A comprehensive theory framework for perturbative calculations of δC in superallowed beta decays
Abstract
The present high precision determination of |Vud| from superallowed beta decays of JP=0+, T=1 nuclei is largely built on top of the ``standard'' calculation of the isospin breaking correction δC to the Fermi matrix element, which assumes the splitting δC=δC1+δC2, where δC1 and δC2 represent the ``isospin mixing'' correction and the ``radial mismatch'' correction, respectively. In this paper I show that this formalism violates the rule of nucleon basis independence, similar to the gauge invariance requirement in quantum field theory, therefore its outcome is inevitably subject to uncontrolled systematic errors. I further argue that the perturbative formalism is the only approach that allows the computation of δC at the precision level required for the test of the Cabibbo unitarity. Advancing from existing literature, I develop the full ``generating function approach'' to compute δC perturbatively, with connections to nuclear mass splittings and the isospin breaking in nuclear charge radii as theory benchmarks.
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BibTeX
@misc{seng2026comprehensive,
title = {{A comprehensive theory framework for perturbative calculations of $δ_C$ in superallowed beta decays}},
author = {Chien-Yeah Seng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20448},
eprint = {2609.20448},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20448},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A comprehensive theory framework for perturbative calculations of δ_C in superallowed beta decays
AU - Chien-Yeah Seng
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20448
UR - https://arxiv.org/abs/2609.20448
AB - The present high precision determination of |V_ud| from superallowed beta decays of J^P=0^+, T=1 nuclei is largely built on top of the ``standard'' calculation of the isospin breaking correction δ_C to the Fermi matrix element, which assumes the splitting δ_C=δ_C1+δ_C2, where δ_C1 and δ_C2 represent the ``isospin mixing'' correction and the ``radial mismatch'' correction, respectively. In this paper I show that this formalism violates the rule of nucleon basis independence, similar to the gauge invariance requirement in quantum field theory, therefore its outcome is inevitably subject to uncontrolled systematic errors. I further argue that the perturbative formalism is the only approach that allows the computation of δ_C at the precision level required for the test of the Cabibbo unitarity. Advancing from existing literature, I develop the full ``generating function approach'' to compute δ_C perturbatively, with connections to nuclear mass splittings and the isospin breaking in nuclear charge radii as theory benchmarks.
ER -