Isospin-breaking corrections to superallowed Fermiβdecay in isospin- and angular-momentum-projected nuclear density functional theory

Abstract

Background: Superallowed $\ensuremath{\beta}$-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 $\ensuremath{\beta}$ decays and estimate theoretical uncertainties related to the basis truncation, to 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: Isospin-breaking corrections to the $I={0}^{+}$, $T=1\ensuremath{\rightarrow}I={0}^{+}$, $T=1$ pure Fermi transitions are computed for nuclei from $A=10$ to $A=98$ and, for the first time, to the Fermi branch of the $I,T=1/2\ensuremath{\rightarrow}I$, $T=1/2$ 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 of better than 0.1$%$.