Measurement of GEp/GMp in →ep→e→p to q2=5.6 GeV2
O. Gayou,1,7 K.A. Aniol,9 T. Averett,1 F. Benmokhtar,2 W. Bertozzi,24 L. Bimbot,26 E.J. Brash,4 J.R. Calarco,25 C. Cavata,27 Z. Chai,24 C.-C. Chang,23 T. Chang,15 J.-P. Chen,5 E. Chudakov,5 R. De Leo,16 S. Dieterich,2 R. Endres,2 M.B. Epstein,9 S. Escoffier,27 K.G. Fissum,22 H. Fonvieille,7 S. Frullani,18 J. Gao,8 F. Garibaldi,18 S. Gilad,24 R. Gilman,2,5 A. Glamazdin,21 C. Glashausser,2 J. Gomez,5 V. Gorbenko,21 J.-O. Hansen,5 D.W. Higinbotham,24,1 G.M. Huber,4 M. Iodice,17 C.W. de Jager,5 X. Jiang,2 M.K. Jones,5 J.J. Kelly,23 M. Khandaker,3 A. Kozlov,4 K.M. Kramer,1 G. Kumbartzki,2 J.J. LeRose,5 D. Lhuillier,27 R.A. Lindgren,26 N. Liyanage,5 G.J. Lolos,4 D.J. Margaziotis,9 F. Marie,27 P. Markowitz,12 K. McCormick,20 R. Michaels,5 B.D. Milbrath,11 S.K. Nanda,5 D. Neyret,27 Z. Papandreou,4 L. Pentchev,1,2 C.F. Perdrisat,1 N.M. Piskunov,19 V. Punjabi,3 T. Pussieux,27 G. Quéméner,14 R.D. Ransome,2 B.A. Raue,12 R. Roché,13 M. Rvachev,24 A. Saha,5 C. Salgado,3 S. Širca,24 I. Sitnik,19 S. Strauch,2,3 L. Todor,10 E. Tomasi-Gustafsson,27 G.M. Urciuoli,18 H. Voskanyan,29 K. Wijesooriya,6 B.B. Wojtsekhowski,5 X. Zheng,24 L. Zhu24 (for the Jefferson Lab Hall A Collaboration)
1College of William and Mary, Williamsburg, VA 23187
2Rutgers, The State University of New Jersey, Piscataway, NJ 08855
3Norfolk State University, Norfolk, VA 23504
4University of Regina, Regina, SK S4S OA2, Canada
5Thomas Jefferson National Accelerator Facility, Newport News, VA 23606
6Argonne National Laboratory, Argonne, IL 60439
7Université Blaise Pascal/CNRS-IN2P3, F-63177 Aubière, France
8California Institute of Technology, Pasadena, CA 91125
9California State University, Los Angeles, CA 90032
10Carnegie-Mellon University, Pittsburgh, PA 15213
11Eastern Kentucky University, Richmond, KY 40475
12Florida International University, Miami, FL 33199
13Florida State University, Tallahassee, FL 32306
14Institut des Sciences Nucléaires, CNRS-IN2P3, F-38026 Grenoble, France
15University of Illinois, Urbana-Champagne, IL 61801
16INFN, Sezione di Bari and University of Bari, 70126 Bari, Italy
17INFN, Sezione di Roma-III, 00146 Roma, Italy
18INFN, Sezione Sanità and Istituto Superiore di Sanità, 00161 Rome, Italy
19JINR-LHE, 141980 Dubna, Moscow Region, Russian Federation
20Kent State University, Kent, OH 44242
21Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine
22University of Lund, PO Box 118, S-221 00 Lund, Sweden
23University of Maryland, College Park, MD 20742
24Massachusetts Institute of Technology, Cambridge, MA 02139
25University of New Hampshire, Durham, NH 03824
26Institut de Physique Nucléaire, F-91406 Orsay, France
27DAPNIA/SPhN CEA/Saclay, F-91191 Gif-sur-Yvette, France
28University of Virginia, Charlottesville, VA 22901
29Yerevan Physics Institute, Yerevan 375036, Armenia
11Currently at Thomas Jefferson National Accelerator Facility
22On leave of absence from Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria
33Currently at George Washington University, Washington, DC 20052
The ratio of the electric and magnetic form factors of the proton, GEp/GMp, was measured at the Thomas Jefferson National Accelerator Facility (JLab) using the recoil polarization technique. The ratio of the form factors is directly proportional to the ratio of the transverse to longitudinal components of the polarization of the recoil proton in the elastic →ep→e→p reaction. The new data presented in this article span the range 3.5<Q2<5.6 GeV2 and are well described by a linear Q2 fit. Also, the ratio QF2p/F1p reaches a constant value above Q2=2 GeV2.
