Quantum Monte Carlo calculation of δNS in ¹⁰C using an effective field theory approach

We compute radiative corrections to the superallowed $β$ decay of ¹⁰ C in an effective field theory approach using nuclear matrix elements obtained from quantum Monte Carlo calculations. These corrections are an important ingredient in the extraction of the Cabibbo-Kobayashi-Masakawa quark mixing matrix element Vud, and the role of this work is to illuminate the uncertainties arising from nuclear structure. Our results provide good agreement with both the traditional extraction of Vud, as well as with a more recent evaluation performed using the no-core shell model and a dispersion formalism. The dominant uncertainty in this approach is the presence of two unknown low-energy constants that enter into the relevant nuclear matrix elements. Future determinations of these low-energy constants -- either from QCD or modeling them with two nucleon amplitudes -- would improve the precision of the extraction in this formalism.