Towards $\it{ab}$-$\it{initio}$ nuclear theory calculations of $\delta_\mathrm{C}$

TL;DR

This paper introduces a new theoretical framework for calculating the isospin-symmetry breaking correction $ ext{delta}_C$ in nuclear beta decays, linking it to measurable nuclear radii and proposing an ab-initio computational strategy.

Contribution

It develops a novel theory connecting $ ext{delta}_C$ to nuclear radii and outlines an ab-initio calculation method using the Lanczos algorithm.

Findings

Establishes a connection between $ ext{delta}_C$ and electroweak nuclear radii.

Proposes a new ab-initio calculation strategy for $ ext{delta}_C$.

Provides a theoretical basis for experimental validation of $ ext{delta}_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.