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arXiv · 2211.10214

Dispersive formalism for the nuclear structure correction $\delta_\mathrm{NS}$ to the $\beta$ decay rate

Chien-Yeah Seng·Mikhail Gorchtein
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Abstract

We analyze the axial $\gamma W$-box diagram for $I(J^P)=1(0^+)$ nuclei and provide a dispersion representation of the nuclear-structure correction $\delta_\text{NS}$ including its energy-dependent part. We also summarize useful isospin rotation formula and representations in nuclear theory that could facilitate the calculation of the parity-odd nuclear structure function $F_3(\nu,Q^2)$. They provide a rigorous theory framework for the future, high-precision calculation of the nuclear structure correction $\delta_\text{NS}$ necessary for the extraction of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ud}|$ from superallowed nuclear $\beta$ decays.

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Chien-Yeah Seng, Mikhail Gorchtein. 2022-11-18. Dispersive formalism for the nuclear structure correction $\delta_\mathrm{NS}$ to the $\beta$ decay rate. https://doi.org/10.1103/physrevc.107.035503

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