Dispersive formalism for the nuclear structure correction $\delta_\mathrm{NS}$ to the $\beta$ decay rate
- Resource Type
- Working Paper
- Authors
- Seng, Chien-Yeah; Gorchtein, Mikhail
- Source
- Phys. Rev. C 107, 035503 (2023)
- Subject
- Nuclear Theory
High Energy Physics - Experiment
High Energy Physics - Lattice
High Energy Physics - Phenomenology
Nuclear Experiment
- Language
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.
Comment: Version accepted by Physical Review C