Bled Workshops in Physics Vol. 8, No. 1 p. 70
Proceedings of the Mini-Workshop Hadron Structure and Lattice QCD Bled, Slovenia, July 9-16, 2007

Exclusive processes on the nucleon at MAMI and Jefferson Lab
S. Sircaa,b
a Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia b Jozef Stefan Institute, 1000 Ljubljana, Slovenia
Abstract. The MAMI accelerator (Mainz, Germany) and the CEBAF at Jefferson Laboratory (Newport News, USA) are the world leading electron-scattering facilities in the several 100 MeV to several 1 GeV energy range. A large fraction of the experimental program in these laboratories has recently been focused on the electroweak properties of the nucleon, its spin structure, and on nucleon resonance excitation. Latest results from MAMI (A1 Collaboration) and Jefferson Lab (mostly Hall A) are described.
1 Electroweak properties of nucleons
The elastic form factors of the nucleon remain of prime interest. New measurements of the proton electric-to-magnetic form-factor ratio have been performed or are being planned in order to resolve the persistent discrepancy between the double-polarization measurement [1] versus a precise Rosenbluth-separation determination [2], which exhibit different Q2-dependencies. Presently the main reason for the disagreement is believed to be the two-photon correction to the elastic scattering process, which contributes differently in both cases. One should also mention the recent precise results at the other end of the spectrum, at very low Q2 where pion-cloud effects play the dominant role. These were obtained by the BLAST Collaboration at MIT-Bates [3].
An extension of the double-polarized measurement to about 9 (GeV/c)2 is in progress at Jefferson Lab (Hall C), while a high-precision unpolarized (Rosen-bluth) measurement of Gp and GM at low Q2 is being pursued at MAMI. Measurements of GE to as high as 15 (GeV/c)2 and GM to 18 (GeV/c)2 are planned with the 12 GeV-upgrade of CEBAF. There are also efforts in JLab Hall B which are concentrated around the measurement of cross-section differences for electrons versus positrons, which are an independent means of distinguishing the role of the two-photon contributions.
An exciting development in the form-factor arena is the recent high-Q2 measurement of the neutron charge form-factor GE in Hall A. These measurements are relevant both to explore the transition to pQCD (two-gluon exchanges) and to test the importance of the handbag diagrams (from the perspective of generalized parton distributions (GPDs)), as well as for nucleon spin (sum rules) and lattice QCD. Preliminary results at intermediate Q2 have been reported at various
conferences this Fall and indicate values of GE which lie above the conventional (Platchkov) parameterization.
The HAPPEX Collaboration at Jefferson Lab is dedicated to the determination of the strange-quark contributions to the distributions of charge (GE) and magnetization (GM) within the proton. The parity-violating asymmetry on hydrogen is proportional to a linear combination of GE and GM, while it is proportional to GE only in the case of the spin-less 4He nucleus. Both targets have been used at HAPPEX in different kinematical conditions. Most recent results have now been published [5], and the results of this experiment only (i.e. without averaging over other experiments) are
GE = 0.002 ± 0.014 ± 0.007 , GE + 0.09 GM = 0.007 ± 0.011 ± 0.006 .
Real-photon Compton scattering (RCS) and its virtual counterpart (VCS) are being utilized to access further information on the electromagnetic structure of the proton. The E99-114 experiment at Hall A has measured polarization transfer in RCS off the proton at high momentum transfer [6]. Polarization transfer parameters Kll and Kls were extracted and were shown to be in disagreement with the prediction of perturbative QCD based on a two-gluon exchange mechanism. Specifically, the nonzero value of the ratio
— oc — =0.21 ±0.11 ±0.03
Kll Rv
implies that the proton helicity is flipped in the RCS process (which is forbidden in leading-twist pQCD). The RCS studies have been forwarded another step by examining the scaling
da f(9) dt ^ sn
of the RCS cross-section (at a fixed angle), where pQCD predicts n = 6 based on constituent scaling rules. In contrast to this expectation, a relatively precise value of n = 8.0 ± 0.2 has been found [7]. The scaling result also disagrees with the predictions based on the handbag reaction mechanism.
