Radiative corrections to semileptonic beta decays: Progress and challenges

TL;DR

This paper reviews recent advances in calculating electroweak radiative corrections for semileptonic decays, emphasizing a method that separates calculable and incalculable parts, improving precision in Standard Model tests.

Contribution

It revitalizes Sirlin's representation for clearer separation of perturbative and non-perturbative contributions, enhancing the accuracy of radiative correction calculations.

Findings

Improved precision in radiative corrections for pion, kaon, neutron, and nuclei decays.

Systematic approach using dispersion relations and lattice QCD.

Identification of unresolved issues and future research directions.

Abstract

We review some recent progress in the theory of electroweak radiative corrections in semileptonic decay processes. The resurrection of the so-called Sirlin's representation based on current algebra relations permits a clear separation between the perturbatively-calculable and incalculable pieces in the $\mathcal{O}(G_F\alpha)$ radiative corrections. The latter are expressed as compact hadronic matrix elements that allow systematic non-perturbative analysis such as dispersion relation and lattice QCD. This brings substantial improvements to the precision of the electroweak radiative corrections in semileptonic decays of pion, kaon, free neutron and $J^P=0^+$ nuclei that are important theory inputs in precision tests of the Standard Model. Unresolved issues and future prospects are discussed.