Lepton number violation in supersymmetry and neutrinoless double beta decay

Lepton number violating processes, such as neutrinoless double beta decay, can arise in supersymmetric models either if R-parity is broken or if finite "Majorana" masses for the neutrino and its superpartner, the sneutrino, exist. For the R-parity broken supersymmetric models absence of neutrinoless double beta decay gives stringent limits on R-p parameters. Moreover, it can be shown that finite (B - L) violating masses must exist in any consistent model of supersymmetry in both the neutrino and sneutrino sectors, or in none of them. If R-parity is conserved neutrinoless double beta decay then occurs either through the usual mass mechanism or through supersymmetric box diagrams. The latter, together with upper limits on neutrino masses, can be used to derive limits on the (B - L) violating mass of the sneutrino. Basically, one can state that for first generation sneutrinos these constraints are rather stringent. However, for second and third generation sneutrinos future accelerator experiments might have a chance to search for lepton number violation in the sneutrino sector.