Toward <i>ab-initio</i> nuclear theory calculations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>δ</mml:mi><mml:mi>C</mml:mi></mml:msub></mml:math>
Chien-Yeah Seng, Mikhail Gorchtein
Abstract
We propose a theory framework to study the isospin-symmetry breaking correction ${\ensuremath{\delta}}_{\text{C}}$ in superallowed nuclear $\ensuremath{\beta}$ decays, crucial for the precise determination of $|{V}_{ud}|$. Based on a general assumptions of the isovector dominance in isospin-symmetry breaking 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 ${\ensuremath{\delta}}_{\text{C}}$ to measurable electroweak nuclear radii is established, providing an experimental gauge of the theory accuracy of ${\ensuremath{\delta}}_{\text{C}}$. 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 $\ensuremath{\beta}$ decays.