Measurement of deeply virtual Compton scattering off Helium-4 with CLAS at Jefferson Lab
R. Dupré, M. Hattawy, N.A. Baltzell, S. Bültmann, R. De Vita, A. El Alaoui, L. El Fassi, H. Egiyan, F.X. Girod, M. Guidal, K. Hafidi, D. Jenkins, S. Liuti, Y. Perrin, S. Stepanyan, B. Torayev, E. Voutier, M.J. Amaryan, W.R. Armstrong, H. Atac, C. Ayerbe Gayoso, L. Barion, M. Battaglieri, I. Bedlinskiy, F. Benmokhtar, A. Bianconi, A.S. Biselli, M. Bondi, F. Bossù, S. Boiarinov, W.J. Briscoe, D. Bulumulla, V. Burkert, D.S. Carman, J.C. Carvajal, M. Caudron, A. Celentano, P. Chatagnon, V. Chesnokov, T. Chetry, G. Ciullo, B.A. Clary, P.L. Cole, M. Contalbrigo, G. Costantini, V. Crede, A. D'Angelo, N. Dashyan, M. Defurne, A. Deur, S. Diehl, C. Djalali, M. Ehrhart, L. Elouadrhiri, P. Eugenio, S. Fegan, A. Filippi, T.A. Forest, Y. Ghandilyan, G.P. Gilfoyle, R.W. Gothe, K.A. Griffioen, H. Hakobyan, T.B. Hayward, K. Hicks, A. Hobart, M. Holtrop, Y. Ilieva, D.G. Ireland, E.L. Isupov, H.S. Jo, K. Joo, S. Joosten, D. Keller, G. Khachatryan, A. Khanal, M. Khandaker, A. Kim, W. Kim, A. Kripko, V. Kubarovsky, S.E. Kuhn, L. Lanza, K. Livingston, M.L. Kabir, M. Leali, P. Lenisa, I.J.D. MacGregor, D. Marchand, N. Markov, V. Mascagna, M. Mayer, B. McKinnon, M. Mirazita, V.I. Mokeev, K. Neupane, S. Niccolai, T. R. O'Connell, M. Osipenko, M. Paolone, et al. (41 additional authors not shown)
MMeasurement of deeply virtual Compton scattering off Helium-4with CLAS at Jefferson Lab
R. Dupré,
1, 21, ∗ M. Hattawy,
1, 21, 33
N.A. Baltzell,
1, 40
S. Bültmann, R. De Vita, A. El Alaoui,
1, 41
L. El Fassi,
1, 27
H. Egiyan, F.X. Girod, M. Guidal, K. Hafidi, D. Jenkins, S. Liuti, Y. Perrin, S. Stepanyan, B. Torayev, E. Voutier,
21, 25
M.J. Amaryan, W.R. Armstrong, H. Atac, C. Ayerbe Gayoso, L. Barion, M. Battaglieri,
40, 17
I. Bedlinskiy, F. Benmokhtar, A. Bianconi,
43, 20
A.S. Biselli, M. Bondi, F. Bossù, S. Boiarinov, W.J. Briscoe, D. Bulumulla, V. Burkert, D.S. Carman, J.C. Carvajal, M. Caudron, A. Celentano, P. Chatagnon, V. Chesnokov, T. Chetry,
27, 32
G. Ciullo,
15, 10
B.A. Clary, P.L. Cole, M. Contalbrigo, G. Costantini,
43, 20
V. Crede, A. D’Angelo,
18, 36
N. Dashyan, M. Defurne, A. Deur, S. Diehl,
34, 6
C. Djalali, M. Ehrhart,
1, 21
L. Elouadrhiri, P. Eugenio, S. Fegan, A. Filippi, T.A. Forest, Y. Ghandilyan, G.P. Gilfoyle, R.W. Gothe, K.A. Griffioen, H. Hakobyan,
41, 49
T.B. Hayward, K. Hicks, A. Hobart, M. Holtrop, Y. Ilieva, D.G. Ireland, E.L. Isupov, H.S. Jo, K. Joo, S. Joosten, D. Keller, G. Khachatryan, A. Khanal, M. Khandaker, A. Kim, W. Kim, A. Kripko, V. Kubarovsky, S.E. Kuhn, L. Lanza, K. Livingston, M.L. Kabir, M. Leali,
43, 20
P. Lenisa,
15, 10
I.J.D. MacGregor, D. Marchand, N. Markov,
40, 6
V. Mascagna,
42, 20
M. Mayer, B. McKinnon, M. Mirazita, V.I. Mokeev, K. Neupane, S. Niccolai, T. R. O’Connell, M. Osipenko, M. Paolone,
30, 39
L.L. Pappalardo,
15, 10
R. Paremuzyan,
40, 29
E. Pasyuk, D. Payette, W. Phelps, N. Pivnyuk, O. Pogorelko, J. Poudel, Y. Prok, M. Ripani, J. Ritman, A. Rizzo,
18, 36
G. Rosner, P. Rossi,
16, 40
J. Rowley, F. Sabatié, C. Salgado, A. Schmidt,
13, 26
R. Schumacher, V. Sergeyeva, Y. Sharabian, U. Shrestha, D. Sokhan, O. Soto,
16, 41
N. Sparveris, I.I. Strakovsky, S. Strauch, N. Tyler, M. Ungaro,
40, 6
L. Venturelli,
43, 20
H. Voskanyan, A. Vossen,
7, 40
D. Watts, K. Wei, X. Wei, L.B. Weinstein, R. Wishart, M.H. Wood, B. Yale, N. Zachariou, and J. Zhang (The CLAS Collaboration) Argonne National Laboratory, Argonne, Illinois 60439 a r X i v : . [ nu c l - e x ] F e b Canisius College, Buffalo, NY Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France Christopher Newport University, Newport News, Virginia 23606 University of Connecticut, Storrs, Connecticut 06269 Duke University, Durham, North Carolina 27708-0305 Duquesne University, 600 Forbes Avenue, Pittsburgh, PA 15282 Fairfield University, Fairfield CT 06824 Universita’ di Ferrara , 44121 Ferrara, Italy Florida International University, Miami, Florida 33199 Florida State University, Tallahassee, Florida 32306 The George Washington University, Washington, DC 20052 Idaho State University, Pocatello, Idaho 83209 INFN, Sezione di Ferrara, 44100 Ferrara, Italy INFN, Laboratori Nazionali di Frascati, 00044 Frascati, Italy INFN, Sezione di Genova, 16146 Genova, Italy INFN, Sezione di Roma Tor Vergata, 00133 Rome, Italy INFN, Sezione di Torino, 10125 Torino, Italy INFN, Sezione di Pavia, 27100 Pavia, Italy Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France Institute fur Kernphysik (Juelich), Juelich, Germany Kyungpook National University, Daegu 41566, Republic of Korea Lamar University, 4400 MLK Blvd, PO Box 10046, Beaumont, Texas 77710 LPSC, Université Grenoble-Alpes, CNRS/IN2P3, 38026 Grenoble, France Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307 Mississippi State University, Mississippi State, MS 39762-5167 National Research Centre Kurchatov Institute - ITEP, Moscow, 117259, Russia University of New Hampshire, Durham, New Hampshire 03824-3568 New Mexico State University, PO Box 30001, Las Cruces, NM 88003, USA Norfolk State University, Norfolk, Virginia 23504 Ohio University, Athens, Ohio 45701 Old Dominion University, Norfolk, Virginia 23529 II Physikalisches Institut der Universitaet Giessen, 35392 Giessen, Germany University of Richmond, Richmond, Virginia 23173 Universita’ di Roma Tor Vergata, 00133 Rome Italy Skobeltsyn Institute of Nuclear Physics, LomonosovMoscow State University, 119234 Moscow, Russia University of South Carolina, Columbia, South Carolina 29208 Temple University, Philadelphia, PA 19122 Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606 Universidad Técnica Federico Santa María, Casilla 110-V Valparaíso, Chile Università degli Studi dell’Insubria, 22100 Como, Italy Università degli Studi di Brescia, 25123 Brescia, Italy University of Glasgow, Glasgow G12 8QQ, United Kingdom University of York, York YO10 5DD, United Kingdom University of Virginia, Charlottesville, Virginia 22901 Virginia Tech, Blacksburg, Virginia 24061-0435 College of William and Mary, Williamsburg, Virginia 23187-8795 Yerevan Physics Institute, 375036 Yerevan, Armenia (Dated: February 16, 2021) bstract We report on the measurement of the beam spin asymmetry in the deeply virtual Comptonscattering off He using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab usinga 6 GeV longitudinally polarized electron beam incident on a pressurized He gaseous target. Wedetail the method used to ensure the exclusivity of the measured reactions, in particular the upgradeof CLAS with a radial time projection chamber to detect the low-energy recoiling He nuclei andan inner calorimeter to extend the photon detection acceptance at forward angles. Our resultsconfirm the theoretically predicted enhancement of the coherent ( e He → e He γ ) beam spinasymmetries compared to those observed on the