Model dependence of the γZ dispersion correction to the parity-violating asymmetry in elastic ep scattering

We analyze the dispersion correction to elastic parity violating electron-proton scattering due to gamma Z exchange. In particular, we explore the theoretical uncertainties associated with modeling contributions of hadronic intermediate states. Taking into account constraints from low-and high-energy, parity-conserving electroproduction measurements, choosing different models for contributions from the nonresonant processes, and performing the corresponding flavor rotations to obtain the electroweak amplitude, we arrive at an estimate of the uncertainty in the total contribution to the parity-violating asymmetry. At the kinematics of the Q-Weak experiment, we obtain a correction to the asymmetry equivalent to a shift in the proton weak charge of (0.0054 +/- 0.0020). This should be compared to the value of the proton's weak charge of Q(W)(p) = 0.0713 +/- 0.0008 that includes Standard Model contributions at tree level and one-loop radiative corrections. Therefore, we obtain a new Standard Model prediction for the parity-violating asymmetry in the kinematics of the Q-Weak experiment of (0.0767 +/- 0.0008 +/- 0.0020(gamma Z)). The latter error leads to a relative uncertainty of 2.8% in the determination of the proton's weak charge and is dominated by the uncertainty in the isospin structure of the inclusive cross section. We argue that future parity-violating inelastic ep asymmetry measurements at low to moderate Q(2) and W-2 could be exploited to reduce the uncertainty associated with the dispersion correction. Because the corresponding shift and error bar decrease monotonically with decreasing beam energy, a determination of the proton's weak charge with a lower-energy experiment or measurements of isotope ratios in atomic parity violation could provide a useful cross-check on any implications for physics beyond the Standard Model derived from the Q-Weak measurement.