Effective Lagrangian approach to neutrinoless double beta decay and neutrino masses

TL;DR

This paper classifies lepton number violating operators affecting neutrinoless double beta decay and neutrino masses, analyzing their contributions, dimensions, and implications for underlying models and experimental searches.

Contribution

It provides a systematic classification of LNV operators with different chiralities and their impact on neutrinoless double beta decay and neutrino mass generation.

Findings

Each chirality case has a unique lowest-dimension LNV operator.

Neutrino masses can be generated at different loop levels depending on operator structure.

Comparison of decay rates and neutrino masses can reveal the underlying effective scenario.

Abstract

Neutrinoless double beta ($0\nu\beta\beta$) decay can in general produce electrons of either chirality, in contrast with the minimal Standard Model (SM) extension with only the addition of the Weinberg operator, which predicts two left-handed electrons in the final state. We classify the lepton number violating (LNV) effective operators with two leptons of either chirality but no quarks, ordered according to the magnitude of their contribution to \znbb decay. We point out that, for each of the three chirality assignments, $e_Le_L, e_Le_R$ and $e_Re_R$, there is only one LNV operator of the corresponding type to lowest order, and these have dimensions 5, 7 and 9, respectively. Neutrino masses are always induced by these extra operators but can be delayed to one or two loops, depending on the number of RH leptons entering in the operator. Then, the comparison of the $0\nu\beta\beta$ decay rate and neutrino masses should indicate the effective scenario at work, which confronted with the LHC searches should also eventually decide on the specific model elected by nature. We also list the SM additions generating these operators upon integration of the heavy modes, and discuss simple realistic examples of renormalizable theories for each case.