elastic electron-proton scattering.
Phys. Rev. , 142:922–931, Feb 1966. doi: .[54] J Litt et al. Measurement of the ratio of the proton form-factors, G E /G M , at high momentum transfers and the question of scaling. Phys. Lett. , B31:40–44, 1970.[55] C Berger, V. Burkert, G. Knop, B. Langenbeck, and K. Rith. Electromagnetic form-factors of the proton at squared four momentum transfers between 10-fm**-2 and 50 fm**-2.
Phys. Lett. B , 35:87–89, 1971. doi: .[56] W Bartel et al. Measurement of proton and neutron electromagnetic form factors at squared four-momentum transfers up to 3 (GeV /c ) . Nucl. Phys. , B58(2):429–475, 1973.[57] L Andivahis et al. Measurements of the electric and magnetic form factors of the proton from Q = 1.75 to 8.83 (GeV/c) . Phys. Rev. , D50:5491–5517, 1994.[58] R C Walker et al. Measurements of the proton elastic form factors for ≤ Q ≤ (GeV/c) at SLAC. Phys. Rev. , D49(11):5671–5689, June 1994.[59] M E Christy et al. Measurements of electron-proton elastic cross sections for . < Q < . (GeV /c ) . Phys. Rev. , C70:015206, 2004.[60] I A Qattan et al. Precision Rosenbluth measurement of the proton elastic form factors.
Phys. Rev. Lett. , 94:142301, 2005.[61] J. Arrington, W. Melnitchouk, and J.A. Tjon. Global analysis of proton elastic form factor data with two-photon exchange corrections.
Phys. Rev. C , 76:035205, 2007.[62] Luke W. Mo and Yung-Su Tsai. Radiative Corrections to Elastic and Inelastic e p and mu p Scattering.
Rev.Mod.Phys. , 41:205–235, 1969. doi: .[63] L. C. Maximon and J. A. Tjon. Radiative corrections to electron-proton scattering.
Phys. Rev. C , 62(5):054320, Oct 2000. doi: .[64] I. A. Rachek et al. Measurement of the two-photon exchange contribution to the elastic e ± p scattering cross sections at the VEPP-3 storage ring. Phys. Rev. Lett. , 114(6):062005, 2015.[65] D. Adikaram et al. Towards a resolution of the proton form factor problem: new electron and positron scattering data.
Phys. Rev. Lett. , 114:062003, 2015.[66] D. Rimal et al. Measurement of two-photon exchange effect by comparing elastic e ± p cross sections. Phys. Rev. , C95(6):065201, 2017.[67] B. S. Henderson et al. Hard Two-Photon Contribution to Elastic Lepton-Proton Scattering: Determined by the OLYMPUS Experiment.
Phys. Rev. Lett. , 118(9):092501, 2017.[68] O. Tomalak and M. Vanderhaeghen. Subtracted dispersion relation formalism for the two-photon exchange correction to elastic electron-proton scattering: comparison with data.
Eur. Phys. J. ,A51(2):24, 2015. doi: .[69] P. G. Blunden and W. Melnitchouk. Dispersive approach to two-photon exchange in elastic electron-proton scattering.
Phys. Rev. , C95(6):065209, 2017. doi: . e + @JLab White Paper | 79
70] Y.C. Chen, A. Afanasev, S.J. Brodsky, C.E. Carlson, and M. Vanderhaeghen. Partonic calculation of the two-photon exchange contribution to elastic electron-proton scattering at large momentumtransfer.
Phys.Rev.Lett. , 93:122301, 2004. doi: .[71] Andrei V. Afanasev, Stanley J. Brodsky, Carl E. Carlson, Yu-Chun Chen, and Marc Vanderhaeghen. The Two-photon exchange contribution to elastic electron-nucleon scattering at large momentumtransfer.
Phys.Rev. , D72:013008, 2005. doi: .[72] Nikolai Kivel and Marc Vanderhaeghen. Two-photon exchange in elastic electron-proton scattering: QCD factorization approach.
Phys. Rev. Lett. , 103:092004, 2009. doi: .[73] E. Cisbani, M. K. Jones, N. Liyanage, L. P. Pentchev, A. J. R. Puckett, and B. Wojtsekhowski. Update on E12-07-109 to PAC 47: Large Acceptance Proton Form Factor Ratio Measurements at 13and 15 GeV Using Recoil Polarization Method. https://puckett.physics.uconn.edu/wp-content/uploads/sites/1958/2019/08/gep_update.pdf , 2019.[74] Xiang-Dong Ji. Deeply virtual Compton scattering.
Phys.Rev. , D55:7114–7125, 1997. doi: .[75] Xiang-Dong Ji, W. Melnitchouk, and X. Song. A Study of off forward parton distributions.
Phys.Rev. , D56:5511–5523, 1997. doi: .[76] A.V. Radyushkin. Scaling limit of deeply virtual Compton scattering.
Phys.Lett. , B380:417–425, 1996. doi: .[77] M. Diehl, T. Gousset, B. Pire, and J.P. Ralston. Testing the handbag contribution to exclusive virtual compton scattering.
Phys. Lett. , B411:193–202, 1997.[78] A. Airapetian et al. The Beam-charge azimuthal asymmetry and deeply virtual compton scattering.
Phys.Rev. , D75:011103, 2007. doi: .[79] V. M. Braun, A.N. Manashov, D. Müller, and B.M. Pirnay. Deeply Virtual Compton Scattering to the twist-four accuracy: Impact of finite- t and target mass corrections. Phys. Rev. , D89(7):074022,2014. doi: .[80] K. Kumeriˇcki and D. Müller. Deeply virtual Compton scattering at small x(B) and the access to the GPD H.
