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Influence of the recoil-order and radiative correction on the beta decay correlation coefficients in mirror decays

Measurements of the beta decay correlation coefficients in nuclear decay aim for a precision below $1\%$ and theoretical predictions should follow this trend. In this work, the influence of the two dominant Standard Model correction terms, i.e. the recoil-order and the radiative correction, are studied for the most commonly measured beta correlations, i.e. the $β$-asymmetry parameter ($A_β$) and the $β-ν$ angular correlation ($a_{βν}$). The recoil-order correction is calculated with the well-known Holstein formalism using the impulse approximation to evaluate experimentally inaccessible form factors. For the $β-ν$ angular correlation previously unpublished, semi-analytical radiative correction values are tabulated. Results are presented for the mirror beta decays up to $A=45$. We examine the effect of both corrections and provide a comparison between different isotopes. This comparison will help planning, analysing, and comparing future experimental efforts.