Double Beta Decay and the Majorana Mass of the Electron Neutrino

Abstract

We have calculated the two-neutrino and no-neutrino, lepton-number-nonconserving double beta decay rates for ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$ and ${}_{}{}^{82}{}_{}{}^{}\mathrm{Se}$. Our result for the two-neutrino decay of ${}_{}{}^{82}{}_{}{}^{}\mathrm{Se}$ is in agreement with a recent cloud-chamber measurement and thus in disagreement with the geochemical determination. We find that a constraint on the Majorana mass of the electron neutrino of ${〈m〉}_{\nu }\gtrsim 15$ eV follows from the comparison of our calculations and the experimental limits on the neutrinoless decays of ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$ and ${}_{}{}^{82}{}_{}{}^{}\mathrm{Se}$.