Radiative and exchange corrections for two-neutrino double-beta decay

Abstract

We investigate the impact of radiative and atomic exchange corrections in the two-neutrino double-beta ($2\nu \beta \beta$)-decay of ${}^{100}$Mo. In the calculation of the exchange correction, the electron wave functions are obtained from a modified Dirac-Hartree-Fock-Slater self-consistent framework that ensures orthogonality between continuum and bound states. The atomic exchange correction causes a steep increase in the low-energy region of the single-electron spectrum, consistent with previous studies on $\beta$-decay, while the radiative correction primarily accounts for a 5\% increase in the decay rate of ${}^{100}$Mo. When combined, the radiative and exchange effects cause a leftward shift of approximately 10 keV in the maximum of the summed electron spectrum. This shift may impact current constraints on parameters governing potential new physics scenarios in $2\nu \beta \beta$-decay. The exchange and radiative corrections are introduced on top of our previous description of $2\nu \beta \beta$-decay, where we used a Taylor expansion for the lepton energy parameters within the nuclear matrix elements denominators. This approach results in multiple components for each observable, controlled by the measurable ${\xi }_{31}$ and ${\xi }_{51}$ parameters. We explore the effects of different ${\xi }_{31}$ and ${\xi }_{51}$ values, including their experimental measurements, on the total corrected spectra. These refined theoretical predictions can serve as precise inputs for double-beta decay experiments investigating standard and new physics scenarios within $2\nu \beta \beta$-decay.

12 pages, 5 figures

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