The nucleon electromagnetic form factors are a key ingredient to describe its internal structure, and eventually understand the strong interaction. Experimental values for the proton have been obtained over the last 50 years via electron-proton scattering, often using the Rosenbluth separation technique [1] . They show that the magnetic form factor, GMp, follows approximately a dipole form factor GD=(1+Q2/0.71(GeV2))−2 where Q2 is the four-momentum transfer squared [2, 3, 4, 5, 6, 7, 8] . However, measuring the charge form factor GEp by Rosenbluth separation becomes difficult for Q2>1 GeV2, because the charge scattering contributes only little to the differential cross section. Extending the measurement of the form factors to larger Q2 is important, for example to test the perturbative QCD (pQCD) scaling predictions for the Dirac and Pauli form factors F1p and F2p [9] . The recoil polarization method, proposed in the 1970's [10] , has been established as the most effective available technique for measuring the ratio GEp/GMp at large Q2 [11, 12, 13, 14] . The results of Ref. [11] showed a surprising, roughly linear, decrease of this ratio as a function of Q2 up to 3.5 GeV2. In a non-relativistic approach, this faster decrease of GEp can be interpretated as confinement of the charge distribution in the Breit frame to a larger region of space than the magnetism distribution.
In the one-photon exchange approximation for elastic ep scattering, a longitudinally polarized electron beam transfers its polarization to the recoil proton with two non-zero components, Pt, perpendicular to, and Pℓ, parallel to, the proton momentum in the scattering plane. Pt and Pℓ are proportional to GEpGMp and G2Mp, respectively, so that the ratio of the form factors follows directly from the simultaneous measurements of these two polarization components [10] :
GEpGMp=−PtPℓ(Ee+Ee′)2mtanθe2 (1)
Here m is the proton mass, θe is the lab scattering angle, and Ee and Ee′ are the incident and scattered energies of the electron.
We present the results of new measurements of the ratio μpGEp/GMp, where μp is the magnetic moment of the proton, up to Q2=5.6 GeV2 performed in Hall A at Jefferson Lab. A polarized electron beam from the Continuous Electron Beam Accelerator was scattered on a 15 cm-long circulating liquid hydrogen target. A strained GaAs crystal excited by circularly polarized laser light produced the polarized electron beam, with an average current of 40 μA. A typical longitudinal beam polarization at the target of ∼0.70 was measured with both a Møller polarimeter [15] (with an uncertainty of ∼3%) and a Compton polarimeter [16] (with an uncertainty of ∼1.4% [17] ). The helicity of the beam was flipped pseudo-randomly at 30 Hz.
Recoil protons were detected in the left high resolution spectrometer (HRS) [18] . The HRS has a central bend angle of 45∘, and accepts a maximum central momentum of 4 GeV/c with a 6.5 msr acceptance; it has a ±5% momentum acceptance and a <2×10−4 momentum resolution. Two vertical drift chambers located at the focal plane, along with the knowledge of the optics of the three quadrupoles and the dipole of the HRS, allow precise position and angle measurements of the proton trajectory at the target. As the data acquisition was triggered by a single proton in the HRS, we also detected the scattered electron in order to isolate elastic ep scattering events and reject the significant background in the spectrometer, mostly from pion electroproduction. The polarization transfer in this reaction can be different in magnitude and sign from the polarization transfer in elastic scattering.
