Nuclear shell model study of neutrinoless double beta decay under Left-Right symmetric model

Abstract

We use the large scale nuclear shell model to calculate the nuclear matrix elements for the neutrino mediated neutrinoless double beta decay within the Left-Right symmetric model for four nuclei: \(^{76}\)Ge, \(^{82}\)Se, \(^{130}\)Te and \(^{136}\)Xe. We perform a systematic analysis on the general magnitude of different terms for related mechanisms. For the \(\eta\) mechanism, we find that the weak magnetism \(R\) term dominates the decay rate while the \(p\)-wave effect is suppressed. While for the \(\lambda\) mechanism, the \(\omega\) and the \(q\) terms are with equal importance. For the latter \(q\) term, important contributions from weak-magnetism MM part are observed. Finally, we give the constraints on the new physics parameters \(m_{\beta\beta}\), \(\lambda\) and \(\eta\) from current experiments.