PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

Field H l 1 D l e R µ R τ R ∆ φ e ξ
S 3 1 1 2 1 1 1 2 2 2
Z 4 i −1 1 1 −i 1 −1 i −1
Z 3 1 1 1 1 ω ω 2 1 ω 1
Table 6.1: Transformation properties of matter and flavon fields under the flavor groups.
which transforms as singlet under S 3 . The Higgs ∆ 1 and ∆ 2 are SU(2) L
triplets with
hypercharge Y = +2,
( ∆
+
i
∆ i =
/√ )
2 ∆ ++
i
∆ 0 i −∆ + i /√ , (6.2)
2 ,
which transform as a doublet
∆ =
(
∆1
∆ 2
)
, (6.3)
under S 3 . Other than these fields, we also have two additional S 3 scalar doublets φ e and
ξ,
( ) ( )
φ1 ξ1
φ e = , ξ = , (6.4)
φ 2 ξ 2
which are singlets under SU(2) L
×U Y (1). The SU(2) L
×U Y (1) lepton doublets are distributed
in the S 3 multiplets as follows:
( )
L2
D l = , (6.5)
L 3
transforms as a doublet under S 3 , where L 2 = L µ = (ν µL ,µ L ) T and L 3 = L τ = (ν τL ,τ L ) T ,
while
( )
νeL
L 1 = L e = , (6.6)
e L
transforms as a singlet. The right-handed fields e R , µ R and τ R transform as 1 under S 3 .
The corresponding charges of the particles under Z 4 andZ 3 has been summarized in Table
6.1.
6.2.1 Neutrino Masses and Mixing
Given the field content of our model and their charge assignments presented in Table 6.1,
the most general S 3 ×Z 4 ×Z 3 invariant Yukawa part of the Lagrangian (leading order)
giving the neutrino mass can be written as
−L y ν = y 2
Λ (D lD l ) 1 (ξ∆) 1 + y 1
Λ (D lD l ) 2 (ξ∆) 2 +2y 3 l 1 D l ∆+ y 4
Λ l 1l 1 ξ∆+h.c.+... (6.7)
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