free proton, while the incoherent ( e He → e p γ X )asymmetries exhibit a 30% suppression. From the coherent data, we were able to extract, in amodel-independent way, the real and imaginary parts of the only He Compton form factor, H A ,leading the way toward 3D imaging of the partonic structure of nuclei. ∗ corresponding author: [email protected] . INTRODUCTION In the past few decades, the study of the proton structure has made significant progressthanks to the theoretical and experimental developments of three dimensional structurefunctions [1]. These studies, which have focused on generalized parton distributions (GPDs)and transverse momentum dependent parton distribution functions (TMDs) can be generalizedto the nucleus and offer a unique opportunity to revisit the quark structure of the nucleuswith an original perspective [2]. This new approach is particularly needed as the quarkstructure of the nucleus remains today the subject of numerous controversies. Indeed, whilemuch progress has been made in measuring the nuclear parton distribution functions, theirshape can be explained with very different model assumptions [3–5].In nuclei, the GPDs can be probed conveniently through the measurement of the spinasymmetries generated by the deeply virtual Compton scattering (DVCS) process [6–9].The measurement of the exclusive production of a photon limits the possibilities of finalstate interactions (FSIs) in the nuclear medium and offers a unique opportunity to make ameasurement free of them. Moreover, with a spin-0 nuclear target, the extraction of the GPDfrom the DVCS data is significantly simplified since a single GPD is involved in the process atleading order. However, the measurement of the nuclear DVCS is challenging experimentallyand the first attempts by the HERMES Collaboration [10] led to controversial conclusions.We present here in detail the more recent measurements by the CLAS Collaboration, whichhas been already partially presented in two short letters [11, 12]. We extend in this articlethe description of the CLAS nuclear DVCS experiment, detail the methods used for the dataanalysis and produce the complete experimental results for each channel measured.
II. THEORETICAL FRAMEWORKA. The GPD Formalism
The theory of GPDs has been already reviewed in detail in various publications [6–9],and we summarize here only the necessary elements to discuss the present experimentalresults. The GPDs are real structure functions F q ( x, ξ, t ), where x + ξ and x − ξ are theincoming and outgoing quark momenta respectively and t = ∆ is the squared transferred5 IG. 1: General representation for the GPDs of a nucleon represented by the triple lines and noted N . Single lines can represent quarks or anti-quarks probed in the nucleon shown by the triple lines. four momentum to the target, as illustrated in Fig. 1.The different possible spin states lead to several independent GPDs for any given hadron.The proper accounting of the number of GPDs must be done with regard to the symmetriesof the system. At leading order and leading twist, we find that there are 2(2 J + 1) GPDs fora particle of spin J . Therefore for a spin-0 hadron like the helium-4 nucleus, we will have twoGPDs, and for a spin-1/2 hadron like the proton, eight GPDs. Half of these involve a partonhelicity flip, they are called transversity GPDs and do not contribute to the DVCS process.DVCS is the main experimental probe of the GPDs. However, this process does not allowfor an extraction of the GPDs in the full phase space of the parameters. Instead, DVCSgives access to the GPDs integrated over x . To account for this and simplify the notation,we define the complex Compton form factors (CFF, noted with curved F for a given GPD F ) for each GPD as follows: < e ( F ( ξ, t )) = X q e q P Z − dxF q ( x, ξ, t ) " x − ξ ∓ x + ξ , (1) = m ( F ( ξ, t )) = − π X q e q [ F q ( ξ, ξ, t ) ∓ F q ( − ξ, ξ, t )] . (2)These are the quantities directly present in the DVCS cross sections. We note that they aresummed over the different quark flavors present in the hadron, as the electromagnetic probedoes not differentiate quark flavors.Experimentally, another process is indistinguishable from DVCS, the Bethe-Heitler (BH)process in which the final state photon is emitted by the scattering lepton rather than the6 IG. 2: Illustration of the scattering (or leptonic) and production (or hadronic) planes in the DVCSprocess. hadron. In this case, the photon-hadron interaction is the same as in elastic scattering anddepends on the target form factors rather than its GPDs. The DVCS and BH processes areexperimentally indistinguishable as they have identical final states, such that they interferein the squared amplitude of the exclusive photo-production process: | T | = | T DV CS | + | T BH | + T ∗ DV CS T BH + T DV CS T ∗ BH . (3)The interference terms significantly increase the cross section in specific parts of the phasespace and lead to significant beam spin asymmetries (BSAs), which are the focus of themeasurements presented here.Finally, we need to define the kinematics. We use the conventions from Fig. 2 for anglesand the experimental kinematic variables used here are defined as: − t = − ( p p − p p ) = ∆ and x B = Q M N ν ∼ ξ ξ , with M N the nucleon mass and ν the energy transfer to the target, ν = E − E . B. Coherent Nuclear DVCS
The first reaction measured in the experiment is the coherent electro-production of aphoton on helium e + He → e + γ + He at large 4-momentum transfer squared ( Q ).The leading order diagram of the nuclear coherent DVCS is represented in Fig. 3. In the7 IG. 3: Diagram representing the coherent nuclear DVCS, where we indicate the limit between thehard and the soft components with the dot-dashed factorization line. present experiment, we focused on the measurement of the BSA noted A LU with L for thelongitudinally polarized electron beam and U the unpolarized target, which is defined as: A LU = d σ + − d σ − d σ + + d σ − , (4)where d σ + ( d σ − ) is the differential cross section for a positive (negative) beam helicity. Atleading order and leading twist, the BSA can be expressed as [13]: A LU = x A (1 + (cid:15) ) y s INT sin( φ ) , " n =2 X n =0 c BHn cos ( nφ ) + (5) x A t (1 + (cid:15) ) Q P ( φ ) P ( φ ) c DV CS + x A (1 + (cid:15) ) y n =1 X n =0 c INTn cos ( nφ ) , where P ( φ ) and P ( φ ) are the BH propagators, and x A = M p · xM He . The factors: c BH , , , c DV CS , c INT , and s INT are the Fourier coefficients of the BH, the DVCS and the interferenceamplitudes for a spin-zero target, respectively. The explicit expressions of these coefficients,which have been derived based on the work of Kirchner and Müller [13], can be found inAppendix A.This formula can be expressed in a simplified manner for a spin-0 target as [14]: A LU ( φ ) = α ( φ ) = m ( H A ) α ( φ ) + α ( φ ) < e ( H A ) + α ( φ ) (cid:16) < e ( H A ) + = m ( H A ) (cid:17) , (6)where = m ( H A ) and < e ( H A ) are the imaginary and real parts,respectively, of the CFF8 IG. 4: Coefficients presented in Eqs. 7 to 10. Note the prescaling factors used for α , α and α . H A associated with the GPD H A of the spin-0 nucleus. The α i factors are φ -dependentkinematical terms that depend on the nuclear form factor F A and the independent variables Q , x and t . These factors have the following simplified expressions: α ( φ ) = x A (1 + (cid:15) ) y S ++ (1) sin( φ ) (7) α ( φ ) = c BH + c BH cos( φ ) + c BH cos(2 φ ) (8) α ( φ ) = x A (1 + (cid:15) ) y ( C ++ (0) + C ++ (1) cos( φ )) (9) α ( φ ) = x A t (1 + (cid:15) ) y P ( φ ) P ( φ ) · − y + y + (cid:15) y (cid:15) , (10)where S ++ (1), C ++ (0), and C ++ (1) are the Fourier harmonics found in the leptonic tensor[14]. Their explicit expression are provided in Appendix A.Eq. 6 is particularly convenient to perform an extraction of = m ( H A ) and < e ( H A ) througha fit of the BSA as a function of φ . As can be seen in Fig. 4, the form of each α coefficient hasa characteristic φ dependence, such that a fit can easily separate their respective contributions.The only caveat is the large difference of magnitude between the α factors, which can lead torather different error propagation for the two parts of the CFF.An important issue with the use of this theoretical framework is the large mass of thehelium nucleus. Recent work indicates that the effect of this correction is moderate [15],however the applicability to such a large mass remains to be fully explored from the theoreticalpoint of view. 9 (k) e'(k')(q) * g (q') gx x- x x+N(p) N'(p') t = (q-q'), t) x GPDs(x, He X Factorization
FIG. 5: Diagram representing the incoherent nuclear DVCS.
C. Incoherent Nuclear DVCS
The incoherent nuclear DVCS process, is the DVCS off a bound nucleon in a nucleus asrepresented in Fig. 5 for an helium-4 target. The remnants of the nucleus ( X ) contain onlythe missing three nucleons. The theory for incoherent DVCS on the nucleon is largely basedon the free proton theory already reviewed widely in the literature [6, 7, 9]. Two importantdifferences need to be accounted for however: the different initial state and the addition ofFSIs. In the initial state, the intrinsic Fermi motion of the nucleons in the nucleus leads to anuncertainty on the exact kinematics of the reaction. Moreover, in general, the nucleon is inan off-shell state that is not exactly identical to its final state. In the final state, interactionsbetween the outgoing nucleon from the DVCS reaction and the remnants of the nucleartarget are possible. The latter leads to contamination from other channels; in particular,charge exchange processes can lead to a large contribution from such background reactions.Since DVCS is a process selected using tight exclusivity constraints, some of the initialand final-state effects are automatically mitigated. Selection criterion on missing energy andmomentum are performed, constraining the range of initial Fermi motion and FSIs possible.However, no theoretical calculation is available to correct for the reminder of these effects yet.Modern calculations exist for such effects in deep inelastic scattering [16] and quasi-elasticscattering [17], and we can expect them to be extended to the DVCS process as more data10ecome available. Another avenue of progress on this topic will be the use of experimentaltechniques like tagging. This process can help to control both initial and final state effectsby detecting the nuclear remnant. In the tagged process the target breaks in two, thusmeasuring the nuclear remnant provides information about the initial state of the strucknucleon, while a backward fragment also limits significantly the probability of FSIs. III. PAST NUCLEAR DVCS MEASUREMENTS
The first measurement of nuclear DVCS was performed by the HERMES Collaboration [10].This experiment covered an array of nuclear targets and looked at the A dependence of theBSA signal. Their main results, reproduced in Figs. 6 and 7, suffer from large uncertainties,which makes them consistent with the free proton data and prevents us to reach strongconclusions about possible nuclear effects. Yet, in the coherent DVCS case a rather strongeffect was expected, leading to a conflict between the HERMES results and theoreticalexpectations.An issue with the HERMES measurement and how it is obtained from data has beenraised in Ref. [18] to explain the discrepancy with theoretical expectations. The mainconcern is that the DVCS process is not fully detected and the scattered target is insteadreconstructed through a missing mass measurement of the other reaction products. The issuewith this method is that the detector resolution is not good enough to separate the coherentand incoherent channels properly. Instead, the results are labeled "coherent enriched" and"incoherent enriched" at low and high − t , respectively. This label is based on the assumptionthat the very different behavior of the cross sections of the two channels in t will lead to aclear differentiation. However, the results in Fig. 7 show similar behaviors in both sectorsof t , which challenges this assumption and could explain the tension between theory andexperiment.Altogether, large error bars and the failure to properly separate the coherent and incoherentchannels have strongly impaired the interpretation of the measurement and the conclusionsthat can be obtained from it. The CLAS experiment presented here has profited largelyfrom this result and was designed specifically to solve these two issues of low statistics andexclusivity. 11 IG. 6: The sin( φ ) moment of the BSA as a function of − t measured by HERMES for a series ofnuclei [10]. The gray bands represent the systematic uncertainties.FIG. 7: The sin( φ ) moment of the BSA at low and high − t as a function of A measured byHERMES [10]. The inner error bars represent the statistical uncertainty, while the outer representthe quadratic sum of the statistical and systematic uncertainties. V. THE CLAS NUCLEAR DVCS EXPERIMENTAL SETUP
The CLAS nuclear DVCS experiment had as its main objectives to explore coherentDVCS on helium-4, to assess if the predicted BSA increase could be observed, and to extractthe helium-4 GPD. In order to perform this measurement however, several instrumentationchallenges needed to be resolved. First, to measure the scattered electron and the small anglephoton from DVCS, we used CLAS in its DVCS setup, i.e. with the addition of a forwardangle calorimeter and a 5-T solenoid magnet. Second, a radial time projection chamber(RTPC) was installed to measure the helium recoils and thus ensure the exclusivity of theprocess in the coherent channel. In this section, we will review the important elements ofthis detection setup.