Nucl.Phys. , B841:1–58, 2010.[81] K. Kumeriˇcki, S. Liuti, and H. Moutarde. GPD phenomenology and DVCS fitting.
Eur. Phys. J. , A52(6):157, 2016. doi: .[82] R. Dupré, M. Guidal, and M. Vanderhaeghen. Tomographic image of the proton.
Phys. Rev. , D95(1):011501, 2017. doi: .[83] A.V. Belitsky, Di. Müller, and Y. Ji. Compton scattering: from deeply virtual to quasi-real.
Nucl. Phys. , B878:214–268, 2014. doi: .[84] C. Muñoz Camacho, T. Horn, C. Hyde, R. Paremuzyan, J. Roche et al. Hard. experiment E12-13-010 (Hall C), 2010.[85] Y. Liang et al. Measurement of R = sigma(L) / sigma(T) and the separated longitudinal and transverse structure functions in the nucleon resonance region. 2004.[86] D. Müller and K. Kumeriˇcki. Model 3: http://calculon.phy.pmf.unizg.hr/gpd/.[87] Peter Kroll, Herve Moutarde, and Franck Sabatie. From hard exclusive meson electroproduction to deeply virtual Compton scattering.
Eur.Phys.J. , C73:2278, 2013. doi: .[88] H. Moutarde. TGV code for fast calculation of DVCS cross sections from CFFs, private communication, 2013.[89] P.A.M. Guichon and M. Vanderhaeghen. Analytic ee γ cross section, in Atelier DVCS, Laboratoire de Physique Corpusculaire, Clermont-Ferrand, June 30 - July 01, 2008.[90] M. Defurne et al. E00-110 experiment at Jefferson Lab Hall A: Deeply virtual Compton scattering off the proton at 6 GeV. Phys. Rev. , C92(5):055202, 2015. doi: .[91] M. Diehl. Physics with positron beams. In
CLAS12 European Workshop, Genova (Italy) , 2009.[92] I.V. Anikin and O.V. Teryaev. Dispersion relations and subtractions in hard exclusive processes.
Phys. Rev. , D76:056007, 2007. doi: .[93] M. Diehl and D.-Y. Ivanov. Dispersion representations for hard exclusive processes: beyond the Born approximation.
Eur. Phys. J. , C52:919–932, 2007. doi: .[94] M.V. Polyakov. Tomography for amplitudes of hard exclusive processes.
Phys. Lett. B , 659:542–550, 2008. doi: .[95] M.V. Polyakov and C. Weiss. Skewed and double distributions in pion and nucleon.
Phys. Rev. , D60:114017, 1999. doi: .[96] M.V. Polyakov. Generalized parton distributions and strong forces inside nucleons and nuclei.
Phys. Lett. , B555:57–62, 2003. doi: .[97] V.D. Burkert, L. Elouadrhiri, and F.X. Girod. The pressure distribution inside the proton.
Nature , 557(7705):396–399, 2018. doi: .[98] M.V. Polyakov and P. Schweitzer. Forces inside hadrons: pressure, surface tension, mechanical radius, and all that.
Int. J. Mod. Phys. , A33(26):1830025, 2018. doi: .[99] K. Kumeriˇcki. Measurability of pressure inside the proton.
Nature , 570(7759):E1–E2, 2019. doi: .[100] A.V. Belitsky and D. Mueller. Exclusive electroproduction revisited: treating kinematical effects.
Phys.Rev. , D82:074010, 2010. doi: .[101] B. Berthou, D. Binosi, N. Chouika, M. Guidal, C. Mezrag, H. Moutarde, F. Sabatié, P. Sznajder, and J. Wagner. PARTONS: PARtonic Tomography Of Nucleon Software. A computing platform forthe phenomenology of Generalized Parton Distributions. 2015.[102] M. Vanderhaeghen, P. Guichon and M. Guidal.
Phys. Rev. , D60:094017, 1999.[103] V.D. Burkert et al. The CLAS12 Spectrometer at Jefferson Laboratory.
Nucl. Instrum. Meth. A , 959:163419, 2020. doi: .[104] A. Afanasev, P. G. Blunden, D. Hasell, and B. A. Raue. Two-photon exchange in elastic electron–proton scattering.
Prog. Part. Nucl. Phys. , 95:245–278, 2017. doi: .[105] A.V. Belitsky, D. Müller, and A. Kirchner. Theory of deeply virtual Compton scattering on the nucleon.
Nucl. Phys. , B629:323–392, 2002. doi: .[106] M. Diehl.
Generalized parton distributions . PhD thesis, 2003.[107] A.V. Belitsky and A.V. Radyushkin. Unraveling hadron structure with generalized parton distributions.
Physics Reports , 418(1):1 – 387, 2005. ISSN 0370-1573. doi: https://doi.org/10.1016/j.physrep.2005.06.002 .[108] M. Guidal. A Fitter code for Deep Virtual Compton Scattering and Generalized Parton Distributions.
Eur.Phys.J. , A37:319–332, 2008. doi: .[109] K. Kumeriˇcki, D. Müller, and A. Schäfer. Neural network generated parametrizations of deeply virtual Compton form factors.
JHEP , 1107:073, 2011. doi: .[110] H. Moutarde, P. Sznajder, and J. Wagner. Unbiased determination of DVCS Compton Form Factors.
