A ug 2 01 1 High-precision measurement of the proton elastic form factor ratio

We report a new, high-precision measurement of the proton elastic form factor ratio μpGE/GM for the four-momentum transfer squared Q 2 = 0.3– 0.7 (GeV/c). The measurement was performed at Jefferson Lab (JLab) in Hall A using recoil polarimetry. With a total uncertainty of approximately 1%, the new data clearly show that the deviation of the ratio μpGE/GM from unity observed in previous polarization measurements at high Q continues down to the lowest Q value of this measurement. The updated global fit that includes the new results yields an electric (magnetic) form factor roughly 2% smaller (1% larger) than the previous global fit in this Q range. We obtain new extractions of the proton electric and magnetic radii, which are 〈r E〉 1/2 = 0.875± 0.010 fm and 〈r M 〉 1/2 = 0.867± 0.020 fm. The charge radius is consistent with other recent extractions based on the electron-proton interaction, including the atomic hydrogen Lamb shift measurements, which suggests a missing correction in the comparison of measurements of the proton charge radius using electron probes and the recent extraction from the muonic hydrogen Lamb shift. The nucleon electromagnetic form factors are fundamental quantities which relate to the charge and magnetization distributions within the nucleon. For over 40 years, the form factors have been studied extensively by Rosenbluth separations of the unpolarized electron-proton scattering cross section. Recent advances in the technology of intense polarized beams, polarized targets and polarimetry ushered in a new generation of experiments that measure double polarization observables [1, 2, 3]. Although the proton electric to magnetic form factor ratio R ≡ μpGE/GM determined by unpolarized measurements showed minimal Q dependence up to Q ≈ 6 (GeV/c), experiments at JLab with highquality polarized electron beams measuring recoil polarization [4, 5, 6] revealed that the ratio μpGE/GM drops almost linearly with Q 2 for Q>1 (GeV/c). These findings led to an explosion of experimental and theoretical efforts to understand the proton form factors [7, 2, 3]. The difference between the polarization and cross section measurements is now believed to be the result of two-photon exchange (TPE) contributions [8, 9, 10, 11], which have little impact on the polarization measurements but significantly affect the Rosenbluth extractions of GE at large Q . While measurements at large momentum transfer have provided information on the fine details of the proton structure and relate to the quark orbital angular momentum, the low Q form factor behavior is sensitive to the long-range structure which is believed to be dominated by the “pion cloud”. High-precision measurements at low Q were motivated by a recent semi-phenomenological Preprint submitted to Elsevier January 11, 2013 Table 1: Kinematic settings for the experiment. θe (θp) is the scattered electron (proton) angle in the lab frame, Pp is the proton central momentum, ε is the virtual photon polarization. Q θe θp Pp ε Analyzer (GeV/c) (deg) (deg) (GeV/c) thickness 0.298 28.5 60.0 0.565 0.88 2.25” 0.346 31.3 57.5 0.616 0.85 2.25” 0.402 34.2 55.0 0.668 0.82 3.75” 0.449 36.7 53.0 0.710 0.80 3.75” 0.494 39.2 51.0 0.752 0.78 3.75” 0.547 41.9 49.0 0.794 0.75 3.75” 0.599 44.6 47.0 0.836 0.72 3.75” 0.695 49.8 43.5 0.913 0.66 3.75” fit [12], which suggested that structure might be present in all four nucleon form factors at Q ≈ 0.3 (GeV/c). Later polarization measurements from MIT-Bates [13] and JLab [14] probed this region with a precision of ∼2%, but found no indication of such structure in the ratio μpGE/GM . This Letter reports on a new, high-precision polarization transfer measurement (JLab E08-007) of the proton form factor ratio μpGE/GM at Q 2 values between 0.3 and 0.7 (GeV/c) . In the one-photon exchange (Born) formalism, the ratio of the transferred transverse to longitudinal polarizations is related to the proton form factors [2]: R ≡ μp GE GM = −μp Ee + E ′ e 2Mp tan( θe 2 ) Pt Pl , (1) where Mp and μp are the proton mass and magnetic moment, Ee (E ′ e) is the incident (scattered) electron energy, θe is the electron scattering angle and Pt (Pl) is the transverse (longitudinal) component of the polarization transfer. The experiment was performed at Jefferson Lab in Hall A [15]. A 1.2 GeV polarized electron beam of between 4 and 15 μA was incident on a 6 cm thick liquid hydrogen target. The beam helicity was changed at 30 Hz, with a quartet structure selected pseudorandomly between (+ − −+) and (− + +−) for each set of four helicity states. The beam polarization was near 83%, as measured by the Møller polarimeter in the Hall [15]. The recoil proton was detected by the left High Resolution Spectrometer (LHRS) in coincidence with the elastically scattered electron detected in a large acceptance spectrometer (“BigBite”). The transferred proton polarization was measured by a focal plane polarimeter (FPP) in the LHRS [15]. The trigger was a coincidence between detection of a charged particle in the HRS and a signal in the BigBite calorimeter used to select energetic electrons. Since elastic events can be well identified using the proton kinematics, only information from the BigBite calorimeter was used in the analysis; the tracking detectors were not turned on for the experiment. The kinematic settings are given in Table 1. The FPP measured the azimuthal asymmetry due to the spin-orbit coupling in proton scattering from carbon nuclei. The proton’s transferred polarization