0νββ decay to the first 2+ state with a two-nucleon mechanism for a L−R …

We develop the formalism for calculating the decay rate of neutrinoless double $\ensuremath{\beta}$ decay to the ${2}^{+}$ excited states within the L-R symmetric model. We consider the effects from induced hadronic currents up to next to leading order. The quasiparticle random phase approximation method in a spherical basis is adopted for the nuclear many-body calculation and the corresponding nuclear matrix elements are given. Also, the phase space factors are obtained with numerical electron wave functions. Our results suggest that the nuclear matrix elements are nucleus dependent and they are generally smaller than that of the decay to the ground states. And finally, we give a naive analysis of how current experiment data constrains the L-R symmetric model.