On the effective theory of neutrino-electron and neutrino-quark interactions

TL;DR

This paper refines the effective theory of neutrino interactions with electrons and quarks by including higher-order electroweak corrections, providing precise four-fermion coefficients relevant for low-energy neutrino processes.

Contribution

It presents a comprehensive calculation of neutrino interaction coefficients incorporating two-loop matching and three-loop running, improving precision in the effective theory.

Findings

Derived four-fermion coefficients for different flavor thresholds.

Connected low-energy neutrino charge radii to matter effects.

Included higher-order electroweak corrections in the effective theory.

Abstract

We determine the four Fermi effective theory of neutrino interactions within the Standard Model including one-loop electroweak radiative corrections, in combination with the measured muon lifetime and precision electroweak data. Including two-loop matching and three-loop running corrections, we determine lepton coefficients accounting for all large logarithms through relative order $\cal{O}(\alpha \alpha_s)$ and quark coefficients accounting for all large logarithms through ${\cal{O}}(\alpha)$. We present four-fermion coefficients valid in $n_f=3$ and $n_f=4$ flavor quark theories, as well as in the extreme low-energy limit. We relate the coefficients in this limit to neutrino charge radii governing matter effects via forward neutrino scattering on charged particles.