Measurement of the Charge-Averaged Elastic Lepton-Proton Scattering Cross Sectionby the OLYMPUS Experiment
J. C. Bernauer, A. Schmidt, B. S. Henderson, L. D. Ice, D. Khaneft, C. O'Connor, R. Russell, N. Akopov, R. Alarcon, O. Ates, A. Avetisyan, R. Beck, S. Belostotski, J. Bessuille, F. Brinker, J. R. Calarco, V. Carassiti, E. Cisbani, G. Ciullo, M. Contalbrigo, R. De Leo, J. Diefenbach, T. W. Donnelly, K. Dow, G. Elbakian, P. D. Eversheim, S. Frullani, Ch. Funke, G. Gavrilov, B. Gläser, N. Görrissen, D. K. Hasell, J. Hauschildt, Ph. Hoffmeister, Y. Holler, E. Ihloff, A. Izotov, R. Kaiser, G. Karyan, J. Kelsey, A. Kiselev, P. Klassen, A. Krivshich, M. Kohl, I. Lehmann, P. Lenisa, D. Lenz, S. Lumsden, Y. Ma, F. Maas, H. Marukyan, O. Miklukho, R. G. Milner, A. Movsisyan, M. Murray, Y. Naryshkin, R. Perez Benito, R. Perrino, R. P. Redwine, D. Rodríguez Piñeiro, G. Rosner, U. Schneekloth, B. Seitz, M. Statera, A. Thiel, H. Vardanyan, D. Veretennikov, C. Vidal, A. Winnebeck, V. Yeganov
OOLYMPUS: First measurement of the charge-averaged elastic lepton-protonscattering cross section
J. C. Bernauer, ∗ A. Schmidt, † B. S. Henderson, L.D. Ice, D. Khaneft, C. O’Connor, R. Russell, N. Akopov, R. Alarcon, O. Ates, A. Avetisyan, R. Beck, S. Belostotski, ‡ J. Bessuille, F. Brinker, J. R. Calarco, V. Carassiti, E. Cisbani, G. Ciullo, M. Contalbrigo, R. De Leo, J. Diefenbach, T. W. Donnelly, K. Dow, G. Elbakian, P. D. Eversheim, S. Frullani, ‡ Ch. Funke, G. Gavrilov, B. Gl¨aser, N. G¨orrissen, D. K. Hasell, J. Hauschildt, Ph. Hoffmeister, Y. Holler, E. Ihloff, A. Izotov, R. Kaiser, G. Karyan, J. Kelsey, A. Kiselev, P. Klassen, A. Krivshich, M. Kohl, § I. Lehmann, P. Lenisa, D. Lenz, S. Lumsden, Y. Ma, F. Maas, H. Marukyan, O. Miklukho, R. G. Milner, A. Movsisyan,
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M. Murray, Y. Naryshkin, R. Perez Benito, R. Perrino, R. P. Redwine, D. Rodr´ıguez Pi˜neiro, G. Rosner, U. Schneekloth, B. Seitz, M. Statera, A. Thiel, H. Vardanyan, D. Veretennikov, C. Vidal, A. Winnebeck, and V. Yeganov (The OLYMPUS Collaboration) Massachusetts Institute of Technology, Cambridge, MA 02139, USA Arizona State University, Tempe, AZ 85281, USA Johannes Gutenberg-Universit¨at, Mainz, Germany Alikhanyan National Science Laboratory (Yerevan Physics Institute), Yerevan, Armenia Hampton University, Hampton, VA 23668, USA Rheinische Friedrich-Wilhelms-Universit¨at, Bonn, Germany Petersburg Nuclear Physics Institute, Gatchina, Russia Deutsches Elektronen-Synchrotron, Hamburg, Germany University of New Hampshire, Durham, NH 03824, USA Universit`a degli Studi di Ferrara and Istituto Nazionale di Fisica Nucleare sezione di Ferrara, Ferrara, Italy Istituto Nazionale di Fisica Nucleare sezione di Roma and Istituto Superiore di Sanit`a, Rome, Italy Istituto Nazionale di Fisica Nucleare sezione di Bari, Bari, Italy University of Glasgow, Glasgow, United Kingdom (Dated: August 13, 2020)We report the first measurement of the average of the electron-proton and positron-proton elasticscattering cross sections. This lepton charge-averaged cross section is insensitive to the leadingeffects of hard two-photon exchange, giving more robust access to the proton’s electromagneticform factors. The cross section was extracted from data taken by the OLYMPUS experiment atDESY, in which alternating stored electron and positron beams were scattered from a windowlessgaseous hydrogen target. Elastic scattering events were identified from the coincident detection ofthe scattered lepton and recoil proton in a large-acceptance toroidal spectrometer. The luminositywas determined from the rates of Møller, Bhabha and elastic scattering in forward electromagneticcalorimeters. The data provide some selectivity between existing form factor global fits and willprovide valuable constraints to future fits.
