$0\nu\beta\beta$ to the first $2^+$ state with two-nucleon mechanism for L-R symmetric model

TL;DR

This paper develops a formalism to calculate neutrinoless double beta decay rates to the first 2+ excited states within the L-R symmetric model, considering hadronic currents and nuclear effects.

Contribution

It introduces a new formalism for decay rate calculations to excited states in the L-R symmetric model, including NLO hadronic currents and nuclear matrix elements.

Findings

Nuclear matrix elements vary by nucleus and are smaller than those for ground state decay.

The phase space factors are computed using numerical electron wave functions.

Current experimental data impose constraints on the L-R symmetric model.

Abstract

We develop the formalism for calculating the decay rate of neutrinoless double beta decay to the $2^+$ excited states within L-R symmetric model. We consider the effects from induced hadronic currents up to NLO. The QRPA 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.