The OOPS Collaboration at MIT-Bates has finished analyzing the data from experiments in virtual Compton scattering (VCS) off the proton at low Q2 [8]. The mean-square electric polarizability of the proton
{r2a) = 2.16 ± 0.31 fm2
(basically the slope of the Q2-dependent electric polarizability a(Q2) at low Q2) has been determined for the first time in a VCS process. The magnetic polarizability (3 (Q2), on the other hand, could not be determined well due to poor statistics, although the data is consistent with ( having a positive slope at origin, corresponding to a negative magnetic polarizability mean-square radius and characteristic of a diamagnetic contribution from the pion cloud. Unfortunately, the statistics and systematics of the data gathered over the years at MIT-Bates,
MAMI and JLab, are still insufficient to allow for a reliable determination of the Q2-dependence of the polarizabilities.
The VCS program on nucleon targets has recently evolved into a much broader effort by including polarization degrees of freedom. Single-spin (beam) asymmetries at low energies have been measured at MAMI/A1 on the proton [9], as well as in the deep-inelastic regime (so-called deeply virtual Compton scattering, DVCS) at JLab Hall A on both the proton and the neutron. The analysis of the Mainz experiment, the goal of which is to determine three different linear combinations of generalized polarizabilities contained in the ¥0, A¥x0, and A¥z0 structure functions is underway while the proton DVCS results from Hall A appeared recently [10]. This is a first DVCS experiment in the valence-quark region (large Bjorken x). Real and imaginary parts of twist-2 and twist-3 coefficients of the angular expansion of the cross-section have been measured with great accuracy. One of the conclusions was that perturbative scaling applies in DVCS, indicating that the GPDs are in principle accessible already at modest values of Q2 in this process.
2 Nucleon spin structure
The neutron DVCS experiment E03-106 utilizes the same (single-spin) technique as the proton DVCS to constrain E, the least-known GPD, and as such complements nicely the proton case which predominantly depends on H and H. In addition, the neutron channel is particularly important because the of the nucleon total angular momentum sum rule J = Jq + Jg = \ (quarks plus gluons), where
Jq = ^AI + Lq = l
dxx
H(x,^,0) - E(x,£,,0)
While the spin part A! can be determined in DIS experiments (and Lg in experiments like COMPASS), the nDVCS at high values of Bjorken x has a unique opportunity to help determine the orbital contribution Lq. The analysis of the neutron DVCS experiment is underway.
3 Nucleon resonances
The multipole character of the N —> A(1232) transition is being probed with ever increasing accuracy and at varying kinematical conditions (in particular, at several values of Q2 accessible at different laboratories). In fact, the experimental methods have been improved to a degree that allows for a rather clear determination of the individual transition amplitudes, such that the model dependence usually dominates the final uncertainties.
Sadly, professor Jim Kelly, the spokesperson and the spiritus agens of the landmark N —> A(1232) experiment in Hall A at Jefferson Lab, has passed away this year. It is in respect and admiration that we look at the extensive paper on that experiment [11] which he managed to bring to completion in the very last weeks of his illness.
The A1 Collaboration atMAMI has reported on new precise p(e, e'p)n0 measurements at the peak of the A(1232) resonance at Q2 = 0.20 (GeV/c)2 [12]. The new data are sensitive to both the electric (E2) and the Coulomb (C2) quadrupole amplitudes of the N A transition. New precise values for the quadrupole to dipole amplitude ratios
CMR = (-5.09 ± 0.28 (stat + sys) ± 0.30 (model))% , EMR = (-1.96 ± 0.68 (stat + sys) ± 0.41 (model))%
have been obtained, with a value for the dominant magnetic dipole amplitude
M1+ = (39.57 ± 0.75 (stat + sys) ± 0.40 (model)) • 10-3/m+ .