Precise determination of the proton form factors is crit-ical for the understanding of the proton internal dynam-ics, giving direct access to the distribution of charge andmagnetization in the nucleon. They are touchstones forthe verification of theoretical descriptions and computa-tional approaches. For large Q , the progress in precisionmeasurements is hampered by the unresolved discrep-ancy between measurements of the proton’s elastic formfactor ratio, µ p G pE /G pM , using polarization techniques [1–8], and those obtained using the traditional Rosenbluthtechnique in unpolarized cross section measurements [9–14].One hypothesis for the cause of this discrepancy is acontribution to the cross section from hard two-photonexchange (TPE), which is not included in standard ra-diative corrections and would affect the two measurement techniques differently [15–20].Standard radiative correction prescriptions account fortwo-photon exchange only in the soft limit, in which onephoton carries negligible momentum [21, 22]. There is nomodel-independent formalism for calculating hard TPE.Some model-dependent calculations suggest that TPE isresponsible for the form factor discrepancy [17–20] whileothers contradict that finding [23, 24]. The current statusof the recent experimental and theoretical progress ontwo-photon exchange is summarized in Ref. [25].While most models predict negligible effects of hardtwo-photon exchange on measurements using polariza-tion, such measurements can only extract the form fac-tor ratio. A separation of G E and G M requires absolutemeasurements of the lepton-proton cross section, whichare affected by hard TPE. To leading order, TPE effects a r X i v : . [ nu c l - e x ] A ug depend on the charge sign of the lepton. Therefore, acharge-averaged cross section is far less sensitive to TPE.We report here on the first precision determination of acharge-averaged cross section of e ± − p scattering.OLYMPUS’s main goal was to measure the ratio ofthe cross sections for positron-proton and electron-protonscattering, a quantity which gives direct access to thetwo-photon exchange correction. OLYMPUS was opti-mized for this purpose, and the results were publishedin Ref. [26]. However, careful further analysis allowed usto extract charge-averaged cross sections. They cover aninteresting kinematical region, where existing form fac-tor fits show a turn-over behavior for G M , and where theexisting data for e − − p scattering are somewhat lacking,leading to large model uncertainties.Only a brief overview of the OLYMPUS experiment isgiven here, and we refer to [27] for a detailed descriptionof the detector. OLYMPUS was the last experiment totake data at the DORIS electron/positron storage ringat DESY, Hamburg, Germany. In total, an integratedluminosity of 4 . − was collected. The 2.01 GeV storedbeams with up to 65 mA of current passed through aninternal, unpolarized hydrogen gas target with an arealdensity of approximately 3 × atoms/cm [28]. Theaccelerator magnet power supplies were modified to allowthe daily change of beam species.The main detector, a toroidal magnetic spectrome-ter, was based on the former MIT-Bates BLAST detec-tor [29], with the two horizontal sections instrumentedwith large acceptance (20 ◦ < θ < ◦ , − ◦ < φ < ◦ )drift chambers (DC) for 3D particle tracking and wallsof time-of-flight scintillator bars (ToF) for triggering andparticle identification. The left-right symmetry of thedetector system was used as a cross-check in the anal-ysis. The data presented here were collected entirelywith positive-tracks-outbending toroid polarity in orderto suppress background rates in the DC, so that low-energy electrons were bent back to the beam axis andaway from the detectors.Two new detector systems were designed and builtto monitor the luminosity. These were symmetricMøller/Bhabha calorimeters (SYMB) at 1 . ◦ [30] andtwo telescopes of three triple gas electron multiplier(GEM) detectors [31] interleaved with three multi-wireproportional chambers (MWPC) mounted at 12 ◦ .The trigger system selected candidate events that re-sulted from a lepton and proton detected in coincidencein opposite sectors. The data were acquired and storedvia the CBELSA/TAPS data acquisition system [32].The positions of all detector elements were determinedvia optical surveys and the magnetic field was mappedin-situ throughout the complete tracking volume [33].Acceptances, radiative corrections and efficiencies wereaccounted for via a sophisticated Monte Carlo (MC) sim-ulation, which matched the measured time-dependenceof the beam current and position, rigorously treating the correlations between effects. The MC simulationused a radiative event generator developed specificallyfor OLYMPUS [34, 35]. This generator produced lepton-proton events weighted by several different radiative crosssection models. In this letter, we present the results fol-lowing the Maximon-Tjon [22] prescription. Higher orderradiative corrections are taken into account through ex-ponentiation.Particle trajectories and energy losses were simulatedusing Geant4, with custom digitization routines to pro-duce output identical in format to actual measured data.This step included efficiency and resolution simulationswhose parameters were determined from data. Both thesimulated and the real data were then analyzed with iden-tical software.Track reconstruction used a fast hierarchical patternmatching