A. The CEBAF Large Acceptance Spectrometer (CLAS)
The CLAS [19] spectrometer was installed in Hall B of Jefferson Lab (JLab) continuouselectron beam accelerator facility (CEBAF). This detector was specifically designed tostudy the multi-particles final states that cannot be observed conveniently with multi-arm spectrometers. It was naturally well-suited for measuring DVCS, and several DVCSexperiments were successfully conducted before this experiment using multiple differentconfigurations. CLAS was composed of six identical sectors separated by the coils of atoroidal magnet, with each sector made of four detectors as shown in Fig. 8. Three regions ofdrift chambers [20] were placed between the torus magnet to reconstruct the charged particles’tracks and calculate their momentum. An array of scintillators was placed behind the driftchambers to measure the precise time-of-flight for each track [21]. These detectors coveredthe polar angle from 8 to 142 degrees. In the forward region, from 8 to 45 degrees, thesedetectors were complemented with Cerenkov counters [22] and electromagnetic calorimeters[23], important for electron identification and photon detection.Altogether, CLAS provided a large acceptance for momenta starting at 200 MeV. Thenuclear DVCS experiment took place from October to December 2009 at an electron beamenergy of 6.064 GeV, with the beam intensity varying between 120 and 150 nA. This beam,on the helium-4 target pressurized between 5 and 6 atm, corresponds to luminosities in therange of 1 to 1 . × cm − s − . During the experiment, the data acquisition operated at a13 IG. 8: View of the CLAS detector setup. rate of about 3 kHz with about 70% live-time using an inclusive electron trigger.
B. Adaptations for DVCS
The CLAS Collaboration has established a specific setup to measure the typically smallangle photons of the DVCS process. This setup is composed of an inner calorimeter anda solenoid and has been employed for numerous DVCS measurements on proton targets[24–26].The inner calorimeter, illustrated in Fig. 9, is a homogeneous calorimeter composed of424 lead tungstate (PbWO) crystals read out by 5 × avalanche photo-diodes (APDs).It covers angles from 4 to 15 degrees. However, placing a detector at such small angles makesit particularly sensitive to the low energy Moller electrons scattered from the target. Toprotect the calorimeter from this background, a 5 T solenoid was placed around the targetto form a magnetic shield. Thanks to this field, low energy charged particles (particularlyelectrons) curled around the beamline and never made it to the calorimeter or other CLASdetectors as illustrated by the simulation results presented in Fig. 10. This allows to runmuch higher luminosity experiments, a necessity for low rate processes like DVCS.14 IG. 9: Representation of the inner calorimeter (IC) of CLAS. The crystals that compose thesensitive part of the detector are represented in purple.FIG. 10: Representation of the center of CLAS with the beam background in red with and withoutthe solenoid field activated, right and left, respectively.
C. The Radial Time Projection Chamber
The recoil helium nuclei from coherent DVCS are mostly emitted between 150 and 200MeV at the beam energy of 6 GeV. Therefore, a specific detector was needed to detect them.To design the present setup, inspiration was drawn from the BONUS setup that also used aGEM-based RTPC [27] in CLAS to detect slow protons coming out of a deuterium target [28].In such an RTPC the ionization electrons drift toward large radii rather than toward theendcaps, as is more traditional in time projection chambers. This design allows to reducesignificantly the drift time and reduce the amount of pile-up from accidental events. The15TPC design, its operation, calibration and the track reconstruction have been described inmore details elsewhere [29]. Here a summary of key elements is provided.In order to detect the recoil helium nuclei from a DVCS reaction, we first need to ensurethat it will come out of the target. For this, we used a light straw target made of a thinkapton wall of 27 µ m filled with helium at 6 atm pressure. The entrance and exit windowsare thin aluminum foils and an helium bag was placed downstream of the target to avoidinteraction with air in the gap between the target and the beamline vacuum. The cylindricalchamber surrounds the target as illustrated in Fig. 11. Here we list the elements composingit based on their radii:• Up to a radius of 3 mm the pressurized helium target.• From 3 to 20 mm a keep-out zone filled with 1 atm of helium to minimize the productionof secondaries.• At 20 mm a grounded foil made of 4 µ m aluminized Mylar to isolate the chamber fromthe beamline region and collect charges. It also serves to separate the gas regions.• From 20 to 30 mm a dead zone filled with the drift gas to separate the ground fromthe cathode.• At 30 mm the cathode foil made of 4 µ m aluminized Mylar.• From 30 to 60 mm the drift region filled with the drift gas, a mix of neon and dimethylether (DME) in an 80/20 proportion.• From 60 to 69 mm the amplification regions, filled with drift gas, with GEM foilsplaced at 60, 63 and 66 mm.• At 69 mm the collection pads connected to the preamplifers placed directly outside thechamber.The time-to-position calibration of the detector has been performed with a dependence on z , the position along the beamline axis, due to variations in the magnetic fields. To performthis calibration we took dedicated data at 1.2 GeV beam energy. In this data set, we wereable to select elastic events, for which the kinematics of the helium recoil can be calculatedfrom the electron kinematics and directly compared to the measurement in the RTPC. This16 IG. 11: Cut view of the RTPC. comparison helped to map the correspondence between time and position in the chamberand determine the drift path of electrons. A more detailed description of the calibrationprocess is available in Ref. [29].
