Supersymmetry 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 LLE and LQD 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 µ-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.

Lepton number violation in supersymmetric grand unified theories

“…Depending on the U(1) A charges assigned to the matter and Higgs superfields involved, one can generically obtain at low energies either the bilinear model or the trilinear one considered here. The bilinear model also leads to LNV-Yukawa coupling alignment, by virtue of which many predictions of both models concerning quark flavour conservation are very similar [15]. However, there are principal differences as well.…”

“…As a result, we are driven to a simple picture where the flavour structure, as well as the hierarchies of the trilinear LNV couplings in ∆W (1), are essentially aligned with the down quark and charged lepton mass and mixing hierarchies. At the same time, the effective bilinear LNV terms appear to be generically suppressed by the custodial U(1) A symmetry (for a detailed exposition see a recent paper [15]). …”

“…This is in fact a general consequence of the symmetry breaking pattern involved. The point is that neither of the other mass-terms M mm and M nm can be allowed by U(1) A symmetry for any generalisation of the superpotential W mix (15). Otherwise the dangerous ϕ (k) Σϕ (k) couplings inevitably appear as well.…”

“…Therefore one of the two pairs of weak doublets in (20), as well as the colour triplets, must further become heavy in order to get the ordinary picture of MSSM at low energies. This happens as a result of mixing H and H with the specially introduced heavy scalar supermultiplets Φ [ABC] and Φ [ABC] (being 35-plets of SU (7)) in the basic Higgs superpotential (15) in a general SU(N) context (for SU (7) there appears only one pair of such singlets, S and T ). It should be clear now that the W H couplings (21) will rearrange the mass spectrum of the states (20), so as to leave just one pair of massless weak-doublets as needed for the MSSM.…”

“…The effective dimension-5 interactions (23-25) could be generated by the exchange of some heavy states, such as massive string modes. When generated by the exchange of the same superheavy multiplet (that is a vector-like pair of fundamental septets 7 + 7), the resulting operators (24) and (25) have effective coupling constants (26) aligned in flavour space [15]:…”