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

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.