Shell model nuclear matrix elements for double<i>β</i>decay

Abstract

The nuclear matrix elements for the $^{76}$Ge${\ensuremath{\rightarrow}}^{76}$Se, $^{80}$Se${\ensuremath{\rightarrow}}^{80}$Kr, $^{82}$Se${\ensuremath{\rightarrow}}^{82}$Kr, and $^{86}$Kr${\ensuremath{\rightarrow}}^{86}$Sr double \ensuremath{\beta} decay were calculated in a shell-model space consisting of the 0${g}_{9/2}$, 1${p}_{1/2}$, 1${p}_{3/2}$, and 0${f}_{5/2}$ orbitals for both protons and neutrons, and using an effective interaction that contained second-order corrections. For light intermediate neutrinos our results are in agreement with the previously available Los Alamos matrix elements. We have, however, obtained nuclear matrix elements relevant for intermediate heavy neutrinos, Higgs bosons, and supersymmetric particles. Using these matrix elements and the available experimental limits for neutrinoless double \ensuremath{\beta} decay, we obtained the following mass limits: \ensuremath{\Vert}〈${\mathit{m}}_{\mathit{v}}$〉\ensuremath{\Vert}1.1 eV, (〈1/${\mathit{M}}_{\mathrm{N}}$〉${)}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\gtrsim}1.0\ifmmode\times\else\texttimes\fi{}${10}^{5}$ GeV for the light left-handed and heavy right-handed neutrinos, the squark, and the selectron, respectively. We also obtained the limits \ensuremath{\Vert}${g}_{\mathrm{ee}\mathrm{\ensuremath{\Vert}}4\ifmmode\times\else\texttimes\fi{}{10}^{\mathrm{\ensuremath{-}}5}}$ and \ensuremath{\eta}1.3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$ for the majoron neutrino coupling and the admixture of right-handed currents, respectively.