An improved calculation of the isospin-symmetry-breaking corrections to superallowed Fermi beta decay

TL;DR

This paper presents improved shell-model calculations of isospin-symmetry-breaking corrections in superallowed Fermi beta decay, including core orbitals and updated radiative corrections, leading to more consistent Ft values and CKM matrix unitarity.

Contribution

The study introduces the inclusion of core orbitals in calculations and reorganizes radiative corrections, enhancing the accuracy of superallowed beta decay analyses.

Findings

Corrected Ft values are now statistically consistent.

CKM matrix unitarity is confirmed with the new corrections.

Anomalous 46V result is resolved.

Abstract

We report new shell-model calculations of the isospin-symmetry-breaking correction to superallowed nuclear beta decay. The most important improvement is the inclusion of core orbitals, which are demonstrated to have a significant impact on the mismatch in the radial wave functions of the parent and daughter states. We determine which core orbitals are important to include from an examination of measured spectroscopic factors in single-nucleon pick-up reactions. We also examine the new radiative-correction calculation by Marciano and Sirlin and, by a simple reorganization, show that it is possible to preserve the conventional separation into a nucleus-independent inner radiative term and a nucleus-dependent outer term. We tabulate new values for the three theoretical corrections for twenty superallowed transitions, including the thirteen well-studied cases. With these new correction terms the corrected Ft values for the thirteen cases are statistically consistent with one another and the anomalousness of the 46V result disappears. These new calculations lead to a lower average Ft value and a higher value of Vud. The sum of squares of the top-row elements of the CKM matrix now agrees exactly with unitarity.