Eur. Phys. J. C , 79(7):614, 2019. doi: .[111] K. Kumericki, D. Müller, and K. Passek-Kumericki. Towards a fitting procedure for deeply virtual Compton scattering at next-to-leading order and beyond.
Nucl. Phys. B , 794:244–323, 2008. doi: .[112] Elke-Caroline Aschenauer, Salvatore Fazio, Kresimir Kumericki, and Dieter Mueller. Deeply Virtual Compton Scattering at a Proposed High-Luminosity Electron-Ion Collider.
JHEP , 09:093, 2013.doi: .[113] M. Diehl and S. Sapeta. On the analysis of lepton scattering on longitudinally or transversely polarized protons.
Eur. Phys. J. , C41:515–533, 2005. doi: .[114] M. Mazouz et al. Deeply virtual compton scattering off the neutron.
Phys.Rev.Lett. , 99:242501, 2007. doi: .[115] M. Guidal, H. Moutarde, and M. Vanderhaeghen. Generalized Parton Distributions in the valence region from Deeply Virtual Compton Scattering.
Rept. Prog. Phys. , 76:066202, 2013. doi: .[116] M. Vanderhaeghen, Pierre A. M. Guichon, and M. Guidal. Deeply virtual electroproduction of photons and mesons on the nucleon: Leading order amplitudes and power corrections.
Phys. Rev. ,D60:094017, 1999. doi: .[117] R. Dupré and S. Scopetta. 3D Structure and Nuclear Targets.
Eur. Phys. J. , A52(6):159, 2016. doi: .[118] I. C. Cloët et al. Exposing Novel Quark and Gluon Effects in Nuclei.
J. Phys. , G46(9):093001, 2019. doi: .[119] M. Hattawy et al. First Exclusive Measurement of Deeply Virtual Compton Scattering off He: Toward the 3D Tomography of Nuclei.
Phys. Rev. Lett. , 119(20):202004, 2017. doi: .[120] M. Hattawy et al. Exploring the Structure of the Bound Proton with Deeply Virtual Compton Scattering.
Phys. Rev. Lett. , 123(3):032502, 2019. doi: .[121] A.V. Belitsky and D. Müller. Refined analysis of photon leptoproduction off spinless target.
Phys. Rev. , D79:014017, 2009. doi: .[122] S. Fucini, S. Scopetta, and M. Viviani. Coherent deeply virtual Compton scattering off He.
Phys. Rev. , C98(1):015203, 2018. doi: .[123] S. Liuti and S.K. Taneja. Microscopic description of deeply virtual Compton scattering off spin-0 nuclei.
Phys. Rev. C , 72:032201, 2005. doi: .[124] V. Guzey and M. Strikman. DVCS on spinless nuclear targets in impulse approximation.
Phys. Rev. C , 68:015204, 2003. doi: .[125] W.R. Armstrong et al. Partonic Structure of Light Nuclei.
Jefferson Lab Proposal , PR12-16-011A, 2016.[126] A.V. Radyushkin. Generalized Parton Distributions and Their Singularities.
Phys. Rev. , D83:076006, 2011. doi: .[127] B. Pasquini, M.V. Polyakov, and M. Vanderhaeghen. Dispersive evaluation of the D-term form factor in deeply virtual Compton scattering.
Phys. Lett. , B739:133–138, 2014. doi: .[128] V. Guzey and M. Siddikov. On the A-dependence of nuclear generalized parton distributions.
J. Phys. G , 32:251–268, 2006. doi: .[129] S. Scopetta. Generalized parton distributions of He-3.
Phys. Rev. , C70:015205, 2004. doi: .[130] S. Scopetta. Conventional nuclear effects on generalized parton distributions of trinucleons.
Phys. Rev. , C79:025207, 2009. doi: .[131] M. Rinaldi and S. Scopetta. Extracting generalized neutron parton distributions from He data. Phys. Rev. C , C87(3):035208, 2013. doi: .[132] M. Rinaldi and S. Scopetta. Neutron orbital structure from generalized parton distributions of 3He.
Phys. Rev. , C85:062201, 2012. doi: .[133] S. Fucini, S. Scopetta, and M. Viviani. Catching a glimpse of the parton structure of the bound proton.
Phys. Rev. , D101(7):071501, 2020. doi: .[134] W.R. Armstrong et al. Spectator-Tagged Deeply Virtual Compton Scattering on Light Nuclei.
Jefferson Lab Proposal , PR12-16-011B, 2016.[135] J.-H. Jung, U. Yakhshiev, H.-C. Kim, and P. Schweitzer. In-medium modified energy-momentum tensor form factors of the nucleon within the framework of a π - ρ - ω soliton model. Phys. Rev. , D89(11):114021, 2014. doi: .[136] M. Guidal and M. Vanderhaeghen. Double deeply virtual compton scattering off the nucleon.
Phys. Rev. Lett. , 90:012001, Jan 2003. doi: .[137] A. V. Belitsky and D. Müller. Exclusive electroproduction of lepton pairs as a probe of nucleon structure.
Phys. Rev. Lett. , 90:022001, Jan 2003. doi: .[138] A. V. Belitsky and D. Müller. Probing generalized parton distributions with electroproduction of lepton pairs off the nucleon.
Phys. Rev. D , 68:116005, Dec 2003. doi: .[139] M. Boer, A. Camsonne, K. Gnanvo, E. Voutier, Z. Zhao, et al. Measurement of double deeply virtual compton scattering in the di-muon channel with the solid spectrometer.
