Since there are no leptons in the initial state, but two in the final state, the observation of neutrinoless double beta decay constitutes an irrefutable proof that lepton number
is violated by nature.
where [N.sup.[alpha].sub.R] and [S.sup.[beta].sub.L] are two SM-singlet heavy neutrinos with the same lepton numbers
, [m.sub.N] is the Dirac mass matrix, and [mu] is a small Majorana mass matrix violating the lepton numbers
As profound applications of the classic inverse seesaw mechanism it has been noted that the presence of heavy pseudo Dirac fermions would manifest through LFV decays [33,184-188] and also in lepton number violation [208, 209].
In this section we summarise how, in the absence of SUSY, the classic inverse seesaw and the extended seesaw could still serve as powerful mechanisms to confront neutrino mass, observable lepton flavor violation [109,166], and, in addition, dominant lepton number violation [110,175-177] in non-SUSY SO(10).
The mass terms of fermion singlets violate the global lepton number symmetry of the SM.
The particles in the lepton triplet have different lepton numbers (1 and 0), so the lepton number in the model does not commute with the gauge symmetry unlike the SM.
To provide the Majorana masses for the neutrinos, the lepton number must be broken.
In Table 2 we will explicitly point out the lepton number (L) and lepton parity ([P.sub.l]) of the model particles (notice that the family indices are suppressed).
(i) its underlying symmetries, such as total lepton number,
Models with m > 3 are especially interesting, where one can exploit the extra freedom to realize symmetries, such as lepton number L, so as to avoid seesaw-induced neutrino masses, naturally allowing for TeV-scale messengers.
The lepton number L of the two sets of fields [N.sub.R] and [S.sub.L] can be assigned as L([N.sub.R]) = +1 and L([S.sub.L]) = +1.
Khan), while another focused on having a viable dark matter candidate in a popular model where baryon and lepton numbers
are promoted to gauge symmetries ("Z7 Portal Dark Matter in the Minimal B-L Model", by S.