Nucleon Electromagnetic Form Factors

NUCLEON ELECTROMAGNETIC FORM FACTORS Haiyan Gao Triangle Universities Nuclear Laboratory, and Department of Physics, Duke University, Durham, North Carolina 27708, U.S.A. arXiv:nucl-ex/0411015v1 8 Nov 2004 Abstract The nucleon electromagnetic form factors have been studied in the past extensively from unpolarized electron scattering experiments. With the development in polarized beam, recoil polarimetry, and polarized target technologies, polarization experiments have provided more precise data on these quantities. In this talk, I review recent experimental progress on this subject. 1 INTRODUCTION The electromagnetic form factors of the nucleon are fundamental quantities describing the distribution of charge and magnetization within nucleons. Quantum Chromodynamics (QCD) is the theory of strong interaction in terms of quark and gluon degrees of freedom. While QCD has been extremely well tested in the high energy regime, where perturbative QCD is applicable, understanding confinement and hadron structure in the non-perturbative region of QCD remains challenging. Knowledge of the internal structure of protons and neutrons in terms of quark and gluon degrees of freedom is not only essential for testing QCD in the confinement regime, but it also provides a basis for understanding more complex, strongly interacting matter at the level of quarks and gluons. PROTON ELECTROMAGNETIC FORM FACTORS The proton electric (GpE ) and magnetic (GpM ) form factors have been studied extensively in the past from unpolarized electron-proton (ep) elastic scattering using the Rosenbluth separation technique [1]. New data from polarization transfer experiments [2, 3], which measure this ratio directly with unprecedented precision, show very intriguing behavior at µGpE 2 higher Q . The form factor ratio, Gp drops to approximately 0.5 at a Q2 value above 3 M (GeV/c)2 , and to approximately 0.3 at the highest measured Q2 value (∼ 5.5 (GeV/c)2 ). No such dramatic behavior in this ratio had been observed from unpolarized cross section measurements. Fig. 1 shows the proton electric to magnetic form factor ratio as a function of Q2 from recoil proton polarization measurements at Jefferson Lab [2, 3], together with data from SLAC using Rosenbluth separation technique [4]. These new data [2, 3] suggest that the proton Dirac (F1 (Q2 )) and Pauli form factor (F2 (Q2 )) scale as Q FF21 ∼ constant at large values of Q2 . Contributions from nonzero parton orbital angular momentum are power suppressed as shown by Lepage and Brodsky [7]. However, they are shown to lead to asymptotic scaling of the proton form factor ratio: F2 (Q2 )/F1 (Q2 ) ∼ (log2 Q2 /Λ2 )/Q2 with 0.2 √ GeV≤ Λ ≤0.4 GeV based on an explicit pQCD calculation [8] or F2 (Q2 )/F1 (Q2 ) ∼ 1/ Q2 [9, 10] that agrees with the JLab proton form factor data [2, 3]. A recent nonperturbative analysis [11] of the hadronic form factors based on light-front wave functions also describes the JLab proton form factor data [2, 3] well. While the intriguing Q2 dependence of the proton form factor ratio can be described [8, 9, 10, 11], it is important to understand the discrepancy between results obtained from recoil proton polarization measurements and those from Rosenbluth method. New Jefferson Lab data [12] (solid circles in Fig. 1) from Rosenbluth separation are in good agreement with previous SLAC results. Recently, a new, “SuperRosenbluth” experiment was carried out at Jefferson Lab [13], in which the struck protons were detected to minimize systematic uncertainties associated with regular Rosenbluth technique in which scattered electron is detected. Preliminary results [14] from the “SuperRosenbluth” experiment agree with previous Rosenbluth experiments. Two-photon exchange contributions [15] are believed to contribute to the observed discrepancy between the polarization method and the Rosenbluth technique. Currently, there are intensive efforts both in theory [16] and in experiment [17] aiming at understanding the two-photon exchange contributions to electron scattering in general, particularly to the aforementioned discrepancy in the proton form 2 factor ratio. A new experiment [18] in which longitudinally polarized electrons scattering off a polarized proton target is currently ongoing at MIT-Bates and the proton electric to magnetic form factor ratio will be extracted with high precision up to a Q2 value of about 0.8 (GeV/c)2 . Such a double-polarization experiment is important because it employs a completely different experimental technique with different systematic uncertainties than recoil proton polarization measurements. FIG. 1: Proton electric to magnetic form factor ratio as a function of Q2 . Data from JLab recoil proton polarization measurements [2, 3] are shown as solid squares, the new Jefferson Lab data from Rosenbluth separation [12] are shown as solid circles together with the error band representing the absolute uncertainty due to the scattering angle uncertainty. The SLAC data are shown as solid triangles [4]. The dashed line is a reanalysis [5] of global unpolarized data [4]. The dotted line [6] is a fit by combining the cross-section data and the recoil polarization data. NEUTRON ELECTROMAGNETIC FORM FACTORS Measurements of the neutron electric form factor are extremely challenging because of the lack of free neutron targets, the smallness of the GnE , and the dominance of the magnetic contribution to the unpolarized differential cross-section. A promising approach to measure GnE is by using polarization degrees of freedom. For coincidence elastic scattering of longitudinally polarized electrons from “free” neutrons, n(~e, e′~n) process, the recoil neutron polarization ratio PPxz is sensitive to the neutron electric to magnetic form factor ratio [19]. Experiments with