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.

Version accepted by PRC

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Cited by in corpus (6)

• Ab-initio electroweak corrections to superallowed $\beta$ decays and their impact on $V_{ud}$
• Radiative corrections to superallowed $\beta$ decays in effective field theory
• Data-driven reevaluation of $ft$-values in superallowed $\beta$ decays
• Opportunities and open questions in modern $\beta$ decay
• Cabibbo-Kobayashi-Maskawa unitarity deficit reduction via finite nuclear size
• Pion $\beta$ decay and $\tau \to \pi \pi {\nu }_{\tau }$ beyond leading logarithms