**W. Satula, J. Dobaczewski, W. Nazarewicz, and T.R. Werner**

**Background**- The superallowed -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 -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 pure Fermi transitions are computed for nuclei from =10 to =98 and, for the first time, to the Fermi branch of the transitions in mirror nuclei from =11 to =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%.

- Introduction
- The model
- Isospin- and angular-momentum-projected DFT approach
- The choice of Skyrme interaction
- Numerical details

- ISB corrections to the superallowed
Fermi transitions
- Shape-current orientation
- Nearly degenerate -orbitals
- Theoretical uncertainties and error analysis
- The survey of ISB corrections in nuclei
- Confidence level test
- ISB corrections in nuclei

- ISB corrections to the Fermi matrix elements in mirror-symmetric nuclei
- The ISB correction to the Fermi decay branch in Cl
- Summary and perspectives
- Bibliography
- About this document ...