Jefferson Lab Letter ofIntent , LOI12-15-005, 2015.
80 | e + @JLab White Paper j/ψ electroproduction. Jefferson Lab Letter of Intent , LOI12-16-004, 2016.[141] I.V. Anikin et al. Nucleon and nuclear structure through dilepton production.
Acta Phys. Pol. B , 49:741, 2018. doi: .[142] S. Zhao et al. Studying nucleon structure via double deeply virtual compton scattering (ddvcs).
PoS , SPIN2018:068, 2019. doi: .[143] SoLID Collaboration. Solid (solenoidal large intensity device) updated preliminary conceptual design report. Technical Report LOI12-16-004, Jefferson Lab, 2019.[144] M. Vanderhaeghen, P. A. M. Guichon, and M. Guidal. Hard electroproduction of photons and mesons on the nucleon.
Phys. Rev. Lett. , 80:5064–5067, Jun 1998. doi: .[145] M. Vanderhaeghen, P. A. M. Guichon, and M. Guidal. Deeply virtual electroproduction of photons and mesons on the nucleon: Leading order amplitudes and power corrections.
Phys. Rev. D , 60:094017, Oct 1999. doi: .[146] M. Guidal, M. V. Polyakov, A. V. Radyushkin, and M. Vanderhaeghen. Nucleon form factors from generalized parton distributions.
Phys. Rev. D , 72:054013, Sep 2005. doi: .[147] Carl E. Carlson and Marc Vanderhaeghen. Two-Photon Physics in Hadronic Processes.
Ann. Rev. Nucl. Part. Sci. , 57:171–204, 2007. doi: .[148] J. Arrington, P. G. Blunden, and W. Melnitchouk. Review of two-photon exchange in electron scattering.
Prog. Part. Nucl. Phys. , 66:782–833, 2011.[149] J.C. Bernauer et al. Electric and magnetic form factors of the proton.
Phys. Rev. , C90(1):015206, 2014.[150] M. Moteabbed et al. Demonstration of a novel technique to measure two-photon exchange effects in elastic e ± p scattering. Phys. Rev. , C88:025210, 2013.[151] Lawrence Cardman, Rolf Ent, Nathan Isgur, Jean-Marc Laget, Christoph Leemann, Curtis Meyer, and Zein-Eddine Meziani. The science driving the 12 gev upgrade of cebaf. 2 2011.[152] V. Tvaskis, J. Arrington, M.E. Christy, R. Ent, C.E. Keppel, Y. Liang, and G. Vittorini. Experimental constraints on non-linearities induced by two-photon effects in elastic and inelastic Rosenbluthseparations.
Phys. Rev. C , 73:025206, 2006.[153] Mikhail Yurov and John Arrington. Super-Rosenbluth measurements with electrons and protons.
AIP Conf. Proc. , 1970(1):020004, 2018. doi: .[154] J. Arrington. How well do we know the electromagnetic form-factors of the proton?
Phys. Rev. C , 68:034325, 2003.[155] J. Arrington. Implications of the discrepancy between proton form-factor measurements.
Phys. Rev. C , 69:022201, 2004.[156] John Arrington, Kees de Jager, and Charles F. Perdrisat. Nucleon Form Factors: A Jefferson Lab Perspective.
J. Phys. Conf. Ser. , 299:012002, 2011.[157] Andrei V Afanasev and Carl E Carlson. Two-photon-exchange correction to parity-violating elastic electron-proton scattering.
Phys. Rev. Lett. , 94:212301, 2005.[158] Dmitry Borisyuk and Alexander Kobushkin. Box diagram in the elastic electron-proton scattering.
Phys. Rev. , C74:065203, 2006.[159] J Arrington. Evidence for two photon exchange contributions in electron proton and positron proton elastic scattering.
Phys. Rev. , C69(3):032201, 2004.[160] I.A. Qattan, J. Arrington, and A. Alsaad. Flavor decomposition of the nucleon electromagnetic form factors at low Q . Phys. Rev. C , 91(6):065203, 2015. doi: .[161] Issam A. Qattan.
Precision Rosenbluth Measurement of the Proton Elastic Electromagnetic Form Factors and Their Ratio at Q**2 = 2.64-GeV**2, 3.20-GeV**2 and 4.10-GeV**2 . Phd thesis,Northwestern University, 2005, nucl-ex/0610006.[162] Mikhail Yurov.
Measurements of Proton Electromagnetic Form Factors and Two-photon Exchange in Elastic Electron-Proton Scattering . Phd thesis, University of Virginia, 2017.[163] J. Arrington. spokesperson, Jefferson Lab experiment E05-017.[164] Peter E. Bosted. An Empirical fit to the nucleon electromagnetic form-factors.
Phys. Rev. C , 51:409–411, 1995.[165] E. A. Kuraev, V. V. Bytev, S. Bakmaev, and E. Tomasi-Gustafsson. Charge asymmetry for electron (positron)-proton elastic scattering at large angle.
Phys. Rev. , C78:015205, 2008. doi: .[166] M. Meziane et al. Search for effects beyond the Born approximation in polarization transfer observables in ~ep elastic scattering.
Phys. Rev. Lett. , 106:132501, 2011. doi: .[167] Kondo Gnanvo, Nilanga Liyanage, Vladimir Nelyubin, Kiadtisak Saenboonruang, Seth Sacher, and Bogdan Wojtsekhowski. Large Size GEM for Super Bigbite Spectrometer (SBS) Polarimeter forHall A 12 GeV program at JLab.
