Investigation of Lorentz symmetry violation in double beta decay

Abstract

Effects of Lorentz symmetry violation can be investigated at low energy scale in double-beta decay, for example by a detailed analysis of the summed energy electrons spectra emitted in the two-neutrino double beta decay mode. In this work we present new calculations of the phase space factors (G2ν) and their deviations due to Lorentz violation effects (δG2ν) for this decay mode, which lead to improved theoretical predictions of these spectra. In our method we use Fermi functions built up from electron wave functions obtained as solutions of a Dirac equation in a Coulomb-type potential given by a realistic distribution of the protons in the daughter nucleus and with inclusion of finite nuclear size (FNS) and screening effects. In the phase space factors formulas kinetic factors are also introduced, which were omitted in previous analyzes. Our study is done for four experimentally interesting nuclei, namely 48Ca, 82Se, 100Mo and 136Xe. We found that the differences between the G2ν and δG2ν values calculated with our method and with previous methods, where approximate Fermi functions were used, raise generally with the atomic number Z and amount up to 28%. Our results are of interest for investigations of Lorentz violation (LV) in DBD experiments and can lead to relevant improvements of the actual constraints on the (aof(3))00 coefficient, which appears in the Standard-Model Extension (SME) theory and controls the LV effects associated with the time-like component of the countershaded operator.