Radiative corrections to superallowed $\beta$ decays in effective field theory

TL;DR

This paper develops an effective field theory approach to evaluate nucleus-dependent radiative corrections in superallowed beta decays, aiming to improve the precision of $V_{ud}$ determinations by reducing theoretical uncertainties.

Contribution

It introduces an EFT framework to systematically calculate the nucleus-dependent correction $ ext{delta}_ ext{NS}$, connecting EFT predictions with dispersive methods and enabling ab-initio calculations.

Findings

EFT predicts dominant terms in $ ext{delta}_ ext{NS}$ based on power counting.

Comparison shows EFT scaling applies even for low-lying states.

Framework facilitates more accurate $V_{ud}$ extraction by addressing key uncertainties.

Abstract

The accuracy of $V_{ud}$ determinations from superallowed $\beta$ decays critically hinges on control over radiative corrections. Recently, substantial progress has been made on the single-nucleon, universal corrections, while nucleus-dependent effects, typically parameterized by a quantity $\delta_\text{NS}$, are much less well constrained. Here, we lay out a program to evaluate this correction from effective field theory (EFT), highlighting the dominant terms as predicted by the EFT power counting. Moreover, we compare the results to a dispersive representation of $\delta_\text{NS}$ and show that the expected momentum scaling applies even in the case of low-lying intermediate states. Our EFT framework paves the way towards ab-initio calculations of $\delta_\text{NS}$ and thereby addresses the dominant uncertainty in $V_{ud}$.