Nucl. Instrum. Meth. A , 782:77–86, 2015. doi: .[168] S. N. Basilev et al. Measurement of neutron and proton analyzing powers on C , CH , CH and Cu targets in the momentum region 3-4.2 GeV/c. Eur. Phys. J. , A56(1):26, 2020. doi: .[169] M. Diehl, Th. Feldmann, R. Jakob, and P. Kroll. Generalized parton distributions from nucleon form-factor data.
Eur. Phys. J. , C39:1–39, 2005. doi: .[170] Jorge Segovia, Ian C. Cloet, Craig D. Roberts, and Sebastian M. Schmidt. Nucleon and ∆ elastic and transition form factors. Few Body Syst. , 55:1185–1222, 2014. doi: .[171] Earle L. Lomon. Effect of revised R(n) measurements on extended Gari-Krumpelmann model fits to nucleon electromagnetic form factors. 2006.[172] Earle L. Lomon and Simone Pacetti. Time-like and space-like electromagnetic form factors of nucleons, a unified description.
Phys. Rev. , D85:113004, 2012. doi: . [Erratum: Phys. Rev.D86,039901(2012)].[173] Franz Gross, G. Ramalho, and M. T. Pena. A Pure S-wave covariant model for the nucleon.
Phys. Rev. , C77:015202, 2008. doi: .[174] Ian C. Cloet and Gerald A. Miller. Nucleon form factors and spin content in a quark-diquark model with a pion cloud.
Phys. Rev. , C86:015208, 2012. doi: .[175] Gerald A. Miller. Light front cloudy bag model: Nucleon electromagnetic form-factors.
Phys. Rev. , C66:032201, 2002. doi: .[176] J. R. Chen et al. Test of Time-Reversal Invariance in Electroproduction Interactions Using a Polarized Proton Target.
Phys. Rev. Lett. , 21:1279–1282, 1968. doi: .[177] J. A. Appel et al. Search for violation of time-reversal invariance in inelastic e-p scattering.
Phys. Rev. , D1:1285–1303, 1970. doi: .[178] Stephen Rock et al. Search for T-Violation in the Inelastic Scattering of Electrons from a Polarized Proton Target.
Phys. Rev. Lett. , 24:748–752, 1970. doi: .[179] A. Airapetian et al. Search for a Two-Photon Exchange Contribution to Inclusive Deep-Inelastic Scattering.
Phys. Lett. , B682:351–354, 2010. doi: .[180] J. Katich et al. Measurement of the Target-Normal Single-Spin Asymmetry in Deep-Inelastic Scattering from the Reaction He ↑ ( e,e ) X . Phys. Rev. Lett. , 113(2):022502, 2014. doi: .[181] Y. W. Zhang et al. Measurement of the Target-Normal Single-Spin Asymmetry in Quasielastic Scattering from the Reaction He ↑ ( e,e ) . Phys. Rev. Lett. , 115(17):172502, 2015. doi: .[182] Axel Schmidt. Polarization Observables using Positron Beams.
AIP Conf. Proc. , 1970(1):020006, 2018. doi: .[183] T.D. Averett et al. A Solid polarized target for high luminosity experiments.
Nucl. Instrum. Meth. A , 427:440–454, 1999. doi: .[184] C.D Keith et al. A polarized target for the CLAS detector.
Nucl. Instrum. Meth. A , 501:327–339, 2003. doi: .[185] C.D. Keith, J. Brock, C. Carlin, S.A. Comer, D. Kashy, J. McAndrew, D.G. Meekins, E. Pasyuk, J.J Pierce, and M.L. Seely. The Jefferson Lab Frozen Spin Target.
Nucl. Instrum. Meth. A , 684:27–35,2012. doi: .[186] Joshua Pierce et al. Dynamically polarized target for the g p and G pE experiments at Jefferson Lab. Phys. Part. Nucl. , 45:303–304, 2014. doi: .[187] Ryan Zielinski.
The g2p Experiment: A Measurement of the Proton’s Spin Structure Functions . PhD thesis, New Hampshire U., 2010.[188] G.A. Miller. Defining the proton radius: A unified treatment.
Phys. Rev. C , 99(3):035202, 2019. doi: .[189] Randolf Pohl et al. The size of the proton.
Nature , 466:213–216, 2010. doi: .[190] Aldo Antognini et al. Proton Structure from the Measurement of S − P Transition Frequencies of Muonic Hydrogen.
Science , 339:417–420, 2013. doi: .[191] C.E. Carlson. The Proton Radius Puzzle.
Prog. Part. Nucl. Phys. , 82:59–77, 2015. doi: .[192] Gerald A. Miller. The Proton Radius Puzzle- Why We All Should Care. In , 9 2018.[193] J.C. Bernauer et al. High-precision determination of the electric and magnetic form factors of the proton.
Phys. Rev. Lett. , 105:242001, 2010. doi: .[194] M. Mihoviloviˇc et al. The proton charge radius extracted from the Initial State Radiation experiment at MAMI. 2019.[195] M. Horbatsch and E. A. Hessels. Evaluation of the strength of electron-proton scattering data for determining the proton charge radius.
Phys. Rev. , C93(1):015204, 2016. doi: .[196] Keith Griffioen, Carl Carlson, and Sarah Maddox. Consistency of electron scattering data with a small proton radius.
Phys. Rev. , C93(6):065207, 2016. doi: .[197] Douglas W. Higinbotham, Al Amin Kabir, Vincent Lin, David Meekins, Blaine Norum, and Brad Sawatzky. Proton radius from electron scattering data.
