Sneutrino oscillations and neutrinoless double beta decay

We prove that the neutrino Majorana mass, the B-L violating mass of the sneutrino (ν) and the neutrinoless double beta decay amplitude are intimately related to each other such that if one of them is non-zero the other two are also non-zero and, vice versa, if one of them vanishes the other two vanish as well. The theorem is valid for any weak-scale softly broken supersymmetric model and independent of the mechanisms of neutrinoless double beta decay and (s)neutrino mass generation. The B-L-violating sneutrino mass leads to mass splitting in the sneutrino-antisneutrino (ν − νc) system and to the effect of lepton number violating ν − νc oscillations.