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

TL;DR

This study uses quantum Monte Carlo methods with different nuclear interactions to calculate isospin-symmetry-breaking corrections in the superallowed beta decay of carbon-10, finding consistent results across models.

Contribution

First ab initio quantum Monte Carlo calculation of $oldsymbol{ ext{delta}_C}$ in $^{10} ext{C}$ decay using phenomenological and chiral interactions.

Findings

$oldsymbol{ ext{delta}_C}$ ranges from 0.15% to 0.25%.

Results are consistent across different nuclear Hamiltonians.

Uncertainties are sizable, around 34% to 65%.

Abstract

We perform an ab initio quantum Monte Carlo calculation of the isospin-symmetry-breaking correction $\delta_C$ to the superallowed $\beta$ decay of $^{10}{\rm C}$. 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.