Phys. Rev. , C93(5):055207, 2016. doi: .[198] Gabriel Lee, John R. Arrington, and Richard J. Hill. Extraction of the proton radius from electron-proton scattering data.
Phys. Rev. , D92(1):013013, 2015. doi: .[199] Krzysztof M. Graczyk and Cezary Juszczak. Proton radius from Bayesian inference.
Phys. Rev. , C90:054334, 2014. doi: .[200] I. T. Lorenz and Ulf-G. Meißner. Reduction of the proton radius discrepancy by 3 σ . Phys. Lett. , B737:57–59, 2014. doi: .[201] Marko Horbatsch, Eric A. Hessels, and Antonio Pineda. Proton radius from electron-proton scattering and chiral perturbation theory.
Phys. Rev. , C95(3):035203, 2017. doi: .[202] J. M. Alarcón, D. W. Higinbotham, C. Weiss, and Z. Ye. Proton charge radius extraction from electron scattering data using dispersively improved chiral effective field theory.
Phys. Rev. , C99(4):044303, 2019. doi: .[203] J.M. Alarcón, D.W. Higinbotham, and C. Weiss. Precise determination of proton magnetic radius from electron scattering data. 2 2020.[204] Shuang Zhou, P. Giuliani, J. Piekarewicz, Anirban Bhattacharya, and Debdeep Pati. Reexamining the proton-radius problem using constrained Gaussian processes.
Phys. Rev. , C99(5):055202,2019. doi: .[205] Scott K. Barcus, Douglas W. Higinbotham, and Randall E. McClellan. How Analytic Choices Can Affect the Extraction of Electromagnetic Form Factors from Elastic Electron Scattering CrossSection Data.
Phys. Rev. C , 102:015205, 2020. doi: .[206] Miha Mihoviloviˇc, Douglas W. Higinbotham, Melisa Bevc, and Simon Širca. Reinterpretation of Classic Proton Charge Form Factor Measurements.
Front. in Phys. , 8:36, 2020. doi: . e + @JLab White Paper | 81 Nature , 575(7781):147–150, 2019. doi: .[208] N. Bezginov, T. Valdez, M. Horbatsch, A. Marsman, A.C. Vutha, and E.A. Hessels. A measurement of the atomic hydrogen Lamb shift and the proton charge radius.
Science , 365(6457):1007–1012,2019. doi: .[209] H.-W. Hammer and U.-G. Meißner. The proton radius: From a puzzle to precision.
Sci. Bull. , 65:257–258, 2020. doi: .[210] R. Gilman et al. Studying the Proton "Radius" Puzzle with µ p Elastic Scattering. 3 2013.[211] R. Gilman et al. Technical Design Report for the Paul Scherrer Institute Experiment R-12-01.1: Studying the Proton "Radius" Puzzle with µp Elastic Scattering. 9 2017.[212] A. Gasparian. Performance of PWO crystal detectors for a high resolution hybrid electromagnetic calorimeter at Jefferson Lab. In , pages 208–214, 3 2002.[213] A. Gasparian. A high performance hybrid electromagnetic calorimeter at Jefferson Lab. In , pages 109–115, 32004.[214] X. Yan, D.W. Higinbotham, D. Dutta, H. Gao, A. Gasparian, M. A. Khandaker, N. Liyanage, E. Pasyuk, C. Peng, and W. Xiong. Robust extraction of the proton charge radius from electron-protonscattering data.
Phys. Rev. C , 98(2):025204, 2018. doi: .[215] William J. Marciano and Alberto Sirlin. Improved calculation of electroweak radiative corrections and the value of V(ud).
Phys. Rev. Lett. , 96:032002, 2006. doi: .[216] J.C. Hardy and I.S. Towner. Superallowed + → + nuclear β decays: 2014 critical survey, with precise results for V ud and CKM unitarity. Phys. Rev. C , 91(2):025501, 2015. doi: .[217] D Yount and J Pine. Scattering of High-Energy Positrons from Protons.
Phys. Rev. , 128:1842–1849, November 1962.[218] R.L. Anderson, B. Borgia, G.L. Cassiday, J.W. DeWire, A.S. Ito, et al. Scattering of Positrons and Electrons from Protons.
Phys.Rev.Lett. , 17:407–409, 1966. doi: .[219] W. Bartel, B. Dudelzak, H. Krehbiel, J.M. McElroy, R.J. Morrison, W. Schmidt, V. Walther, and G. Weber. Scattering of positrons and electrons from protons.
Physics Letters B , 25(3):242 – 245,1967. ISSN 0370-2693. doi: http://dx.doi.org/10.1016/0370-2693(67)90055-X .[220] B. Bouquet, D. Benaksas, B. Grossetête, B. Jean-Marie, G. Parrour, J.P. Poux, and R. Tchapoutian. Backward scattering of positrons and electrons on protons.
Physics Letters B , 26(3):178 –180, 1968. ISSN 0370-2693. doi: http://dx.doi.org/10.1016/0370-2693(68)90520-0 .[221] A Browman, F Liu, and C Schaerf. Positron-Proton Scattering.
Phys. Rev. , B139:1079–1085, 1965.[222] G. Cassiday, J. DeWire, H. Fischer, A. Ito, E. Loh, and J. Rutherfoord. Comparison of elastic positron-proton and electron-proton scattering cross sections.
