Systematic decomposition of the neutrinoless double beta decay operator

Abstract

We discuss the systematic decomposition of the dimension nine neutrinoless double beta decay operator, focusing on mechanisms with potentially small contributions to neutrino mass, while being accessible at the LHC. We first provide a (d = 9 tree-level) complete list of diagrams for neutrinoless double beta decay. From this list one can easily recover all previously discussed contributions to the neutrinoless double beta decay process, such as the celebrated mass mechanism or "exotics", such as contributions from left-right symmetric models, R-parity violating supersymmetry and leptoquarks. More interestingly, however, we identify a number of new possibilities which have not been discussed in the literature previously. Contact to earlier works based on a general Lorentz-invariant parametrisation of the neutrinoless double beta decay rate is made, which allows, in principle, to derive limits on all possible contributions. We furthermore discuss possible signals at the LHC for mediators leading to the short-range part of the amplitude with one specific example. The study of such contributions would gain particular importance if there were a tension between different measurements of neutrino mass such as coming from neutrinoless double beta decay and cosmology or single beta decay.

Double beta decay and neutrino mass models

“…Obviously, a four-loop diagram, additionally suppressed by m 2 u m 2 d m 2 e /Λ 5 LNV , can produce only tiny neutrino masses, which are many orders of magnitude below of what is required to explain oscillation data [34]. Nevertheless, the black box theorem, together with the general decomposition of the d = 9 double beta decay operator published in [31], defines the basic idea of our current paper. Indeed we find that all "models" listed in [31] produce neutrino masses at or below the 4-loop order as demanded by the theorem.…”

“…In this paper we discuss the relation between possible models for short-range contribution to 0νββ decay and the neutrino mass-generation mechanism. Our study is based on the complete list of possible decompositions of the d = 9 (short-range) double beta decay operator given in [31]. The general decomposition list given in [31] is equivalent, in principle, to defining all models which can give a contribution to double beta decay, and the black box theorem, see below, guarantees that all these models will produce Majorana neutrino masses at or below four-JHEP05(2015)092 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 Figure 1.…”

“…Our study is based on the complete list of possible decompositions of the d = 9 (short-range) double beta decay operator given in [31]. The general decomposition list given in [31] is equivalent, in principle, to defining all models which can give a contribution to double beta decay, and the black box theorem, see below, guarantees that all these models will produce Majorana neutrino masses at or below four-JHEP05(2015)092 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000 Figure 1. Schematic explanation of the black box theorem: the theorem guarantees that, once 0νββ decay has been observed, Majorana neutrino masses will be generated, independent of the underlying model, at the latest at the four-loop level.…”

“…We can then discuss the expected size of the two contributions to 0νββ: (1) the d = 9 short-range contribution O d=9 and (2) the contribution from the neutrino mass mechanism m ν which is radiatively induced in the corresponding models and conclude model-by-model, which one of the two is expected to dominate. Given that the list of [31] is tree-level complete, our discussion is quite general and covers actually models of neutrino mass from tree-level models to 4-loop models.…”

“…Nevertheless, the black box theorem, together with the general decomposition of the d = 9 double beta decay operator published in [31], defines the basic idea of our current paper. Indeed we find that all "models" listed in [31] produce neutrino masses at or below the 4-loop order as demanded by the theorem.…”