PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

Here M 1,2 are the soft supersymmetry breaking gaugino mass parameters (see Appendix
B), whereas M corresponds to the triplet-fermion bilinear term. We define the 3 × 5
matrix m D as
⎛
⎞
m T D = √ 1 ⎝ −g′ u 1 gu 1 0 Y Σ1 ũ Y Σ1 v 2
−g ′ u 2 gu 2 0 Y Σ2 ũ Y Σ2 v 2
⎠. (4.36)
2
−g ′ u 3 gu 3 0 Y Σ3 ũ Y Σ3 v 2
Defined in this way, the 8×8 neutral fermion mass matrix can be written as
( )
M
′
m
M n = D
m T , (4.37)
D 0
where M ′ represents the 5×5 matrix
⎛√ ⎞
2M
1
√ 0 −g ′ v 1 g ′ v 2 0
M ′ = √ 1 0 2M
2
gv 1 −gv 2 0
2
⎜ −g ′ v 1 gv 1 0 − √ 2µ 0
⎝ g ′ v 2 −gv 2 − √ ∑
2µ 0
i Y ⎟
∑
Σ i
u i
⎠ . (4.38)
0 0 0
i Y √
Σ i
u i 2M
The low energy neutrino mass would be generated once the neutralino and exotic triplet
fermions get integrated out. Hence the low energy neutrino mass matrix m ν is
m ν ∼ −m T D M′ −1 m D . (4.39)
For M ′ in the TeV range, m ν ∼ 1 eV demands that m D should be 10 −3 GeV. If one
takes v 2 ∼ 100 GeV then this sets Y Σ ∼ 10 −5 and the scale of u to be 10 −3 GeV. Since
in our model for small value of u, the ũ and u are proportional to each other, hence we
naturally get ũ ∼ u ∼ 10 −3 GeV. We have discussed in more detail in Appendix C how
the smallness of neutrino mass can restrict the vacuum expectation values u i , ũ and the
Yukawas Y Σi . One can clearly see from Eq. (4.35) that in the u = 0 and ũ = 0 limit, the
gaugino-higgsino sector completely decouples from the standard model neutrino-exotic
neutrino sector and the low energy neutrino mass would be governed via the usual type-
III seesaw only. In the work presented in the previous chapter, we have taken a large
Yukawa coupling Y Σ ∼ 1. In the present work since we do not extend the Higgs sector
than the minimal supersymmetric standard model and in addition we choose a TeV scale
triplet fermion mass parameter M, hence from the neutrino mass constraint the Yukawa
is bounded to take such a small value Y Σ < 10 −5 . However, as of the two Higgs doublet
type-III seesaw model presented in the previous chapter, one can further extend the Higgs
sector of this model by two SU(2) doublet, so that one of the new Higgs contributes to
the neutrino mass generation. In that case, one can choose a small VEV of the new Higgs
doublet and take the large Yukawa.
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