Phys. Rev. Lett. , 19:1191–1192, Nov1967. doi: .[223] Jerry Mar et al. A Comparison of electron-proton and positron-proton elastic scattering at four momentum transfers up to 5.0 (GeV /c ) . Phys. Rev. Lett. , 21:482–484, 1968.[224] H. Dai et al. First measurement of the Ar ( e,e ) X cross section at Jefferson Laboratory. Phys. Rev. C , 99(5):054608, 2019. doi: .[225] I. Sick. Model-independent nuclear charge densities from elastic electron scattering.
Nucl. Phys. A , 218:509–541, 1974. doi: .[226] H. De Vries, C.W. De Jager, and C. De Vries. Nuclear charge and magnetization density distribution parameters from elastic electron scattering.
Atom. Data Nucl. Data Tabl. , 36:495–536, 1987.doi: .[227] S. Abrahamyan et al. Measurement of the Neutron Radius of 208Pb Through Parity-Violation in Electron Scattering.
Phys. Rev. Lett. , 108:112502, 2012. doi: .[228] Francis Halzen and Alan Martin.
Quarks and Leptons .[229] P. A. Zyla et al. The Review of Particle Physics (2020).
Prog. Theor. Exp. Phys. , 2020:083C01, 2020.[230] Jens Erler and Shufang Su. The Weak Neutral Current.
Prog. Part. Nucl. Phys. , 71:119–149, 2013. doi: .[231] D. Wang et al. Measurement of parity violation in electron–quark scattering.
Nature , 506(7486):67–70, 2014. doi: .[232] D. Wang et al. Measurement of Parity-Violating Asymmetry in Electron-Deuteron Inelastic Scattering.
Phys. Rev. C , 91(4):045506, 2015. doi: .[233] Dominik Becker et al. The P2 experiment. 2 2018. doi: .[234] Jens Erler. Theoretical Implications of Precision Measurements. In , pages 274–293, 2020. doi: .[235] J.P. Chen, H. Gao, T.K. Hemmick, Z. E. Meziani, and P.A. Souder. A White Paper on SoLID (Solenoidal Large Intensity Device). September 2014.[236] A. Argento et al. Electroweak Asymmetry in Deep Inelastic Muon - Nucleon Scattering.
Phys. Lett. B , 120:245, 1983. doi: .[237] Jens Erler and Michael J. Ramsey-Musolf. Low energy tests of the weak interaction.
Prog. Part. Nucl. Phys. , 54:351, 2005. doi: .[238] S. M. Berman and Joel R. Primack. WEAK NEUTRAL CURRENTS IN ELECTRON AND MUON SCATTERING.
Phys. Rev. , D9:2171, 1974. doi: .[239] C. Y. Prescott et al. Parity non-conservation in inelastic electron scattering.
Phys. Lett. , B77:347–352, 1978.[240] C. Y. Prescott et al. Further measurements of parity nonconservation in inelastic electron scattering.
Phys. Lett. , B84:524, 1979.[241] X. Zheng, R. Michaels, P.E. Reimer, et al. ~e − H PVDIS at 6 GeV, 2008. Jefferson Lab E08-011.[242] X. Zheng, K. Paschke, P.E. Reimer, et al. Precision Measurement of the Parity-VIlating Asymmetry in Deep Inelastic Scattering off Deuterium using Baseline 12 GeV Equipment in Hall C, 2008.Jefferson Lab 12 GeV Proposal PR12-07-102.[243] SoLID Collaboration. Solid (solenoidal large intensity device) updated preliminary conceptual design report, November 2019.[244] L. Roszkowski et al. WIMP dark matter candidates and searches - current status and future prospects.
Rept. Prog. Phys. , 81(6):066201, 2018.[245] G. Arcadi et al. The waning of the WIMP? A review of models, searches, and constraints.
Eur. Phys. J. , C78(3):203, 2018.[246] B. Holdom. Two U (1) ’s and ε charge shifts. Phys. Lett. B , 166(2):196 – 198, 1986. ISSN 0370-2693.[247] E. Izaguirre et al. New electron beam-dump experiments to search for MeV to few-GeV dark matter.
Phys. Rev. D , 88:114015, Dec 2013.[248] B. Batell et al. Exploring portals to a hidden sector through fixed targets.
Phys. Rev. D , 80:095024, Nov 2009.[249] A.R. Liddle.
An introduction to modern cosmology . 2003.[250] M. Battaglieri et al. US Cosmic Visions: New Ideas in Dark Matter 2017: Community Report. 2017.[251] N. Aghanim et al. Planck 2018 results. VI. Cosmological parameters. 2018.[252] L. Marsicano et al. Novel way to search for light dark matter in lepton beam-dump experiments.
Phys. Rev. Lett. , 121:041802, Jul 2018.[253] A. Celentano. The Heavy Photon Search experiment at Jefferson Laboratory.
J. Phys. Conf. Ser. , 556(1):012064, 2014.[254] G.B. Franklin. The APEX experiment at JLab. Searching for the vector boson A decaying to e + e − . EPJ Web Conf. , 142:01015, 2017.[255] L. Marsicano. The Beam Dump eXperiment.
PoS , ICHEP2018:075, 2019. doi: .[256] R. Corliss. Searching for a dark photon with DarkLight.
Nucl. Instrum. Meth. A , 865:125–127, 2017. doi: .[257] M. Raggi. The PADME experiment at LNF.
EPJ Web Conf. , 142:01026, 2017.[258] E. Izaguirre et al. Testing GeV-scale dark matter with fixed-target missing momentum experiments.
