$\mathbf{\gamma Z}$ Box at Low Energy

TL;DR

This paper calculates the low-energy $\gamma Z$ box correction to electron-quark scattering, providing refined coupling constants crucial for interpreting parity-violating experiments like the proton's weak charge measurement.

Contribution

It presents a detailed calculation of the $\gamma Z$ box correction at low energy, including non-zero electron and quark masses, and derives finite, cutoff-insensitive coupling constants.

Findings

Finite, well-defined couplings obtained with non-zero electron mass.

Results impact the interpretation of proton weak charge measurements.

Analysis of mass limits ensures robustness of low-energy effective theory.

Abstract

We calculate the 1-loop $\gamma Z$ box-graph correction to electron-quark scattering at low energy and low momentum transfer. Both electron and quark masses are kept non-zero. From our result, we extract coupling constants for the low-energy effective Lagrangian with parity-violating 4-fermion interaction terms. We study the zero-mass limits and show that a non-zero electron mass is sufficient to obtain finite, well-defined couplings which are insensitive to a hadronic mass cutoff. We finally discuss the impact of our results on the determination of the weak charge of the proton from polarized electron-proton scattering.