V. DVCS EVENT SELECTIONA. Particle Identification
The scattered electrons were detected with the baseline CLAS detectors. The driftchamber measured the kinematics of the electron and the signal measured in both theCerenkov counter and electromagnetic calorimeter provided the identification. A signal ofgood quality was also required in the time-of-flight system, which served as a time referencefor all detectors. Protons were detected with the baseline CLAS detectors as well, the driftchamber measured the kinematics of the proton and the time-of-flight system ensured itsidentification. Several fiducial cuts are applied to ensure that particles did not go throughpart of the inner calorimeter or the solenoid, as well as to reject the edges of the detectors,where their efficiency is rapidly decreasing. Kinematic corrections are also applied to theelectrons and protons to correct for energy loss and biases in calibration, which are at thesubpercent level except for protons below 500 MeV for which they go up to 10% at the17etection limit of 200 MeV.The photons from DVCS are mainly detected with the inner calorimeter. No specificidentification cuts were used in this detector as large energy deposit was dominantly fromelectrons and photons, which could not be separated reliably. However, the detection of anelectron at large angle in CLAS highly suppressed the number of electrons in the calorimeter;moreover, the exclusivity cuts used later in the analysis further this suppression. Left-overaccidentals were accounted for in the background subtraction described below. The innercalorimeter was calibrated through a series of steps, involving the reconstruction of π fromtheir decay into two photons. Calibration was obtained with an iterative process to adjusteach crystal gain to obtain the most accurate π mass. A global calibration of the calorimeterwas also performed to account for incident angle, energy and time dependent effects.The helium-4 nuclei were detected with the RTPC using a series of constraints on thequality of the track reconstruction. As the chamber was operated at low gain and had verylow efficiency for protons, we did not apply further identification cuts for the helium-4 nucleidetection [29].Finally, we selected events that contain a single electron, a high energy photon ( E > Q > . Also, the transferred momentumsquared to the recoil He was bound by a minimum value based on basic energy-momentumconservation: t min = − Q − x A )(1 − √ (cid:15) ) + (cid:15) x A (1 − x A ) + (cid:15) , (11)where (cid:15) = M He x A Q . For incoherent DVCS, we used a similar cut where x A is replaced by x and M He by M p . B. Exclusive Photo-Production Selection
In principle, a selection based only on the missing energy of the system would be enoughto guarantee the exclusivity of the process. However, in our experiment, where particleswere detected at very different energies and with very different detector resolutions, this18ethod was not sufficient. For instance the momentum of the helium nuclei is negligible inthe missing energy observable, thus this valuable information has no impact on a selectionusing this observable only. To address this issue, we constrained the selection of our exclusiveevents by using seven variables selected to optimize the use of all the detector informationavailable. The seven variables are defined as follows for coherent DVCS case (replace heliumby proton for the incoherent case):• Co-planarity (∆ φ ) of the virtual photon, the real photon and the recoil helium;• Missing energy of the complete final state;• Missing mass of the complete final state;• Missing transverse momentum of the complete final state;• Missing mass of the electron-helium system;• Missing mass of the electron-photon system;• Co-linearity ( θ ) of the measured photon with the missing momentum of the electron-helium system.In the analysis, we applied selection cuts based on a fit of the exclusive peak at 3 σ aroundthe mean value for each variable. This systematic method helps to avoid any bias in theselection of the events. The selection of coherent DVCS with these variables is illustrated inFig. 12. We note on these distributions only a few minor anomalies, where the distributionshave some asymmetries. These are linked with the detector resolution, which impact someof the kinematic variables non-linearly. The selection of incoherent DVCS is presented inFig. 13, with two main differences: wider distributions and larger offset from the nominalexpectations. The wider distributions are mainly attributed to the effect of Fermi motion,but simulations have shown that this effect is not strong enough to fully reproduce thedistribution widths and FSIs must play a role as well. The offsets of some distributionsare caused by slight detector misalignment between CLAS sectors and are within the levelsobtained with free proton targets [26] to which they can be directly compared.19 IG. 12: Distributions of the coherent photon production events before (blue) and after (black linefilled in gray) the exclusivity cuts used to select coherent DVCS represented by the red dashed lines.The histograms are shown as a function of the seven variables used for the exclusivity selectiondescribed in the text, plus the missing P x and P y components, in order left to right and top tobottom. C. Background Subtraction
The main signal contamination comes from the exclusive production of a π , the finalstate of which is very similar to DVCS with only an extra photon. In such an event, ifone of the photons is produced at low energy, it is easy to confuse this process with singlephoton production. In order to estimate the contribution from this channel in the data, wemeasured the exclusive π production in the same way as DVCS, with a series of exclusivitycuts, completed by a selection cut on the invariant mass of the two photons to match the π mass. The events obtained for the coherent and incoherent channels are shown in Figs. 1420 IG. 13: Distributions of the incoherent photon production events before (blue) and after (black linefilled in gray) the exclusivity cuts used to select coherent DVCS represented by the red dashed lines.The histograms are shown as a function of the seven variables used for the exclusivity selectiondescribed in the text, plus the missing P x and P y components, in order left to right and top tobottom. and 15, respectively. Using this sample, we developed an event generator and adjusted itto the data. The result of which is shown with the red histograms of Figs. 14 and 15. Tocorrect the experimental data, we then estimated the number of single photon events comingfrom the exclusive π production as: N Exp γ,π = N Sim γ,π N Sim γ,π × N Exp γ,π , (12)where N Sim γ,π is the number of simulated exclusive π mistaken for DVCS events, N Sim γ,π thenumber of simulated exclusive π fully reconstructed and N Exp γ,π the number of experimentally21easured exclusive π . This number was then subtracted from the experimentally measurednumber of DVCS events ( N ExpDV CS ) to get the corrected result: N CorrDV CS = N ExpDV CS − N Exp γ,π . (13)We show in Fig. 16 the π contamination for the − t bins, where it varies the most fromone bin to another. The study shows 2 to 4% contamination in the coherent channel and 3 to17% in the incoherent channel. After subtracting this contamination from the denominatorof the asymmetry, we make no further correction to the DVCS BSA, i.e ., we assume theexclusive π production has no such asymmetry in either the coherent or incoherent channels.Our own exclusive π data rules out any BSA above approximately 10%, a level which wouldhave an insignificant effect on our results given the small amount of contamination.The second important source of background comes from accidentals. Despite the manyexclusivity cuts, it is possible to have particles from different events being combined andpass all the cuts to get into the data sample. To evaluate the number of such events, weinverted the vertex selection of the two charged particles of the process, electron and helium(or proton in the incoherent case), and requested that they are separate. We found that 4.1%of the coherent and 6.5% of the incoherent samples were accidentals, they are also subtractedfrom the denominator of the asymmetry. D. Systematic Uncertainties
