Erratum: Two-Photon-Exchange andγZ-Exchange Corrections to Parity-Violating Elastic Electron-Proton Scattering [Phys. Rev. Lett.99, 262001 (2007)]

Abstract

Leading electroweak corrections play an important role in precision measurements of the strange form factors. We calculate the two-photon-exchange (TPE) and γZ-exchange corrections to the parity-violating asymmetry of the elastic electron-proton scattering in a simple hadronic model including the finite size of the proton. We find both can reach a few percent and are comparable in size with the current experimental measurements of strange-quark effects in the proton neutral weak current. The effect of γZ-exchange is in general larger than that of TPE, especially at low momentum transfer Q 2 ≤ 1GeV 2 . Their combined effects on the values of G s E + βG s M extracted in recent experiments can be as large as −40% in certain kinematics.PACS numbers: 13.40. Ks, 13.60.Fz, 13.88.+e, 14.20.Dh Strangeness content in the proton remains one of the most intriguing questions in hadron structure. Early indications on the contribution of strange quarks to the nucleon properties came from neutrino and electron deep inelastic scatterings and pion-nucleon sigma term, which suggested that strange quarks might give non-negligible contributions to the spin and mass of the proton [1]. Many other observables were later suggested, including excess φ production in pp annihilation [2], double polarizations in photo-and electroproduction of φ meson [3], and asymmetry in scattering of longitudinally polarized electrons from polarized targets, to probe the strangeness in the nucleon.Parity-violating asymmetryin polarized electron elastic scattering arises from the interference of weak and electromagnetic amplitudes. Weak neutral current elastic scattering is mediated by the Z-exchange and measures form factors which are sensitive to a different linear combination of the three light quark distributions. When combined with proton and neutron electromagnetic form factors and with the use of charge symmetry, the strange electric and magnetic form factors, G s E and G s M , can then be determined [4]. Since this is a rather clean technique to access the charge and magnetization distributions of the strange quark within nucleons, four experimental programs SAMPLE [5], HAPPEX [6], A4 [7], and G0 [8] have been designed to measure this important quantity, which is small and ranges from 0.1 to 100 ppm. This calls for greater efforts to reduce theoretical uncertainty in order to arrive at a more reliable interpretation of experiments.At tree level, parity violation in electron scattering e(p 1 ) + p(p 2 ) → e(p 3 ) + p(p 4 ) comes from the interference of diagrams with one-photon-exchange (OPE) and Z-boson exchange shown, respectively, in Figs. 1(a) and 1(b). Leading order radiative corrections include the box e(p 1 ) diagrams shown in Figs. 1(c) and 1(d) and other diagrams. The radiative corrections to A P V have been discussed in [9,10]. However, theoretical uncertainties remain. Recently, the contribution of the interference of the two-photon-exchange (TPE) process of Fig. 1(c) with diagram of Figs. 1(a) and 1(b) to A P V , has been evaluated in...

Effect of Two-Boson Exchange on Parity-Violatinge−pScattering

“…The results with the dipole form factors are similar, tending to be 5%-10% smaller. With the mono- pole form factors [6], however, the values of are some 50% larger than with the empirical, which suggests insufficient suppression of contributions from large loop momenta. The TBE corrections to A PV may therefore be overestimated using monopole form factors.…”

ConstrainedγZinterference corrections to parity-violating electron scattering

“…We will consider only the inelastic contribution to γZ ; the elastic contribution has previously been considered in Refs. [7,8,21,22] and is strongly suppressed by an additional factor Q p W . For forward scattering, the dispersion relation for the real part of V γZ is given by…”

New Formulation ofγZBox Corrections to the Weak Charge of the Proton

“…It agrees exactly with the direct loop calculations of ✷ A γZ in Refs. [14,15], in which the intermediate nucleon is off-shell. It also agrees exactly at E = 0 with the value L m = 2.04 if the parameters are adjusted to correspond to those of MS [3].…”