Factorization and resummation of QED radiative corrections for neutron beta decay

TL;DR

This paper presents a detailed two-loop analysis of long-distance QED radiative corrections in neutron beta decay, providing explicit factorization formulas and discussing various theoretical aspects affecting the precision of $|V_{ud}|$ determination.

Contribution

It offers the first comprehensive two-loop calculation of QED corrections in neutron beta decay with explicit factorization formulas and discusses their implications for fundamental parameter extraction.

Findings

Explicit expressions for hard, jet, and soft functions are provided.

The analysis clarifies the impact of QED corrections on $|V_{ud}|$ extraction.

Power corrections and scheme dependencies are thoroughly discussed.

Abstract

Details of the two-loop analysis of long-distance QED radiative corrections to neutron beta decay are presented. Explicit expressions are given for hard, jet, and soft functions appearing in the factorization formula that describes the small mass/large energy limit. Power corrections, cancellation of singularities in the small mass expansion, renormalization scheme dependence, and bound state effects are discussed. The results impact the determination of $|V_{ud}|$ from the measured neutron lifetime.