Nuclear shell model study of neutrinoless double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> decay within a left-right symmetric model

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