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

Measurements of the $\ensuremath{\beta}$ 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 $\ensuremath{\beta}$ correlations, i.e., the $\ensuremath{\beta}$-asymmetry parameter (${A}_{\ensuremath{\beta}}$) and the $\ensuremath{\beta}\text{\ensuremath{-}}\ensuremath{\nu}$ angular correlation (${a}_{\ensuremath{\beta}\ensuremath{\nu}}$). The recoil-order correction is calculated with the well-known Holstein formalism using the impulse approximation to evaluate experimentally undetermined form factors. For the $\ensuremath{\beta}\text{\ensuremath{-}}\ensuremath{\nu}$ angular correlation previously unpublished, semianalytical radiative correction values are tabulated. Results are presented for the mirror $\ensuremath{\beta}$ decays up to $A=45$. We examine the effect of both corrections and provide a comparison between different isotopes. This comparison will help planning, analyzing, and comparing future experimental efforts.