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

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.

Comments: 5 pages, 5 figures, references updated; version submitted to PRL