Isospin-breaking corrections to superallowed Fermi beta-decay in isospin- and angular-momentum-projected nuclear Density Functional Theory

TL;DR

This paper systematically calculates isospin-breaking corrections to superallowed Fermi beta-decays using a sophisticated nuclear density functional theory, providing precise estimates that support CKM matrix unitarity within 0.1%.

Contribution

It introduces a comprehensive self-consistent framework for calculating isospin-breaking effects in superallowed beta-decays, including new analyses of uncertainties and application to a broad range of nuclei.

Findings

Calculated corrections for nuclei from A=10 to 98.

Extended analysis to mirror nuclei from A=11 to 49.

Confirmed CKM matrix unitarity with better than 0.1% precision.

Abstract

Background: The superallowed beta-decay rates provide stringent constraints on physics beyond the Standard Model of particle physics. To extract crucial information about the electroweak force, small isospin-breaking corrections to the Fermi matrix element of superallowed transitions must be applied. Purpose: We perform systematic calculations of isospin-breaking corrections to superallowed beta-decays and estimate theoretical uncertainties related to the basis truncation, time-odd polarization effects related to the intrinsic symmetry of the underlying Slater determinants, and to the functional parametrization. Methods: We use the self-consistent isospin- and angular-momentum-projected nuclear density functional theory employing two density functionals derived from the density independent Skyrme interaction. Pairing correlations are ignored. Our framework can simultaneously describe various effects that impact matrix elements of the Fermi decay: symmetry breaking, configuration mixing, and long-range Coulomb polarization. Results: The isospin-breaking corrections to the I=0+,T=1 --> I=0+,T=1 pure Fermi transitions are computed for nuclei from A=10 to A=98 and, for the first time, to the Fermi branch of the I,T=1/2 --> I,T=1/2 transitions in mirror nuclei from A=11 to A=49. We carefully analyze various model assumptions impacting theoretical uncertainties of our calculations and provide theoretical error bars on our predictions. Conclusions: The overall agreement with empirical isospin-breaking corrections is very satisfactory. Using computed isospin-breaking corrections we show that the unitarity of the CKM matrix is satisfied with a precision better than 0.1%.