Hadronic effects in M{\o}ller scattering at NNLO

TL;DR

This paper calculates two-loop electroweak corrections to polarized Moller scattering, showing that hadronic effects are well-controlled and estimating the theoretical uncertainty to be significantly smaller than experimental precision.

Contribution

The study provides a detailed analysis of NNLO electroweak corrections and incorporates hadronic effects via the weak mixing angle, reducing theoretical uncertainties for Moller scattering.

Findings

Finite $Q^2$ corrections are well under control.

Hadronic and QCD corrections introduce a small error in the weak charge.

Electroweak uncertainty is estimated to be five times smaller than experimental precision.

Abstract

Two-loop electroweak corrections to polarized Moller scattering are studied in two different schemes at low energies. We find the finite $Q^2$ corrections to be well under control. The hadronic and perturbative QCD corrections to the $\gamma Z$ two-point function are incorporated through the weak mixing angle at low energies, which introduce an error of $0.08\times10^{-3}$ in the weak charge of the electron $Q^e_W$. Furthermore, by studying the scheme dependence, we obtain an estimate of the current perturbative electroweak uncertainty, $\delta Q^e_W\approx0.23\times10^{-3}$, which is five times smaller than the precision estimated for the MOLLER experiment $(\delta Q_W^e=1.1\times10^{-3})$. Future work is possible to reduce the theory error further.