algorithm to identify track candidates. Initialtrack parameters were then determined via two distincttrack fit algorithms.Particle identification was achieved by a combina-tion of track curvature direction, indicating the parti-cle charge, and the correlation between momentum andtime-of-flight to cleanly separate positrons from protons.The efficiency of the drift chambers was determinedby performing track reconstruction without consideringone of the drift chamber super-layers and then consid-ering whether or not hits were present in the ignoredsuper-layer. This technique was used to develop highlygranular efficiency maps of each drift cell. These mapswere used directly in the detector simulation. While themajority of the drift cells had efficiency > Q . Background remaining after selection cuts was sub-tracted and the statistical uncertainty associated withthis subtraction was propagated to the final result. Be-cause their event selection cuts differed in tightness, thefour analyses varied in the amount of background theysubtracted, ranging between 5–20% for the highest Q bin. Fig. 1 shows an example of the background fit inone analysis for one of the highest Q bins. − ◦ − ◦ − ◦ ◦ ◦ ◦ ◦ e − -left/protons-right . < Q < . GeV /c C o un t s φ R − φ L − ◦ FIG. 1. Background was estimated and subtracted inRef. [35] using fits to the sidebands of the distribution of thedifference in azimuth of lepton ( φ L ) and proton ( φ R ) trackpairs after all other elastic event selection criteria were ap-plied. The background was largest at high Q , as shown here,with little difference between e − and e + modes. The total recorded data were screened for optimal run-ning conditions, and a subset corresponding to 3 . − of integrated luminosity was selected for the results pre-sented here.OLYMPUS was optimized for a measurement of thecross section ratio between the two beam species, andtherefore it employed three independent systems to deter-mine relative luminosity: from the elastic rate in the two12 ◦ telescopes, the Møller/Bhabha rate in the SYMB,and from the beam current and target density recordedby the slow control system. For an absolute measurementof the luminosity, none of the systems is optimal: • Fundamentally, the 12 ◦ telescopes measure thesame process as the main spectrometer and cantherefore not give an absolute measurement. Itcould however extend the Q range of the measure-ment, so that a different determination of the cross section at this smaller value, (for example, froma fit) would give the normalization and then anquasi-absolute cross section for the remaining datapoints. However, the 12 ◦ telescope acceptance andabsolute efficiency is not known well enough to pro-duce a sensible result. The data point is thereforecompletely omitted here. • The slow control system could, in principle, givean absolute normalization. However, uncertaintiesfrom the target temperature, which affects the den-sity, as well as the absolute calibration of the beamcurrent could not be quantified with a reliable errorestimate. • The most robust SYMB analysis made use of multi-interaction events, in which a symmetric Møller orBhabha event occurred in the same bunch as anunrelated forward-scattering elastic ep event. Thismethod takes advantage of the cancellation of manysystematic effects when determining the relative lu-minosity between beam species. However, theseeffects do not cancel in the determination of theabsolute luminosity, resulting in an uncertainty of7%. This method is used for normalizing the crosssections reported in this work.We note that the results of the SYMB and slow controldiffer only by about 1%.We report the cross section determined from the av-erage of the results of the four independent analyses.We further use the variance between the analyses to es-timate some of the systematic uncertainties. To sepa-rate point-to-point and normalization uncertainties, wefit normalization constants to the results of each of thefour analyses, and minimize the difference to the average.We use the remaining variance to estimate the point-to-point systematic uncertainty from event-selection bias,with the variation between constants used to assess thecontribution to the normalization uncertainty (1.5%).The systematic difference between cross sections deter-mined from the lepton-left/proton-right versus proton-right/lepton-left topologies is used to assess the system-atic uncertainty from mis-modeling of the detector accep-tance (0.7%). In total, we achieve a global normalizationuncertainty of 7.5%, dominated by the luminosity uncer-tainty. Table I gives an overview.The OLYMPUS determination of the charge-averagecross section, as a function of (cid:15) and Q is provided in Ta-ble II. A comparison of our results with a selection of fitsis shown in Fig. 2. The fits presented here use differentmethods to minimize the influence of TPE on the ex-tracted form factors. All use both Rosenbluth as well aspolarized data in their fits, and assume that the influenceof TPE on the ratio extracted from polarized data is min-imal. Kelly [41] omits G E results for Q > /c ) and relies on ratio determinations from polarized exper- TABLE I. Contributions to the systematic uncertainty in theglobal normalizationSource Uncertainty in the normalizationLuminosity 7.0%Efficiency 2.0%Event Selection 1.5%Track Reconstruction 1.0%Detector Acceptance 0.7%Live-time Correction 0.5%Total 7.5% . . . . . . .
