Inverse Seesaw Neutrino Mass from Lepton Triplets in the U (1)Σ Model

The inverse seesaw mechanism of neutrino mass, i.e. mν ≃ (m2D/m2N )ǫL where ǫL is small, is discussed in the context of the U(1)Σ model. This is a gauge extension of the Standard Model of particle interactions with lepton triplets (Σ,Σ,Σ) as (Type III) seesaw anchors for obtaining small Majorana neutrino masses. Introduction : If the SU(3)C×SU(2)L×U(1)Y Standard Model (SM) of particle interactions is extended [1, 2] to include a lepton triplet (Σ,Σ,Σ) per family, then the heavy Majorana mass of Σ acts as a seesaw anchor for the neutrino to acquire a small mass, just as in the case of using a singlet N . This is often referred to as Type III seesaw [3]. It has also been shown [4, 5, 6, 7] that this addition admits a new U(1)Σ gauge symmetry, with the following charges: (u, d)L ∼ (3, 2, 1 6 ) : n1, (1) uR ∼ (3, 1, 2 3 ) : n2 = 1 4 (7n1 − 3n4), (2) dR ∼ (3, 1,− 1 3 ) : n3 = 1 4 (n1 + 3n4), (3) (ν, e)L ∼ (1, 2,− 1 2 ) : n4, (4) eR ∼ (1, 1,−1) : n5 = 1 4 (−9n1 + 5n4), (5) (Σ,Σ,Σ)R ∼ (1, 3, 0) : n6 = 1 4 (3n1 + n4). (6) Consider now the inverse seesaw mechanism: a situation is established where mν = 0 because of a symmetry, which is then broken by a small mass parameter [8, 9, 10, 11, 12]. As a result, mν is proportional to this symmetry-breaking parameter (and not inversely proportional to mN as in the usual seesaw). The prototype model is to add a singlet Dirac fermion N , i.e. both NR and NL, with lepton number L = 1 per family to the SM. The 3×3 mass matrix spanning (ν̄L, NR, N̄L) is then given by