To further evaluate the systematic uncertainty of the measurements, we performed severalspecialized studies. We evaluated the impact of changing the exclusivity selection cuts byvarying them from 1 to 5 σ . We also evaluated the impact of changing the binning in φ on the extraction of the BSA at 90°. The beam polarization was measured using Møllerscattering runs, the uncertainty was estimated based on the known precision of the dedicatedapparatus and the spread of the measurements during the complete run period. We studiedhow different methods of simulating the exclusive π production affected the single-photonbackground and further estimated how much bias could arise from an undetected BSA in theprocess. As radiative corrections are expected to be small for this process, we did not applythem, but associated an uncertainty equal to their expected value. These uncertainties are22 IG. 14: The measured (filled blue) and simulated (red) distributions of coherent exclusive π production as a function of x , Q , − t and φ .FIG. 15: The measured (filled blue) and simulated (red) distributions of incoherent exclusive π production as a function of x , Q , − t and φ . /c -t [GeV ] /c -t [GeV FIG. 16: The estimated coherent (left) and incoherent (right) π contamination fraction in the DVCSevents as a function of the transferred momentum squared - t and integrated over the kinematicvariables Q , x B , and φ . Systematic source Coherentchannel Incoherentchannel Type ofsystematic error
Beam polarization 3.5% 3.5% NormalizationDVCS cuts 8 % 6 % Bin to binData binning 5.1% 7.1% Bin to bin π subtraction 0.6% 2.0% Bin to binRadiative corrections 0.1% 0.1% Bin to bin Total bin to bin 10.1 % % Bin to bin TABLE I: The systematic uncertainties on the measured coherent and incoherent BSAs at φ = 90 ◦ . summarized in Tab. I, with their respective evaluated values. They are added quadraticallyto obtain the total systematic uncertainty presented in the results.An extra problem that was studied is the best way to define t in the incoherent channel,which is not completely straightforward. As can be seen in Fig. 5, we can either use t or t (= ( p − p ) ). In principle, the two are identical, but experimentally we face some issues. Themeasurement of t is less precise than t because it involves the photon rather than chargedparticles. However, the exact measurement of t is impossible and one needs to assume aproton at rest in the initial state to calculate t . As it is not obvious which solution is best,we studied the difference between the two results by analyzing the data independently usingthe two definitions. We found no significant difference between them, as is illustrated in Fig.17. We use in the final results t as it is based on the rigorous definition. Since the effect ofresolution appears small and is partly accounted for in the systematic uncertainty associatedto the DVCS cuts, we decided not to associate an extra systematic uncertainty based on this24 ] [GeV Q ) (cid:176) ( I n c o h L U A t definitiont' definition B x ) (cid:176) ( I n c o h L U A ] -t [GeV ) (cid:176) ( I n c o h L U A FIG. 17: The BSA at 90° ( A IncohLU (90 ◦ )) as a function of Q , x B and − t , using the photon based t definition (red) and the proton based t definition (black). study. VI. RESULTSA. Coherent DVCS
In Fig. 18, we present the results for the BSA in the coherent DVCS channel. We observethe dominant sinusoidal component typical of the DVCS BSA, with an amplitude almostdouble that measured for the free proton [25]. This predicted feature of nuclear DVCS [18]is observed here for the first time, due to the fact that this measurement cleanly isolatesthe coherent DVCS process. The absence of this feature in the previous measurement byHERMES [10] and its clear observation here indicates that the recoil detection is necessaryto isolate the effects of the coherent DVCS process from the incoherent background.We show the extraction of the BSA at 90° in Fig. 19 together with the past HERMESCollaboration results [10]. Two models are compared to the data, they are both based onthe hypothesis that the main nuclear effects are included by accounting for the nucleon off-shellness and the kinematics of nucleons in nuclei. The one by Liuti et al. [30, 31] appears toundershoot the results systematically. However, the more recent and independent calculationby Fucini et al. [32], using similar principles but with a non-diagonal nuclear spectral function[33] based on the AV18 nucleon-nucleon potential [34] and the UIV three-body forces [35],has been able to reproduce the data very well. A factor in the difference is that the recentcalculation by Fucini et al. [32] benefited from using the precise kinematics of each of the25oints presented in Appendix B. Including this information appears to have a significantimpact on some points, for instance the − t distribution appears to have a peculiar structurethat is well reproduced when using this information.One of the motivations for the choice of helium-4 for the coherent DVCS measurement wasa simplified extraction of the CFF H A from the data. To perform this step, we used the formfrom Eq. 6 to fit the data in Fig. 18. We present in Fig. 20 the extracted real and imaginaryparts of the single CFF of the helium-4 nucleus. The results are rather encouraging. The twoparts of the CFF are constrained by data without the need for any model assumption. Thiscapacity to obtain a model independent result with such a limited data set offers a strikingcontrast with the situation of the free proton fits [36, 37].The CFF extraction allows us to compare the results to other theoretical calculations.These are performed within the impulse approximation [18, 38] and give the nuclear GPDdirectly from the proton and neutron GPDs. In Fig. 20, we show two versions of this [deg.] f - - - H e L U A / ndf c c c c = 1.143 GeV Q [deg.] f - - - H e L U A / ndf c c c c = 0.132 B x [deg.] f - - - H e L U A / ndf c c c c -t= 0.08 GeV f - - - / ndf c c c c = 1.423 GeV Q f - - - / ndf c c c c = 0.170 B x [deg.] f - - - / ndf c c c c -t= 0.094 GeV [deg.] f - - - / ndf c c c c = 1.902 GeV Q f - - - / ndf c c c c = 0.225 B x [deg.] f - - - / ndf c c c c -t= 0.127 GeV FIG. 18: The BSA in the coherent exclusive photo-production off helium-4 as a function of φ and Q (top panels), x (middle panels) and − t (lower panels). The error bars are statistical and thegray bands represent the systematic uncertainties. The full red lines show the fit of the data withthe form of Eq. 6. ] [GeV Q ) (cid:176) ( H e L U A CLAS (this work)HERMES [10] B x ] -t [GeV FIG. 19: The BSA at 90° as a function of Q (top panel), x (middle panel) and − t (lower panel).Our results are shown with black squares, HERMES results with green circles [10]. The theoreticalprediction by Liuti et al. [30, 31] is shown by the full blue line, while the calculation by Fucini etal. [32] is shown with the magenta dashed line. ] [GeV Q ) A ( H ` ] [GeV Q - - ) A ( H ´ B x B x - - ] -t [GeV CLAS (this work)Guzey et al. [18,38] ] -t [GeV - - Guzey et al. (VGG)Liuti et al. [30,31]