25 0 0 . . . σ e + + σ e − / σ d i p o l e Q [GeV /c ] BernauerKellyArrington 03Arrington 07OLYMPUS FIG. 2. The data for the charge-average cross section as afunction of Q , in comparison with a series of predictions fromform factor fits [28, 38, 39]. The Bernauer [40] prediction isshown with statistical (inner band) and model dependencysystematical error (added linear to statistical error, outerband). As can be deduced from the width of the bands andthe differences between the models, prior data do not stronglyconstrain models in the range of 0 . < Q < . /c ; thiswork can provide some remedy. iments and G M values extracted from e − − p scattering,but does not correct them for hard TPE effects. Whilethe effect of TPE on the extraction is small comparedto the effect on G E at these Q , it is not clear a priori how large the effect is, and how the uncorrected dataat smaller Q affect the high- Q behavior. Arrington 03[42] uses a phenomenological correction to the cross sec-tions with a linear dependence in (cid:15) and fixed scale of 6%.Arrington 07 [39] uses theoretical TPE calculations andcomplements them for data points > /c ) withan ad-hoc additional effect, linear in (cid:15) and with a scalewith logarithmic dependence. Bernauer [28] uses a two-parameter phenomenological model, a combination of theFeshbach correction, valid at Q = 0, and a linear modelwith logarithmic scaling in Q , applied to data at all Q ,fitting form factor parameters and TPE parameters to-gether.The data presented here connect the well-constrainedregion below 1 (GeV /c ) with the region between 1 and 2 (GeV /c ) where TPE effects are more prominent. Thefit by Bernauer preferred a strong cusp-like structure in G M around 1.3 (GeV /c ) , while the other, less flexible,fits, have a smoother transition. The data seem to bein better agreement with the latter, but a more detailedstudy of the effects of the new data set on form factorfits must follow. − . − . − . . . A pp r o x i m a t e RC ( σ M C / σ B o r n - ) Q [GeV/ c ] e − only e + only e − + e + FIG. 3. The approximate radiative correction, estimatedby taking the ratio of the simulated cross sections with andwithout the inclusion of radiative effects. The charge-oddcontribution is a sizeable fraction of the total at high Q . The advantage of the charge-averaging technique is il-lustrated in Fig. 3, which shows the approximate radia-tive correction for the e − , e + , and charge-averaged crosssections, as a function Q . These corrections were es-timated by comparing the simulated cross sections withand without radiative effects, and so also include the con-volution of the effects of detector acceptance, efficiency,and resolution. However, the estimates make clear thatthe charge-odd radiative effects grow to become a siz-able fraction of the total at higher Q . In forming thecharge-average cross section, all of the charge-odd radia-tive effects are suppressed, not only hard TPE, makingthe cross section extraction less sensitive to uncertaintiesin the radiative corrections prescription.We thank the DORIS machine group and the vari-ous DESY groups that made this experiment possible.We gratefully acknowledge the numerous funding agen-cies: the Science Committee of Armenia, grant 18T-1C180, the Deutsche Forschungsgemeinschaft, the Eu-ropean Community-Research Infrastructure Activity, theUnited Kingdom Science and Technology Facilities Coun-cil and the Scottish Universities Physics Alliance, theUnited States Department of Energy and the NationalScience Foundation, and the Ministry of Education andScience of the Russian Federation. R. Milner also ac-knowledges the generous support of the Alexander vonHumboldt Foundation, Germany. TABLE II. Cross sections measured by OLYMPUS, using the exponentiated Maximon and Tjon radiative corrections pre-scription. Uncertainties are statistical and point-to-point systematic. There is a further 7.5% normalization uncertainty thatis common to all data points. (cid:104) Q (cid:105) [GeV /c ] (cid:104) (cid:15) (cid:105) σ e − p /std. dipole σ e + p /std. dipole Avg. σ ep /std. dipole0.624 0.898 1 . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . . ± . ± . ∗ [email protected]; Now at Stony Brook Uni-versity, Stony Brook, NY, 11794, USA and Riken BNLResearch Center, Upton, NY, 11793, USA † [email protected]; Now at George Washington Uni-versity, Washington, DC, 20052, USA ‡ deceased § partially supported by Jefferson Lab[1] B. 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