Field Theory of the Fermi Function

TL;DR

This paper reformulates the Fermi function within a field theory framework, providing a new factorization formula and three-loop anomalous dimensions to improve precision in beta decay calculations.

Contribution

It introduces a field theory approach to the Fermi function, deriving a new factorization formula and calculating three-loop anomalous dimensions for enhanced precision.

Findings

Derived a new factorization formula for QED corrections

Calculated anomalous dimensions through three loops

Resummed logarithmic and $\pi$-enhancements using RG methods

Abstract

The Fermi function $F(Z,E)$ accounts for QED corrections to beta decays that are enhanced at either small electron velocity $\beta$ or large nuclear charge $Z$. For precision applications, the Fermi function must be combined with other radiative corrections and with scale- and scheme-dependent hadronic matrix elements. We formulate the Fermi function as a field theory object and present a new factorization formula for QED radiative corrections to beta decays. We provide new results for the anomalous dimension of the corresponding effective operator complete through three loops, and resum perturbative logarithms and $\pi$-enhancements with renormalization group methods. Our results are important for tests of fundamental physics with precision beta decay and related processes.