# SPIN 2018

9-14 September 2018
University of Ferrara
Europe/Rome timezone
23RD INTERNATIONAL SPIN SYMPOSIUM

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

11 Sep 2018, 16:40
20m

### A10

Parallel Sessions Low Energy Spin Physics with Lepton, Photon and Hadron Probes

### Speaker

Dr Mikhail Gorshteyn (Mainz University)

### Description

We propose a novel dispersion relations-based evaluation of the $\gamma W$-box correction to the universal radiative correction $\Delta_R^V$ to the neutron and nuclear $\beta$ decay. This correction is the main source of the theoretical uncertainty in extracting the value of $V_{ud}$ from those decay processes. We relate the needed input into the dispersion integral to the data on neutrino and antineutrino scattering. This leads to a significant shift in the central value accompanied by a reduction of the uncertainty due to hadronic structure. Applied to the superallowed nuclear $\beta$ decays, these two effect create a tension in the first row CKM unitarity if assuming all other ingredients remain unchanged, $|V_{ud}|^2+|V_{us}|^2+|V_{ub}|^2=0.9983(4)$. We discuss further ways to improve the precision of the calculation of the $\gamma W$-box, and point out that dispersion relations provide a unified formalism for hadronic and nuclear corrections to nuclear beta decay.

### Primary author

Dr Mikhail Gorshteyn (Mainz University)

 Slides