Quantum Monte Carlo calculation of ${\delta }_C$ in the superallowed beta decay of ${}^{10}$C

Abstract

We perform an ab initio quantum Monte Carlo calculation of the isospin-symmetry-breaking correction ${\delta }_C$ to the superallowed $\beta$ decay of ${}^{10}\mathrm{C}$. Using both phenomenological and chiral nuclear interactions, we evaluate the Fermi matrix element and quantify its deviation from the canonical $\sqrt{2}$ value. The resulting ${\delta }_C$ values lie in the range $\approx 0.15$--$0.25\%$ and are consistent, within sizable uncertainties (approximately $34\%$--$65\%$ relative), across Hamiltonians, indicating no statistically significant dependence on the choice of nuclear interaction. The extracted values of $V_{ud}$ are also found to be compatible with current determinations within these uncertainties.

25 pages, 3 figures