The form factor expansion in the precision $\beta$ decay era

TL;DR

This paper critically examines the role of recoil-order approximations in nuclear structure corrections for precision $eta$ decay tests of the Standard Model, highlighting recent advances and open questions.

Contribution

It provides a detailed analysis of recoil-order approximations in nuclear theory and discusses recent progress and unresolved issues in the field.

Findings

Recoil-order approximations are often overlooked in traditional formalisms.

Recent advances in ab initio nuclear theory offer new pathways to reduce uncertainties.

Open questions remain regarding the accuracy and applicability of these approximations.

Abstract

Precision tests of the Standard Model using $\beta$ decay have always relied on a careful choice of transition to minimize residual nuclear structure uncertainties. Following breakthroughs in nucleon-level radiative corrections in the last decade, however, corrections due to nuclear structure are once more a limiting factor in several scenarios. Progress in ab initio nuclear theory provides a path forward, but common recoil-order approximations in traditional formalisms often go unnoticed. Here, we critically examine their origin and address recently resolved and identify open questions.