Hadronic weak charges and parity-violating forward Compton scattering

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, $Q_W^{p,\mathrm{tree}}=1-4{\sin }^2{\theta }_W\approx 0.07$. Modern experiments aim at extracting $Q_W^p$ at $\sim 1\%$ 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.

Few references added; small changes in the text

References in corpus (6)

• Electromagnetic excitation of the Delta(1232)-resonance
• Chiral Perturbation Theory and Baryon Properties
• Global Analysis of Nucleon Strange Form Factors at Low $Q^2$
• Gamma-Z box contributions to parity violating elastic e-p scattering
• Dispersive contributions to $e^{+}p/e^{-}p$ cross section ratio in forward regime
• Forward sum rule for the $2\gamma$-exchange correction to the charge radius extraction from elastic electron scattering