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

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 $V_{ud}$.

arXiv comment7 pages, 1 figure; journal version

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• Pion $\beta$ decay and $\tau \to \pi \pi {\nu }_{\tau }$ beyond leading logarithms