longitudinally polarized electron beams and recoil neutron polarimeters have been carried out at MIT-Bates [20] and Mainz [21, 22] in the relatively low Q2 region, and GnE has been extracted from the d(~e, e′~n) process, using the state-of-the-art two-body calculations by Arenhövel [23]. Most recently, such an approach has been employed at Jefferson Lab up to a Q2 value of 1.5 (GeV/c)2 [24]. Alternatively, one can employ a vector polarized deuteron target or a polarized 3 He ~ e, en) ~ e, en) reaction or the 3 He(~ target to probe the neutron electric form factor by the d(~ 3 process. A polarized 3 He nucleus is an effective neutron target because its ground state is dominated by a spatially symmetric S wave in which the proton spins cancel and the spin of the 3 He nucleus is carried by the unpaired neutron [25, 26]. The spin-dependent ~ e, en) ~ e, en) reaction for vector polarized deuteron and from 3 He(~ asymmetries from the d(~ Gn process give access to the quantity GnE to first order when the target spin direction is M aligned perpendicular to the momentum transfer vector ~q. The neutron electric form factor ~ e, e′ n) measurement at NIKHEF in which a was extracted for the first time [27] from a d(~ vector polarized deuteron target from an atomic beam source was employed. More recently, ~ e, e′ n) experiment [28, 29] using a dynamically polarized solid deuterated ammonia a d(~ target was carried out at Jefferson Lab and GnE was extracted at Q2 values of 0.5 and ~ e, e′ n) at Mainz [30], two 1.0 (GeV/c)2 . Following the first measurement on GnE from 3 He(~ more experiments [31, 32] were carried out. All three experiments employed a high pressure polarized 3 He target achieved by the metastability-exchange optical pumping technique and the compression method. To extract GnE information from these polarized target experiments, corrections for mesonexchange currents, final state interactions, etc. are necessary using the state-of-the-art twobody and three-body calculations. Discussions on these corrections can be found in Ref. [30]. Fig. 2 shows GnE data as a function of Q2 from polarization experiments. Also shown in Fig. 2 are the extracted GnE values from the deuteron quadrupole form factor data by Schivilla and Sick [35], and the Galster parameterization [34]. New precision data [36] on GnE in the low Q2 region will become available in the near future from MIT-Bates, and two approved experiments [37] at Jefferson Lab will extend the measurement of GnE to much higher values of Q2 . 0.1 2 JLab E93-038: 2 → → H(e,e’n) 0.08 GEn → → MIT-Bates: H(e,e’n) 2→ → JLab E93-026: H(e,e’n) 3→ → Mainz A1: He(e,e’n) → → Mainz A3: 2H(e,e’n) 3→ → Mainz A3: He(e,e’n) 2→ → NIKHEF: H(e,e’n) Schiavilla & Sick: GQ 0.06 0.04 0.02 Galster 0 0 0.2 0.4 0.6 New Fit 0.8 2 1 1.2 1.4 1.6 1.8 2 2 Q [(GeV/c) ] FIG. 2: Recent data on GnE from polarization experiments. Also shown are the extracted GnE values from the deuteron quadrupole form factor data by Schivilla and Sick [35]. The Galster parameterization [34] as well as a new fit [24] are also shown. Until recently, most data on GnM had been deduced from elastic and quasi-elastic electrondeuteron scattering. For inclusive measurements, this procedure requires the separation of the longitudinal and transverse cross sections and the subsequent subtraction of a large proton contribution. Thus, it suffers from large theoretical uncertainties due in part to the deuteron model employed and in part to corrections for final-state interactions (FSI) and meson-exchange currents (MEC). These complications can largely be avoided if one measures 4 the cross-section ratio of d(e, e′ n) to d(e, e′ p) at quasi-elastic kinematics. Several recent experiments [39, 40, 41, 42] have employed this technique to extract GnM with uncertainties of <2% [41, 42] at Q2 below 1 (GeV/c)2 . Despite the high precision reported, however, there is considerable disagreement among some of the experiments [38, 39, 40, 41, 42] with respect to the absolute value of GnM . The most recent deuterium data [42] further emphasize this discrepancy. While the discrepancies among the deuterium experiments described above may be understood [43], additional data on GnM , preferably obtained using a complementary ~ e, e′ ) scattering provides just such method, are highly desirable. Inclusive quasi-elastic 3 He(~ an alternative approach [44]. Recently precision data on GnM have been obtained from ~ e, e′ ) process at Jefferson Lab [45, 46]. These new data are in inclusive quasi-elastic 3 He(~ very good agreement with the recent deuterium ratio measurements from Mainz [41, 42], and in disagreement with results by Bruins et al. [40]. The deuterium ratio method was employed recently at Jefferson Lab [47] up to a Q2 value of 4.7 (GeV/c)2 . FIG. 3: The neutron magnetic form factor GnM data published since 1990, in units of the standard dipole form factor parameterization GD , as a function of Q2 . The Q2 points of Anklin 94 [39] and Gao 94 [44] have been shifted slightly for clarity. Also plotted are a few selected models of nucleon form factor calculation and the references are contained in [45]. Acknowledgments I thank Eric Christy, Thia Keppel, Mark Jones, Dick Madey, Bradley Plaster, Andrei Semenov, and Wang Xu for providing helpful information about their experiments and for the preparation of some of the figures. This work is supported by the U.S. Department of Energy under contract number DE-FC02-94ER40818 and DE-FG02-03ER41231. The author also acknowledges the OJI award in Nuclear Physics from the U.S. Department of Energy. [1] M.N. Rosenbluth, Phys. Rev. 79, 615 (1950). 5 [2] M. Jones et al., Phys. Rev. Lett. 84, 1398 (2000). [3] O. Gayou et al., Phys. Rev. Lett. 88, 092301 (2002); O. Gayou et al., Phys. Rev. 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