Theory of QED radiative corrections to neutrino scattering at accelerator energies

TL;DR

This paper develops a theoretical framework using effective field theory to accurately calculate QED radiative corrections in neutrino scattering, crucial for precise neutrino oscillation measurements at accelerator energies.

Contribution

It introduces a factorization approach for QED corrections in neutrino interactions, separating soft, collinear, and hard functions, and analyzes their numerical impact on cross sections.

Findings

QED corrections factorize into soft, collinear, and hard functions.

Large logarithms are contained in soft and collinear functions and are computable.

Leading hadronic and nuclear corrections cancel in relevant observables.

Abstract

Control over quantum electrodynamics (QED) radiative corrections is critical for precise determination of neutrino oscillation probabilities from observed (anti)neutrino detection rates. It is particularly important to understand any difference between such corrections for different flavors of (anti)neutrinos in charged-current interactions. We provide theoretical foundations for calculating these corrections. Using effective field theory, the corrections are shown to factorize into soft, collinear, and hard functions. The soft and collinear functions contain large logarithms in perturbation theory but are computable from QED. The hard function parametrizes hadronic structure but is free from large logarithms. Using a simple model for the hard function, we investigate the numerical impact of QED corrections in charged-current (anti)neutrino-nucleon elastic cross sections and cross-section ratios at GeV energies. We consider the implications of mass singularity theorems that govern the lepton-mass dependence of cross sections for sufficiently inclusive observables and demonstrate the cancellation of leading hadronic and nuclear corrections in phenomenologically relevant observables.