The results are in disagreement with the predictions of the Constituent Quark Model and in qualitative agreement with models that account for mesonic contributions, including recent Lattice QCD calculations. They thus support the conjecture of deformation in hadronic systems with its origin in the dominance of mesonic effects.
-10+
0,0
0,2
-2
0,4
0,6 Q1 (GeV/c)1
0,4	0,6
Q1 (GeV/c)1
0,0
0,2
0,4
0,6 Q1 (GeV/c)1
•	This work	-----------MAID
♦	Stave etal	--------DMT
^ Eisner et al	----------Sato Lee
A Pos ischiletal	SAID
A Bates	...........ChEFT: PV
■ CLAS	OH
0 Beck etal	-¡¡QM
......Ca stick
Lattice QCD
Fig. 1. The extracted values for CMR, EMR and M-|+ as a function of Q2 from recent low-Q2 experiments. The theoretical predictions of models MAID, DMT, SAID, Sato-Lee, Capstick, HQM, the linearly extrapolated Lattice-QCD calculation, ChEFT of Pascalutsa-Vanderhaegen and Gail-Hemmert are also shown.
Similar goals have been set by another experiment at MAMI [13], but at a lower value of Q2 = 0.060 (GeV/c)2. Here, the reported ratios are even more precise,
CMR = (-4.81 ± 0.27 (stat + sys) ± 0.26 (model))% , EMR = (-2.28 ± 0.29 (stat + sys) ± 0.20 (model))%
while the magnetic dipole amplitude is
M1 + = (40.33 ± 0.63 (stat + sys) ± 0.61 (model)) • 10-3/m+ ,
with similar conclusions. A summary of the results from recent experiments at low Q2, where pion cloud physics (long-range effects) is believed to play a most prominent role, is given in Figure 1.
Polarization degrees of freedom have also been exploited in the measurement of p(e, e'p)n0 at Q2 = 0.35 (GeV/c)2 in the resonance region [14]. The results (unpolarized and polarized structure functions) have been compared to calculations based on dispersion relations for VCS and to the phenomenologi-cal pion electroproduction model MAID. There is an overall good agreement between experiment and theoretical calculations. The remaining discrepancies have been mostly attributed to imperfect parameterizations of non-resonant (background) multipoles, to which the measured beam-helicity asymmetry is particularly sensitive.
In another polarized experiment, both beam polarization and proton po-larimetry have been utilized in an experiment inaugurating the MAMI-C accelerator with its new, 1.5 GeV CW beam [15]. The beam-recoil polarization transfer coefficients P^ and P.Z as well as the (induced) recoil polarization Py were measured for the first time in the p(e, e'p)n reaction at Q2 = 0.1 (GeV/c)2, with a center of mass production angle of 120° and spanning a center of mass energy range of 1500 MeV < W < 1550 MeV, thus covering the region of the S11(1535) and D13(1520) resonances. The values obtained are
PX = (-67.6 ± 3.2 (stat) ± 2.6 (sys))% , Py = (16.1 ± 3.2 (stat) ± 2.3 (sys))% , PZ = (-29.3 ± 2.6 (stat) ± 2.6 (sys))% .
The PX and are in good agreement with the phenomenological isobar model (Eta-MAID), while Py shows a significant deviation, consistent with existing photoproduction data on the polarized-target asymmetry from Bonn. However, if a strong phase change between E0+ and (E2- + M2-) multipoles is applied, which gives a good description of the Bonn polarized target data, the electroproduc-tion data point is also in good agreement with the model. Such a strong phase change is incompatible with a standard Breit-Wigner behavior of the S11(1535) resonance. Indeed this appears to be yet another of the peculiarities of this resonance, the most notable one being the remarkably slow Q2-falloff of the helicity amplitude corresponding to n electroproduction seen in Hall B.
References
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