Scotogenic S3 symmetric generation of realistic neutrino mixing

Abstract

Realistic neutrino mixing is achieved at one-loop level radiatively using S3 × Z 2 symmetry. The model comprises of two right-handed neutrinos, maximally mixed to produce the structure of the lefthanded Majorana neutrino mass matrix characterized by θ 13 = 0, θ 23 = π/4 and any value of θ 0 12 particular to the Tribimaximal (TBM), Bimaximal (BM) and Golden Ratio (GR) or other mixings. A small deviation from this maximal mixing between the two right-handed neutrinos could generate non-zero θ 13 , shifts of the atmospheric mixing angle θ 23 from π/4 and also could correct the solar mixing angle θ 12 by a small amount altogether in a single step. In this scotogenic mechanism of generating non-zero θ 13 by shifting from maximal mixing in the right-handed neutrino sector, two Z 2 odd inert scalar SU (2) L doublets were used, the lightest of which can serve as a dark matter candidate. *

S3 Symmetric Scotogenic Model for Realistic Neutrino Mixing

“…The neutrino mass at one-loop level can be given by Fig. (1). The relevant terms 5 of the S3 × Z 2 invariant scalar potential that can contribute to the left-handed Majorana neutrino mass matrix via the four-point scalar vertex in Fig.…”

“…Next we briefly discuss the contribution coming from the loop in Fig. (1) to the left-handed Majorana neutrino mass matrix [8]. For simplicity, let λ represent commonly all the quartic couplings i.e., λ 1 , λ 2 and λ 3 present in the S3 × Z 2 conserving scalar potential in Eq.…”

“…5 The total S3 × Z 2 invariant scalar potential is given in [1] out of which only the (η † φ)(η † φ) terms contribute to the neutrino mass matrix as at the four-point scalar vertex in Fig. (1), two η fields are created and two φ fields are annihilated. 6 The S3 symmetry is broken softly at the scale at which the right-handed neutrinos acquire their mass.…”

“…8 It might appear that the S3 symmetry will cause the η i fields to be equal in masses, but since the S3 symmetry is softly broken at the scale in which N αR gets mass, a small mass splitting between the two η i fields can be achieved. 9 For detailed discussion, see [1].…”

“…This talk is based 1 on [1]. The Pontecorvo, Maki, Nakagawa, Sakata -PMNS -matrix, relating the neutrino mass and flavour eigenstates is given by: The quantities a, b, c and d has to be non-zero for neutrino masses to be non-degenerate and realistic.…”