Hadronic weak charges and parity-violating forward Compton scattering

TL;DR

This paper investigates a novel parity-violating two-photon exchange correction in electron-nucleon scattering, assessing its impact on the precise extraction of the nucleon's weak charge and implications for future experiments.

Contribution

It introduces and analyzes a new class of radiative corrections involving parity violation in two-photon exchange, affecting weak charge measurements.

Findings

The correction's significance increases with beam energy.

The weak charge definition remains valid at zero momentum transfer.

Implications for upcoming precision experiments are discussed.

Abstract

Parity-violating elastic electron-nucleon scattering at low momentum transfer allows one to access the nucleon's weak charge, the vector coupling of the $Z$-boson to the nucleon. In the Standard Model and at tree level, the weak charge of the proton is related to the weak mixing angle and accidentally suppressed, $Q_W^{p,\,{\rm tree}}=1-4\sin^2\theta_W\approx0.07$. Modern experiments aim at extracting $Q_W^p$ at $\sim1\%$ accuracy. Similarly, parity non-conservation in atoms allows to access the weak charge of atomic nuclei. We consider a novel class of radiative corrections, an exchange of two photons with parity violation in the hadronic/nuclear system. These corrections may affect the extraction of $\sin^2\theta_W$ from the experimental data at the relevant level of precision because they are affected by long-range interactions similar to other parity-violating radiative corrections, such as, e.g., the $\gamma Z$-exchange, which has obtained much attention recently. We show that the significance of this new correction increases with the beam energy in parity-violating electron scattering, but the general properties of the parity-violating forward Compton amplitude protect the formal definition of the weak charge as a limit at zero-momentum transfer and zero-energy. We also discuss the relevance of the new correction for upcoming experiments.