FIG. 20: The imaginary (top panels) and real (bottom panels) parts of the helium-4 CFF H A asa function of Q (left panels), x (middle panels) and − t (right panels). The red full line is thetheoretical calculation by Guzey et al. [18, 38], the black dashed line is the same calculation usingthe VGG model as input [39, 40], and the blue long dashed line shows the predictions by Liuti etal. [30, 31]. calculation, where two different nucleon GPD models are used as input, compared with thecalculation previously shown by Liuti et al. [30] with an updated nucleon model [31]. Wecan see that the effect of changing the input nucleon GPD model is of similar size or largerthan the difference between the nuclear models. However, at the level of precision of thepresent data, it is not possible to resolve which variant is best. This feature highlights the27mportance of the choice of nucleon model to study nuclear effects with this data.In summary, this measurement of the BSA in the deeply virtual coherent exclusive photo-production on a nucleus is the first to clearly isolate the effect of coherent nuclear DVCSand of nuclear GPDs. While the statistical precision and the kinematic coverage are stillbehind the experimental results of the proton, the results appear to match very well thepredictions using the GPD framework. Moreover, the extraction of the CFF appears to bevery convenient based on the BSA measurement only. Together, these findings validate therelevance of coherent nuclear DVCS to study the nucleus globally in terms of quarks andgluons. [deg.] f - - - I n c o h L U A / ndf c c c c = 1.40 GeV Q [deg.] f - - - I n c o h L U A / ndf c c c c = 0.16 B x [deg.] f - - - I n c o h L U A / ndf c c c c -t= 0.14 GeV [deg.] f - - - / ndf c c c c = 1.89 GeV Q [deg.] f - - - / ndf c c c c = 0.23 B x [deg.] f - - - / ndf c c c c -t= 0.28 GeV [deg.] f - - - / ndf c c c c = 2.34 GeV Q [deg.] f - - - / ndf c c c c = 0.29 B x [deg.] f - - - / ndf c c c c -t= 0.49 GeV [deg.] f - - - / ndf c c c c = 3.09 GeV Q [deg.] f - - - / ndf c c c c = 0.39 B x [deg.] f - - - / ndf c c c c -t= 1.08 GeV FIG. 21: The BSA in the incoherent exclusive photo-production off a proton bound in helium-4 asa function of φ and Q (top panels), x (middle panels) and − t (lower panels). The error bars arestatistical and the gray bands represent the systematic uncertainties. The data is fitted with theform α sin( φ )1+ β cos( φ ) ; the results of the fits are drawn with black full lines. . Incoherent DVCS The results for the measurement of the BSA in the incoherent DVCS channel are presentedin Fig. 21. They display patterns rather similar to those observed with the free proton, witha clear domination of their sinusoidal component. To compare the data to models, we extractthe BSA at 90° with a fit of the form α sin( φ )1+ β cos( φ ) .The asymmetries at 90° are presented in Fig. 22 together with the theoretical calculationby the same groups as presented in Fig. 19. We observe a significant improvement onthe precision compared to the HERMES data, which offers more constraint on the modelspresented. As in the coherent case, the calculation appears to have issues reproducing theshape of the data, with Fucini et al. [41] doing better than the others. However, this timethe calculations overshoot the data, sometimes by a significant amount.An interesting way to look into this data is to show the result on incoherent nuclear DVCScompared with the free proton one. We can for instance make a ratio, in a fashion similarto the EMC effect, which allows to cancel out the effects from the nucleon structure andhighlight nuclear effects. Such a ratio is presented in Fig. 23. Notably, the calculation byFucini et al. [41] appears closer than the others with this observable. This feature indicatesthat the different raw asymmetry results might be linked to the different input model usedfor the free nucleon GPD rather than to differences in the treatment of the nuclear effects.Also, Fucini et al. appear to roughly reproduce the shape of the x B distribution, which mightindicate that it is linked to correlations between kinematic variables. In conclusion, the BSAin the incoherent DVCS channel is suppressed by 20 to 30% compared to the free proton,which was not expected by most models.The explanation for this surprising behavior can come from different sources both in theinitial state and in the final state. Further work is needed to fully comprehend this newlydiscovered nuclear effect. On the experimental side, the use of tagging methods, where thenuclear fragments are measured appear to offer the best option forward. Indeed, taggingoffers the best chance to understand better this result by offering better control over boththe initial and the final state effects [2]. 29 ] [GeV Q - ) (cid:176) ( I n c oh L U A ] -t [GeV ) (cid:176) ( I n c oh L U A CLAS (This work)HERMES [10]Liuti et al. [30,31]Fucini et al. [41] B x ) (cid:176) ( I n c oh L U A FIG. 22: The BSA at 90° as a function of Q (top left), x (top right) and − t (bottom). Ourmeasurement is represented with black squares and the HERMES measurement [10] with greencircles. The theoretical prediction by Liuti et al. [30, 31] is shown by the full blue line, while thecalculation by Fucini et al. [41] is shown with the magenta dashed line. VII. SUMMARY
We report the measurement of the coherent and incoherent DVCS processes off helium-4with CLAS at JLab. To properly isolate the coherent channel, the experiment used aspecially designed RTPC to detect the scattered helium-4. This coherent DVCS measurementreveals the large BSA ( ∼ ] [GeV Q ) (cid:176) ( p L U / A I n c o h L U A CLAS (This work) Liuti et al. [30,31]HERMES [10] Guzey et al. [38]Fucini et al. [41] ] -t [GeV ) (cid:176) ( p L U / A I n c oh L U A B x ) (cid:176) ( p L U / A I n c oh L U A FIG. 23: DVCS BSA ratio of the bound proton to the free proton as a function of Q (top left), x (top right) and − t (bottom). The present measurement is represented with black squares and theHERMES measurement [10] with green circles. The theoretical prediction by Liuti et al. [30, 31] isshown by the full blue line, the calculation by Fucini et al. [41] is shown with the magenta dashedline, and the black dot-dashed line is the calculation by Guzey et al. [38]. tagging at the upgraded CLAS12 detector with 11 GeV electron beam is planned to addressthis question in the coming years by using a new recoil detector design [42]. VIII. ACKNOWLEDGMENTS
The authors acknowledge the staff of the Accelerator and Physics Divisions at the ThomasJefferson National Accelerator Facility who made this experiment possible. This work wassupported in part by the Chilean Comisión Nacional de Investigación Científica y Tecnológica(CONICYT), by CONICYT PIA grant ACT1413, the Italian Instituto Nazionale di FisicaNucleare, the French Centre National de la Recherche Scientifique, the French Commissariatà l’Energie Atomique, the U.S. Department of Energy under Contract No. DE-AC02-06CH11357, the United Kingdom Science and Technology Facilities Council (STFC), theScottish Universities Physics Alliance (SUPA), the National Research Foundation of Korea,31nd the Office of Research and Economic Development at Mississippi State University.M. Hattawy also acknowledges the support of the Consulat Général de France à Jérusalem.This work has received funding from the European Research Council (ERC) under theEuropean Union’s Horizon 2020 research and innovation programme (Grant agreement No.804480). The Southeastern Universities Research Association operates the Thomas JeffersonNational Accelerator Facility for the United States Department of Energy under ContractNo. DE-AC05-06OR23177. [1] M. Anselmino, M. Guidal, P. Rossi, et al. Topical issue on the 3-D structure of the nucleon.
