Towards $ab$-$initio$ nuclear theory calculations of ${\delta }_{\mathrm{C}}$

Abstract

We propose a new theory framework to study the isospin-symmetry breaking correction ${\delta }_{\text{C}}$ in superallowed nuclear beta decays, crucial for the precise determination of $|V_{ud}|$. Based on a general assumptions of the isovector dominance in ISB interactions, we construct a set of functions $F_{T_z}$ which involve nuclear matrix elements of isovector monopole operators and the nuclear Green's function. Via the functions $F_{T_z}$, a connection of ${\delta }_{\text{C}}$ to measurable electroweak nuclear radii is established, providing an experimental gauge of the theory accuracy of ${\delta }_{\text{C}}$. We outline a strategy to perform ab-initio calculations of $F_{T_z}$ based on the Lanczos algorithm, and discuss its similarity with other nuclear-structure-dependent inputs in nuclear beta decays.

Comments: Version accepted by PRC