Phys. Rev. D , 91:094026, May 2015.[259] E. Nardi et al. Resonant production of dark photons in positron beam dump experiments.
Phys. Rev. D , 97:095004, May 2018.[260] L. Marsicano et al. Dark photon production through positron annihilation in beam-dump experiments.
Phys. Rev. D , 98:015031, Jul 2018.[261] A. Pukhov. Calchep 2.3: Mssm, structure functions, event generation, batchs, and generation of matrix elements for other packages, 2004.[262] S. Agostinelli et al. GEANT4: A Simulation toolkit.
Nucl. Instrum. Meth. , A506:250–303, 2003.[263] E. Leonardi, V. Kozhuharov, M. Raggi, and P. Valente. GEANT4-based full simulation of the PADME experiment at the DA φ NE BTF.
J. Phys. Conf. Ser. , 898(4):042025, 2017. doi: .[264] M. Raggi et al. Performance of the PADME Calorimeter prototype at the DA Φ NE BTF.
Nucl. Instrum. Meth. A , 862:31–35, 2017. doi: .[265] E. Leonardi, M. Raggi, and P. Valente. Development and test of a DRS4-based DAQ system for the PADME experiment at the DA Φ NE BTF.
J. Phys. Conf. Ser. , 898(3):032024, 2017. doi: .[266] M. Tanabashi et al. Review of particle physics.
Phys. Rev. D , 98:030001, Aug 2018.[267] A.B. Chilton. A note on the fluence concept.
Health Physics , 34(6):715–716, 1978.[268] J. Grames and E. Voutier. Private communication, 2020.[269] P. Adzic et al. Radiation hardness qualification of PbWO(4) scintillation crystals for the CMS Electromagnetic Calorimeter.
JINST , 5:P03010, 2010.[270] S. Chatrchyan et al. The CMS Experiment at the CERN LHC.
JINST , 3:S08004, 2008.[271] V. Dormenev et al. Stimulated recovery of the optical transmission of pbwo4 scintillation crystals for electromagnetic calorimeters after radiation damage.
Nucl. Instrum. Meth. A , 623(3):1082 –1085, 2010.[272] S. Fegan et al. Assessing the performance under ionising radiation of lead tungstate scintillators for EM calorimetry in the CLAS12 Forward Tagger.
Nucl. Instrum. Meth. , A789:101–108, 2015.[273] G. Cowan et al. Asymptotic formulae for likelihood-based tests of new physics.
Eur. Phys. J. , C71:1554, 2011. [Erratum: Eur. Phys. J.C73,2501(2013)].[274] T. Åkesson et al. Light Dark Matter eXperiment (LDMX), 2018.[275] D. Banerjee et al. Dark matter search in missing energy events with NA64.
Phys. Rev. Lett. , 123:121801, 2019.[276] A. J. Krasznahorkay et al. Observation of anomalous internal pair creation in Be : A possible indication of a light, neutral boson. Phys. Rev. Lett. , 116:042501, Jan 2016.[277] A.J. Krasznahorkay et al. New evidence supporting the existence of the hypothetic X17 particle. 10 2019.[278] A. M. Baldini et al. .
Eur. Phys. J. , C76:434, 2016.
82 | e + @JLab White Paper Interplay between Particle and Astroparticle physics , 12 2014.[280] A. Schöning, S. Bachmann, and R. Narayan. A novel experiment to search for the decay µ → eee . Phys. Proc. , 17:181–190, 2011. doi: .[281] P. Wintz. Results of the SINDRUM-II experiment.
Conf. Proc. C , 980420:534–546, 1998.[282] MyeongJae Lee. COMET Muon Conversion Experiment in J-PARC.
Front. in Phys. , 6, 2018. doi: .[283] S. Chekanov et al. Search for lepton-flavor violation at HERA.
Eur. Phys. J. C , 44:463–479, 2005. doi: .[284] A.M. Baldini et al. The design of the MEG II experiment.
Eur. Phys. J. C , 78(5):380, 2018. doi: .[285] A. van der Schaaf. SINDRUM II.
J. Phys. G , 29:1503–1506, 2003. doi: .[286] F.D. Aaron et al. Search for Lepton Flavour Violation at HERA.
Phys. Lett. B , 701:20–30, 2011. doi: .[287] W. Buchmuller, R. Ruckl, and D. Wyler. Leptoquarks in Lepton - Quark Collisions.
Phys. Lett. B , 191:442–448, 1987. doi: . [Erratum: Phys.Lett.B 448, 320–320(1999)].[288] Yulia Furletova and Sonny Mantry. Using polarized positrons to probe physics beyond the standard model.
AIP Conf. Proc. , 1970(1):030005, 2018. doi: .[289] J.-P. Chen, H. Gao, T.K. Hemmick, Z.-E. Meziani, P.A. Souder, and the SoLID Collaboration. A white paper on solid (solenoidal large intensity device), 2014.[290] et. al. A. Accardi. Electron ion collider: The next qcd frontier - understanding the glue that binds us all, 2012.[291] Matthew Gonderinger and Michael J. Ramsey-Musolf. Electron-to-tau lepton flavor violation at the electron-ion collider.
Journal of High Energy Physics , 2010(11), Nov 2010. ISSN 1029-8479.doi: .[292] A. Accardi, V. Guzey, A. Prokudin, and C. Weiss. Nuclear physics with a medium-energy Electron-Ion Collider.
Eur. Phys. J. A , 48:92, 2012. doi: .[293] D. Boer et al. Gluons and the quark sea at high energies: distributions, polarization, tomography, 2011. e ++