PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

Hence for small u which is demanded from the smallness of neutrino mass (discussed in
the next section and in Appendix C), ũ will also be of the same order as u unless there
is a cancellation between the terms in the denominator. In this work we will stick to the
possibility of small u and ũ. We will show in the next section that one needs u ∼ 10 −3
GeV to explain the neutrino data. Hence ũ will also have to be 10 −3 GeV. In the u = 0
limit, ũ would also be 0 and this is our usual R-parity conserving scenario.
4.4 Neutralino-Neutrino Mass Matrix
In this section we discuss the consequence of R-parity violation through the neutralinoneutrino
mixing. It is well known [19] that R-parity violation results in mixing between
the neutrino-neutralino states. In our model the neutrino sector is enlarged and includes
both the standard model neutrino ν Li , as well as the heavier neutrino state Σ 0c
R , which
is a component of SU(2) triplet superfield. Since R-parity is violated we get higgsinoneutrino
mixing terms Y Σ √2i
ũ˜H u 0ν L i
and Y Σ √2i
u˜H u 0Σ0c
, in addition to the conventional R-
parity conserving Dirac mass term Y Σ √2i
v u Σ 0c
R ν L i
. The R-parity breaking former two terms
originated from the term Y Σ √2i
ĤuˆΣ 0 0c
Rˆν L i
in Eq. (4.9), once the sneutrino fields ˜ν Li and
˜Σ 0c
R get vacuum expectation values. The third term also has the same origin and it
is the conventional Dirac mass term in type I or type-III seesaw. In addition to the
higgsino-neutrino mixing terms generated from the superpotential W Σ , there would also
be gaugino-neutrino mixing terms generated from the Kähler potential of the ˆL i and ˆΣ c R .
IntheAppendix Bweshowexplicitly thecontributions comingfromW Σ andtheneutrinosneutrino-gaugino
terms originating from the kinetic term of the triplet superfield ˆΣ c R
written down in Eq. (4.10). Here we write the color singlet neutral-fermion mass matrix
of this model in the basis ψ = (˜λ 0 ,˜λ 3 ,˜H 0 d ,˜H 0 u,Σ 0c
R ,ν L 1
,ν L2 ,ν L3 ) T where with one generation
of Σ c R , the neutral fermion mass matrix is a 8×8 matrix. The mass term is given by
R
L n = − 1 2 ψT M n ψ +h.c. (4.34)
where
⎛√ ⎞
2M
1
√ 0 −g ′ v 1 g ′ v 2 0 −g ′ u 1 −g ′ u 2 −g ′ u 3
0 2M
2
gv 1 −gv 2 0 gu 1 gu 2 gu 3
M n = √ 1 −g ′ v 1 gv 1 0 − √ 2µ 0 0 0 0
g ′ v 2 −gv 2 − √ ∑
2µ 0
i
2 Y Σ i
u i Y Σ1 ũ Y Σ2 ũ Y Σ3 ũ
∑
0 0 0
i Y √ Σ i
u i 2M YΣ1 v 2 Y Σ2 v 2 Y Σ3 v 2
(4.35) .
⎜ −g ′ u 1 gu 1 0 Y Σ1 ũ Y Σ1 v 2 0 0 0
⎟
⎝ −g ′ u 2 gu 2 0 Y Σ2 ũ Y Σ2 v 2 0 0 0 ⎠
−g ′ u 3 gu 3 0 Y Σ3 ũ Y Σ3 v 2 0 0 0
97