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

Abstract

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 $\beta$-asymmetry parameter ($A_{\beta }$) and the $\beta -\nu$ angular correlation ($a_{\beta \nu }$). The recoil-order correction is calculated with the well-known Holstein formalism using the impulse approximation to evaluate experimentally inaccessible form factors. For the $\beta -\nu$ angular correlation previously unpublished, semi-analytical radiative correction values are tabulated.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.

arXiv comment16 pages, 10 figures

References in corpus (26)

• Probing Novel Scalar and Tensor Interactions from (Ultra)Cold Neutrons to the LHC
• The neutron and its role in cosmology and particle physics
• New physics searches in nuclear and neutron $\beta$ decay
• Radiative Corrections to Neutron and Nuclear Beta Decays Revisited
• Measurement of the Weak Axial-Vector Coupling Constant in the Decay of Free Neutrons Using a Pulsed Cold Neutron Beam
• Beta Decays and Non-Standard Interactions in the LHC Era
• Dispersive Evaluation of the Inner Radiative Correction in Neutron and Nuclear $\beta$-decay
• Determination of |Vud| from nuclear mirror transitions
• Joint lattice QCD - dispersion theory analysis confirms the quark-mixing top-row unitarity deficit
• High precision analytical description of the allowed $\beta$ spectrum shape
• Ft values of the T = 1/2 mirror beta transitions
• Standard Model $\mathcal{O}(\alpha )$ renormalization of $g_A$ and its impact on new physics searches
• Comprehensive analysis of beta decays within and beyond the Standard Model
• $\gamma W$-box Inside-Out: Nuclear Polarizabilities Distort the Beta Decay Spectrum
• Measurement of the Beta-Neutrino Correlation of Sodium-21 using Shakeoff Electrons
• Electroweak axial structure functions and improved extraction of the $V_{ud}$ CKM matrix element
• Neutron beta decay in effective field theory
• Neutron Beta-Decay as Laboratory for Test of Standard Model
• Sharpening Low-Energy, Standard-Model Tests via Correlation Coefficients in Neutron Beta-Decay
• Radiative Corrections in Precision Electroweak Physics: a Historical Perspective
• Symmetry violations in nuclear and neutron $\beta$ decay
• Measurement of the neutron $\beta$-asymmetry parameter $A_0$ with ultracold neutrons
• Precision measurement of the $\beta$-asymmetry in spin-polarized ${}^{37}\mathrm{K}$ decay
• Precision measurements with LPCTrap at GANIL
• Radiative tritium beta-decay and the neutrino mass
• Consistent description of angular correlations in $\beta$ decay for Beyond Standard Model physics searches

Cited by in corpus (2)

• $\mathcal{F}t$ values of the mirror $\beta$ transitions and the weak magnetism induced current in allowed nuclear $\beta$ decay
• Opportunities and open questions in modern $\beta$ decay