# Reduced uncertainty of the axial $\gamma Z$-box correction to the proton's weak charge

## TL;DR

This paper provides an updated calculation of the $ ext{γ}Z$-box correction to the proton's weak charge, reducing uncertainty and improving the precision of low-energy weak mixing angle measurements.

## Contribution

The authors present a refined analysis of the $ ext{γ}Z$-box correction, incorporating new data and symmetry considerations to halve the uncertainty in the axial contribution.

## Key findings

- Confirmed previous results for the axial contribution to the $ ext{γ}Z$-box correction.
- Reduced the uncertainty in the axial contribution by a factor of 2.
- Estimated the additional contribution from parity-violating photon-hadron interactions and its uncertainty.

## Abstract

We present the fully up-to-date calculation of the $\gamma Z$-box correction which needs to be taken into account to determine the weak mixing angle at low energies from parity-violating electron proton scattering. We make use of neutrino and antineutrino inclusive scattering data to predict the parity-violating structure function $F_3^{\gamma Z}$ by isospin symmetry. Our new analysis confirms previous results for the axial contribution to the $\gamma Z$-box graph, and reduces the uncertainty by a factor of~2. In addition, we note that the presence of parity-violating photon-hadron interactions induces an additional contribution via $F_3^{\gamma \gamma}$. Using experimental and theoretical constraints on the nucleon anapole moment we are able to estimate the uncertainty associated with this contribution. We point out that future measurements are expected to significantly reduce this latter uncertainty.