On SUSY inspired minimal lepton number violation

Abstract

A minimal lepton number violation (LNV) is proposed which could naturally appear in SUSY theories, if Yukawa and LNV couplings had a common origin. According to this idea properly implemented into MSSM with an additional abelian flavor symmetry the prototype LNV appears due to a mixing of leptons with superheavy Higgs doublet mediating Yukawa couplings. As a result, all significant physical manifestations of LNV reduce to those of the effective trilinear couplings $LL\bar{E}$ and $LQ\bar{D}$ aligned, by size and orientation in a flavor space, with the down fermion (charged lepton and down quark) effective Yukawa couplings, while the effective bilinear terms appear generically suppressed relative to an ordinary $\mu $-term of MSSM. Detailed phenomenology of the model related to the flavor-changing processes both in quark and lepton sectors, radiatively induced neutrino masses and decays of the LSP is presented. Remarkably, the model can straightforwardly be extended to a Grand Unified framework and an explicit example with SU(7) GUT is thoroughly discussed.