For the measurement at Q2=3.5 GeV2, the electron was detected in the second (right) HRS, and the trigger was a coincidence between an electron and a proton, as described in Ref. [11] . For the measurements at higher Q2, at a fixed beam energy of 4.6 GeV, the electron was scattered at a larger angle than the proton, and thus defined the rate of the reaction. To maximize the number of elastic events selected, the electron was detected in a calorimeter with a large solid angle. The 1.35×2.55 m2 calorimeter was assembled with blocks of lead-glass with a cross-sectional area of 15×15 cm2 each, in 9 columns and 17 rows. The use of lead-glass, which produces Čerenkov light, provides good pion background suppression. At each Q2, the calorimeter was located at a distance from the target where the electron solid angle matched the proton HRS acceptance according to the Jacobian of the reaction. This distance ranges from 9 m at Q2=5.6 GeV2 to 17 m at Q2=4.0 GeV2. The trigger was defined by a proton in the HRS, signaled by a coincidence of two planes of scintillators in the focal plane. For each single proton event in the left HRS, the ADC and TDC information from the calorimeter was read out for all blocks, and elastic events were selected by applying software cuts to the calorimeter data. Our analysis showed that the calorimeter registered an ADC signal in about ten blocks for each trigger. A tight coincidence time cut was applied to ensure that the particle detected in the calorimeter came from the same reaction that produced the proton. This considerably reduced that part of the pion electroproduction background for which the scattered electron and the photons from decay of the π0 were mainly not in the acceptance of the calorimeter. A cut was applied to the angular correlation between the proton and the electron to reject events where the pion production products happened to be in the acceptance. The remaining background represents less than 1% of the accepted events, and is taken into account in the polarization analysis, by measuring the polarization of the rejected events. The small bump in the elastic region of the rejected events in Fig. 1 shows that about 5% of elastic events are rejected, because of missing lead-glass blocks in the calorimeter.
Figure 1: Selection of elastic events by the calorimeter. The histograms show the spectrum of accepted and rejected events of the momentum difference between the proton momentum expected from its reconstructed scattering angle θ and elastic kinematics calculation, p(θ), and its momentum measured by the HRS, p.
The recoil proton polarization was measured by the focal plane polarimeter (FPP) located behind the focal plane of the left HRS [19] . The FPP determines the two polarization components perpendicular to the momentum, Pfppt and Pfppn, by measuring asymmetries in the azimuthal angular distribution after scattering the proton in an analyzer. To improve the figure of merit, the usual graphite analyzer was replaced by polyethylene, 60 cm thick at Q2=3.5 GeV2 and 100 cm thick for the other kinematics. The angular distribution is measured by detecting the trajectory of the proton in two sets of two straw chambers, one before and one after the scattering in the analyzer; the distribution is given by:
N(ϑ,φ)=N0(ϑ){1+[Ay(ϑ)Pfppt+ain]sinφ
−[Ay(ϑ)Pfppn+bin]cosφ} (2)
where N0(ϑ) is the number of protons scattered in the polarimeter to a polar angle ϑ, φ is the azimuthal angle after scattering, and Ay(ϑ) is the analyzing power; ain and bin are instrumental asymmetries. Such a distribution was measured for the two states of the electron beam helicity, positive and negative. The difference in the beam polarization for these two helicity states was compatible with zero at the 0.3% level [17] . The difference between these two distributions N+/N+0−N−/N−0 cancels the instrumental asymmetries to first order. It also gives us access to the transferred, helicity-dependent polarization, which is the quantity of interest. The induced, helicity-independent polarization is zero in the case of elastic scattering from the proton. Figure 2 shows this difference distribution, fitted (solid line) with a cosine function Ccos(φ+δ), where the amplitude C is √(Pfppn)2+(Pfppt)2 and the phase shift δ is such that tanδ=Pfppt/Pfppn. Since Pfppt is related to the interference term GEpGMp, this phase shift is a measure of GEp. The dashed line represents what the distribution would look like if μpGEp/GMp=1. The vertical lines at φ=90∘ and φ=270∘ emphasize the phase shift δ.
