Reduced hadronic uncertainty in the determination of $V_{ud}$

TL;DR

This paper refines the calculation of a key radiative correction in beta decay using dispersion relations, reducing hadronic uncertainties and updating the value of |V_{ud}|, which impacts CKM unitarity tests.

Contribution

It introduces a dispersive approach to evaluate the hadronic $oxdot$-contribution, leading to a more precise determination of $ ext{V}_{ud}$ with reduced uncertainties.

Findings

Updated $ ext{V}_{ud}$ value: 0.97366(15)

Reduced hadronic uncertainty in $ ext{V}_{ud}$ determination

Highlights potential tension with CKM unitarity

Abstract

We analyze the universal radiative correction $\Delta_R^V$ to neutron and superallowed nuclear $\beta$ decay by expressing the hadronic $\gamma W$-box contribution in terms of a dispersion relation, which we identify as an integral over the first Nachtmann moment of the $\gamma W$ interference structure function $F_3^{(0)}$. By connecting the needed input to existing data on neutrino and antineutrino scattering, we obtain an updated value of $\Delta_R^V = 0.02467(22)$, wherein the hadronic uncertainty is reduced. Assuming other Standard Model theoretical calculations and experimental measurements remain unchanged, we obtain an updated value of $|V_{ud}| = 0.97366(15)$, raising tension with the first row CKM unitarity constraint. We comment on ways current and future experiments can provide input to our dispersive analysis.