Neutrinoless double beta decay, neutrino mass and bilinear R-parity breaking supersymmetry

Neutrinoless double beta ($\text{znbb}$) decay violates lepton number; its absence stringently constrains the parameters of theories beyond the standard model in which the neutrino has a Majorana mass. R-parity violating weak-scale supersymmetry is a prominent example of such models. Double beta decay in supersymmetry with explicit bilinear R-parity breaking is discussed and current limits on the $\text{znbb}$ decay half life of ${}^{76}$Ge are used to extract upper bounds on the R-parity breaking parameters of the first generation. Moreover, it is shown that the effective Majorana neutrino mass, measured in $\text{znbb}$ decay, is non-zero once the 1-loop corrections are taken into account even for the case of perfect alignment ($\Lambda_i:=(< {\tilde \nu}_i > \mu - v_1 \epsilon_i) \equiv 0$) among the R-parity violating parameters.