Constraining theoretical corrections to Gamow-Teller transition rates

We propose two novel constraints for the theoretical corrections to Gamow-Teller transition rates. The first, derived from a two-level model, predicts forbidden regions within the plane defined by the isospin-mixing correction δC1 and the ratio η of the isospin-symmetry Gamow-Teller matrix elements between the upper and lower admixed states. It serves as a filter for the theoretical calculations, particularly effective for small values of |η|. The other employs experimental ft values, incorporating the upper admixed states, and exploits mirror symmetry to eliminate isospin-invariant and nuclear structure-independent quantities presented in the master decay formula. Within the standard model, this approach offers an alternative means for collectively testing the theoretical corrections for isospin and radiative effects beyond tree level. Additionally, it enables an experimental extraction of η2, yielding a sensitive test for the isospin-conserving component of the nuclear Hamiltonian. Our investigation also reveals a substantial cancellation among radiative correction contributions in these tests, suggesting that these corrections are largely invariant under mirror symmetry. Importantly, the remarkable consistency of the nuclear structure corrections achieved in this axial-vector process provides a robust validation for the underlying theoretical approach in the purely vector process, especially the superallowed 0+→0+ nuclear β decay - the most accurate tool for extracting the Vud matrix element.