$R$-parity-conserving supersymmetry, neutrino mass, and neutrinoless double beta decay

We consider contributions of $R$-parity-conserving softly broken supersymmetry (SUSY) to neutrinoless double beta $\left(0\mathrm{}\nu \beta \beta \right)$ decay via the $\left(B-L\right)$-violating sneutrino mass term. The latter is a generic ingredient of any weak-scale SUSY model with a Majorana neutrino mass. The new $R$-parity-conserving SUSY contributions to $0\nu \beta \beta$ are realized at the level of box diagrams. We derive the effective Lagrangian describing the SUSY-box mechanism of $0\nu \beta \beta$ decay and the corresponding nuclear matrix elements. The one-loop sneutrino contribution to the Majorana neutrino mass is also derived. Given the data on the $0\nu \beta \beta$ decay half-life of ${}^{76}$Ge and the neutrino mass we obtain constraints on the $\left(B-L\right)$-violating sneutrino mass. These constraints leave room for accelerator searches for certain manifestations of the second and third generation $\left(B-L\right)$-violating sneutrino mass term, but are most probably too tight for first generation $\left(B-L\right)$-violating sneutrino masses to be searched for directly.