Isospin corrections for superallowed Fermi beta decay in self-consistent relativistic random phase approximation approaches

TL;DR

This paper uses relativistic RPA methods to calculate isospin symmetry-breaking corrections in superallowed Fermi beta decay, confirming the constancy of corrected ft values and discussing implications for V_{ud} and CKM unitarity.

Contribution

It introduces a self-consistent relativistic RPA approach to accurately compute isospin corrections, emphasizing the importance of Coulomb mean field treatment.

Findings

Corrections δ_c are sensitive to Coulomb mean field treatment.

Corrected ft values are consistent across different effective interactions.

Implications for V_{ud} and CKM matrix unitarity are analyzed.

Abstract

Self-consistent random phase approximation (RPA) approaches in the relativistic framework are applied to calculate the isospin symmetry-breaking corrections $\delta_c$ for the $0^+\to0^+$ superallowed transitions. It is found that the corrections $\delta_c$ are sensitive to the proper treatments of the Coulomb mean field, but not so much to specific effective interactions. With these corrections $\delta_c$, the nucleus-independent $\mathcal{F}t$ values are obtained in combination with the experimental $ft$ values in the most recent survey and the improved radiative corrections. It is found that the constancy of the $\mathcal{F}t$ values is satisfied for all effective interactions employed. Furthermore, the element $V_{ud}$ and unitarity of the Cabibbo-Kobayashi-Maskawa matrix are discussed.