The proton spin precesses through the magnetic fields of the HRS. The polarization vector at the analyzer of the FPP, Pfpp, is related to the polarization vector at the target, P, by the spin transfer matrix S: Pfpp=S×P. Because protons with different angles and interaction points at the target see different magnetic fields in the HRS, the matrix elements Sij must be calculated for each event from the reconstructed target coordinates. The matrix elements were determined using a model of the HRS based on optics studies and using the differential algebra-based code COSY [20] .
The polarization components hAyPt and hAyPℓ are obtained by maximizing the likelihood function [21] L(Pt,Pℓ) defined as
L(Pt,Pℓ)=Np∏i=1{1±Ay(ϑi)(Stt,ihPt+Stℓ,ihPℓ)sinφi
∓Ay(ϑi)(Snt,ihPt+Snℓ,ihPℓ)cosφi}, (3)
where the product runs over all events, Np, ± stands for the sign of the beam helicity and h is the beam polarization. The analyzing power and beam helicity eventually cancel in forming the ratio hAyPt/hAyPℓ.
Figure 2: Difference distribution for positive and negative electron beam helicity, for Q2=5.6 GeV2. See text for details.
The new results for the ratio μpGEp/GMp are presented in Fig. 3, with statistical error bars, together with the data of Ref. [11] . The systematic errors are represented by the bands at the top. The new data are tabulated in Table 1, with their statistical and systematic errors. The main sources of systematic errors are related to the spin precession. Those can be divided into three parts. Our analysis shows that the major part is the error associated with the uncertainty in the total bending angle in the non-dispersive plane of the spectrometer, due to misalignment of the magnetic elements of the spectrometer. A careful study of this misalignment has been done recently in Hall A [22] , reducing the systematic error compared to Ref. [11] at Q2=3.5 GeV2 by a factor of six. The other sources of error in the precession are related to uncertainties in the dipole fringe field model, and to the bending angle in the dispersive plane. Systematic errors associated with proton momentum, electron beam energy and electron scattering angle give smaller contributions. No radiative corrections have been applied to the ratio, as no full calculation of polarization observables for ep scattering exists. Afanasev et al. [23] have calculated the single photon emission corrections to the two polarization observables in hadronic variables. The two corrections are of the same sign, negative, and are each of the order of 1%; thus they largely cancel when one takes the ratio. Other contributions due to two photon-exchange, virtual Compton scattering and interference terms are expected to be at the percent level [24] .
A straight line fit has been applied to the ratio μpGEp/GMp in the range 0.5<Q2<5.6 GeV2:
μpGEpGMp=1−0.13(Q2−0.04) (4)
Using this Q2-dependence as a constraint on GEp, the Rosenbluth separation data have been reanalyzed. This brings a correction of the order of 1.5 to 3% to the magnetic form factor [25] .
Figure 3: The ratio μpGEp/GMp from this experiment and Jones et al. (Ref. [11]), compared with theoretical calculations. Systematic errors for both experiments are shown as a band at the top of the figure.