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A proposal to PAC 45 , 2017. ppendix A: Expressions for the BSA of the Coherent DVCS We present in this appendix the detailed expressions used for Eq. 5 and Eqs. 7 to 10.These are adapted from the work of Kirchner and Müller [13] to match the notations andconventions used in this work.First, P ( φ ) and P ( φ ) are BH propagators and defined as: P ( φ ) = ( k − q ) Q = − y (1 + (cid:15) ) h J + 2 K cos( φ ) i (A1) P ( φ ) = ( k − ∆) Q = 1 + tQ + 1 y (1 + (cid:15) ) h J + 2 K cos( φ ) i (A2)with, J = − y − y(cid:15) ! tQ ! − (1 − x A )(2 − y ) tQ (A3) K = − δt (1 − x A ) − y − y (cid:15) !( √ (cid:15) + 4 x A (1 − x A ) + (cid:15) − x A ) δt ) (A4) δt = t − t min Q = tQ + 2(1 − x A ) (cid:16) − √ (cid:15) (cid:17) + (cid:15) x A (1 − x A ) + (cid:15) . (A5)The Fourier coefficients for BH contributions are defined as: c BH = " n (2 − y ) + y (1 + (cid:15) ) o ( (cid:15) Q t + 4(1 − x A ) + (4 x A + (cid:15) ) tQ ) +2 (cid:15) n − y )(3 + 2 (cid:15) ) + y (2 − (cid:15) ) o − x A (2 − y ) (2 + (cid:15) ) tQ +8 K (cid:15) Q t F A ( t ) (A6) c BH = − − y ) K ( x A + (cid:15) − (cid:15) Q t ) F A ( t ) (A7) c BH = 8 K (cid:15) Q t F A ( t ) , (A8)where F A ( t ) is the electromagnetic form factor of He. The coefficient for the DVCScontribution is given by: c DV CS = 2 2 − y + y + (cid:15) y (cid:15) H A H ?A . (A9)35inally, the interference amplitude coefficients are written as: s INT = F A ( t ) = m ( H A ) S ++ (1) , (A10)with S ++ (1) = − K (2 − y ) y (cid:15) − x A + √ (cid:15) − (cid:15) t − t min Q (A11) c INT = F A ( t ) < e ( H A ) C ++ (0) , (A12)with C ++ (0) = − − y )(1 + √ (cid:15) )(1 + (cid:15) ) ( f K Q (2 − y ) √ (cid:15) (A13)+ tQ − y − (cid:15) y ! (2 − x A ) x A (2 − x A + √ (cid:15) − + (cid:15) x A ) tQ + (cid:15) (2 − x A )(1 + √ (cid:15) ) ) c INT = F A ( t ) < e ( H A ) C ++ (1) , (A14)with C ++ (1) = − K (1 − y + (cid:15) y )(1 + (cid:15) ) / ( − x A ) √ (cid:15) − x A + (cid:15) x A ! x A tQ − (cid:15) . ) − K − y + y + (cid:15) y ! √ (cid:15) − (cid:15) (1 + e / ( − (1 − x A ) tQ + 1 − √ (cid:15) + 3 (cid:15) √ (cid:15) − (cid:15) x A tQ ) . (A15) Appendix B: Tables of Results with Kinematics Information Q i h x B i h− t i h φ i A LU ± stat. ± syst.(GeV ) (GeV ) (degree)24 0.133 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± TABLE II: Values of the coherent A LU in Q bins from Fig. 18. Q i h x B i h− t i h φ i A LU ± stat. ± syst.(GeV ) (GeV ) (degree)26 0.017 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± TABLE III: Values of the coherent A LU in x B bins from Fig. 18. Q i h x B i h− t i h φ i A LU ± stat. ± syst.(GeV ) (GeV ) (degree)23 0.238 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± TABLE IV: Values of the coherent A LU in − t bins from Fig. 18. Q i h x B i h− t i h φ i A LU ± stat. ± syst.(GeV ) (GeV ) (degree)21 0.054 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± TABLE V: Values of the incoherent A LU in Q bins from Fig. 21. Q i h x B i h− t i h φ i A LU ± stat. ± syst.(GeV ) (GeV ) (degree)21 0.094 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± TABLE VI: Values of the incoherent A LU in x B bins from Fig. 21. Q i h x B i h− t i h φ i A LU ± stat. ± syst.(GeV ) (GeV ) (degree)22 0.120 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± TABLE VII: Values of the incoherent A LU in − t bins from Fig. 21. Q i h x B i h− t i A LU (90 ◦ ) ± stat. ± syst.(GeV ) (GeV )1.14 0.136 0.096 0.304 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± TABLE VIII: Values of the coherent A LU (90 ◦ ) in Q (top block), x B (middle block), and − t (bottomblock) bins. h Q i h x B i h− t i A LU (90 ◦ ) ± stat. ± syst.(GeV ) (GeV )1.40 0.166 0.376 0.137 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± TABLE IX: Values of the incoherent A LU (90 ◦ ) in Q (top block), x B (middle block), and − t (bottom block) bins.(bottom block) bins.