Model-dependence of the $\gamma Z$ dispersion correction to the parity-violating asymmetry in elastic $ep$ scattering

TL;DR

This paper evaluates the theoretical uncertainties in the gamma-Z dispersion correction to the parity-violating asymmetry in elastic electron-proton scattering, providing a refined Standard Model prediction for the proton's weak charge and suggesting future measurements to reduce uncertainties.

Contribution

It introduces a detailed analysis of model-dependent uncertainties in the gamma-Z dispersion correction, improving the precision of the Standard Model prediction for the proton's weak charge.

Findings

Estimated the gamma-Z correction at Q-Weak kinematics as (0.0054±0.0020) in proton weak charge.

Provided a new Standard Model prediction for the asymmetry: (0.0767±0.0008±0.0020_{γZ}).

Identified future low-energy measurements as a means to reduce theoretical uncertainties.

Abstract

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 non-resonant 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 $(0.0054\pm0.0020)$. This should be compared to the value of the proton's weak charge of $\qwp=0.0713\pm0.0008$ that includes SM 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 $(0.0767\pm0.0008\pm0.0020_{\gamma Z})$. 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.