The $\lambda$ mechanism of the $0\nu\beta\beta$-decay

TL;DR

This paper investigates the $ ext{λ}$ mechanism of neutrinoless double beta decay within left-right symmetric models, revisiting formalism, calculating nuclear matrix elements, and discussing how to distinguish it from the standard light neutrino mass mechanism.

Contribution

The study provides a detailed formalism including higher order nucleon current terms and calculates nuclear matrix elements for the $ ext{λ}$ mechanism, offering insights into distinguishing mechanisms in $0 uetaeta$ decay.

Findings

The $ ext{λ}$ mechanism can potentially be distinguished from the standard mechanism in multiple nuclei.

Nuclear matrix elements are calculated within quasiparticle random phase approximation with isospin symmetry restoration.

The conventional light neutrino mass mechanism dominates under certain neutrino mixing assumptions.

Abstract

The $\lambda$ mechanism ($W_L$-$W_R$ exchange) of the neutrinoless double beta decay ($0\nu\beta\beta$-decay), which has origin in left-right symmetric model with right-handed gauge boson at TeV scale, is investigated. The revisited formalism of the $0\nu\beta\beta$-decay, which includes higher order terms of nucleon current, is exploited. The corresponding nuclear matrix elements are calculated within quasiparticle random phase approximation with partial restoration of the isospin symmetry for nuclei of experimental interest. A possibility to distinguish between the conventional light neutrino mass ($W_L$-$W_L$ exchange) and $\lambda$ mechanisms by observation of the $0\nu\beta\beta$-decay in several nuclei is discussed. A qualitative comparison of effective lepton number violating couplings associated with these two mechanisms is performed. By making viable assumption about the seesaw type mixing of light and heavy neutrinos with the value of Dirac mass $m_D$ within the range $1~ \textrm{MeV} < m_D < 1~ \textrm{GeV}$, it is concluded that there is a dominance of the conventional light neutrino mass mechanism in the decay rate.