Also shown in Fig. 3 are the results of some theoretical calculations which discuss possible interpretations of a decrease of the ratio μpGEp/GMp. Several authors have studied different effects within the framework of the constituent quark model (CQM); all emphasize the necessity of both kinematic and dynamic relativistic corrections. Franck, Jennings and Miller [26] , in their study of nuclear medium effects on nucleon electromagnetic form factors, used Schlumpf's light-front wave function in an early relativistic CQM [27] to compute the free proton elastic form factors (dashed curve). Based on the data of Ref. [11] , Cardarelli and Simula [28] show that a suppression of the ratio can be expected in the CQM, if the relativistic effects generated by the SU(6) symmetry breaking caused by the Melosh rotations of the constituent spins are taken into account. Their prediction is shown using point-like quark constituents (dotted curve) and constituent quark form factors (solid curve). Wagenbrunn et al. [29] (thin long-dashed curve) reach a reasonable agreement with all electroweak nucleon form factors in their point-form spectator approximation (PFSA) prediction of the Goldstone boson exchange CQM [30] . Other types of models try to describe the dynamic features of the nucleon. Holzwarth [31] (thick long-dashed curve) uses a relativistic chiral soliton model, which gives remarkable agreement with the data. Lomon [32] used the world data, including Ref. [11] , to perform a fit within the Vector Meson Dominance (VMD) model, where the ρ meson contribution is determined by dispersion relations (dot-dashed curve). It is worthwhile to note that while some models can reproduce the observed behavior of μpGEp/GMp, they are all based on effective theories and have parameters that can be adjusted to fit the data. No model so far can accurately describe all form factors of the nucleon, as is necessary to fully understand the strong interaction.
The result can also be expressed in terms of the non spin-flip Dirac form factor F1p, and spin-flip Pauli form factor F2p, given by:
F1p=GEp+τGMp1+τ;F2p=GMp−GEpκp(1+τ) (5)
where κp is the anomalous magnetic moment of the proton, and τ=Q2/4m2. The ratio F2p/F1p directly follows from GEp/GMp. In Fig. 4a, the results are compared with the pQCD predictions [9] that the asymptotic behavior of the form factors is F1p∝1Q4 and F2p∝1Q6, so that Q2F2pF1p would reach a constant value at high enough Q2. The data clearly indicate that this asymptotic regime has not been reached yet. Based on the results of Ref. [11] , Ralston et al. [33] postulated a different scaling behavior, where F2p/F1p goes as 1/√Q2 instead of 1/Q2, arguing that it corresponds to the pQCD expectation if one takes into account contributions to the proton quark wave-function from states with non-zero orbital angular momentum. The ratio √Q2F2pF1p is shown on Fig. 4b; a constant value is clearly reached starting at Q2∼2 GeV2.
In conclusion, we have measured GEp/GMp by polarization transfer to Q2=5.6 GeV2. The ratio obtained in this experiment continues to decrease, as observed first in Ref. [11] . Extrapolation of the linear trend indicates that the electric form factor would cross zero at Q2∼7.7 GeV2. This result also reveals a flattening of the ratio QF2p/F1p starting at Q2∼2 GeV2. A measurement of GEp/GMp to yet higher Q2 is planned in the near future [34] .
The collaboration thanks the Hall A technical staff and the Jefferson Lab Accelerator Division for their outstanding support during the experiment. The Southern Universities Research Association (SURA) operates the Thomas Jefferson National Accelerator Facility for the United States Department of Energy under contract DE-AC05-84ER40150. This work was also supported by the U.S. National Science Foundation and Department of Energy, the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Commissariat à l'Energie Atomique (CEA) and Centre National de la Recherche Scientifique (CNRS-IN2P3), the Natural Sciences and Engineering Research Council of Canada (NSERC), and the EEC grant INTAS 99-00125 for the Kharkov Institute of Physics and Technology, and CRDF UP2-2271.
Figure 4: Same legend as Fig. 3, for (a) Q2F2p/F1p and (b) QF2p/F1p.
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⟨Q2⟩±ΔQ2 (GeV2)
μpGEp/GMp
Δstat
Δsys
3.50±0.23
Table 1: The ratio μpGEp/GMp with statistical uncertainty (1σ) Δstat, and systematic uncertainty Δsyst. ⟨Q2⟩ is the value of Q2 weighted-averaged over the acceptance, and ΔQ2 is the Q2 acceptance (1σ).