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gamma-Z corrections to forward-angle parity-violating e-p scattering

We use dispersion relations to evaluate the gamma-Z box contribution to parity-violating electron scattering in the forward limit arising from the axial-vector coupling at the electron vertex. The calculation makes full use of the critical constraints from recent JLab data on electroproduction in the resonance region as well as high energy data from HERA. At the kinematics of the Qweak experiment, this gives a correction of 0.0047{+0.0011}{-0.0004}$ to the Standard Model value 0.0713(8) of the proton weak charge. While the magnitude of the correction is highly significant, the uncertainty is within the anticipated experimental uncertainty of +- 0.003.