Neutrinoless double β decay and effective field theory

We analyze neutrinoless double β decay (0νββ decay) mediated by heavy particles from the standpoint of effective field theory. We show how symmetries of the 0νββ-decay quark operators arising in a given particle physics model determine the form of the corresponding effective, hadronic operators. We classify the latter according to their symmetry transformation properties as well as the order at which they appear in a derivative expansion. We apply this framework to several particle physics models, including R-parity violating supersymmetry (RPV SUSY) and the left-right symmetric model (LRSM) with mixing and a right-handed Majorana neutrino. We show that, in general, the pion exchange contributions to 0νββ decay dominate over the short-range four-nucleon operators. This confirms previously published RPV SUSY results and allows us to derive new constraints on the masses in the LRSM. In particular, we show how a nonzero mixing angle ζ in the left-right symmetry model produces a new potentially dominant contribution to 0νββ decay that substantially modifies previous limits on the masses of the right-handed neutrino and boson stemming from constraints from 0νββ decay and vacuum stability requirements.