PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

The SU(2) triplet fermions are Σ +c
R , Σ−c R
and Σ0c R and their scalar superpartners are represented
as ˜Σ
+c −c 0c
R
, ˜Σ
R
and ˜Σ R respectively. F Σ +c represent the different auxiliary
R ,Σ−c R ,Σ0c R
fields of the above mentioned multiplet. R-parity of ˆΣ c R is −1 where componentwise the
fermions Σ +c
R , Σ−c R
and Σ0c R have R-parity +1 and their scalar superpartners have R-parity
−1. With these field contents, the R-parity conserving superpotential W of our model
will be
W = W MSSM +W Σ , (4.7)
where W MSSM has already been written in Eq. (4.1) and W Σ is given by
T
W Σ = −Y Σi Ĥ u (iσ2 )ˆΣ c RˆL i + M 2 Tr[ˆΣ c RˆΣ c R ]. (4.8)
0c
W Σ is clearly R-parity conserving. The scalar fields ˜Σ R and ˜ν L i
are odd under R-parity.
Hence in this model, R-parity would be spontaneously broken by the vacuum expectation
values of these sneutrino fields. We will analyze the potential and spontaneous R-parity
violation in the next section. On writing explicitly, one will get these following few terms
from the above superpotential W Σ ,
W Σ = Y Σ
√
i
ĤuˆΣ 0 0c
Rˆν Li +Y Σi ĤuˆΣ 0 −cˆl
− Y Σi
R i + √ Ĥ + 0c
−
u ˆΣ Rˆl i −YΣi Ĥ + +c
u ˆΣ
R ˆν L i
2 2
+ M 2
0c 0c ˆΣ R ˆΣ
R +MˆΣ +c
R
ˆΣ
−c
R . (4.9)
The kinetic terms of the ˆΣ c R
field is
L k Σ = ∫
d 4 θTr[ ˆ Σ c R†
e
2gV ˆ Σc R
]. (4.10)
The soft supersymmetry breaking Lagrangian of this model is
L soft = L soft
MSSM +L soft
Σ . (4.11)
For completeness we write the L soft
MSSM Lagrangian in the Appendix A. Lsoft Σ contains the
supersymmetry breaking terms corresponding to scalar ˜Σ c R fields and is given by
where
L soft
Σ = −m2 c†
ΣTr[˜Σ ˜ RΣ c R ]−(˜m2 Tr[ Σ ˜c
˜ RΣ c R ]+h.c)−(A Σ i
Hu T iσ 2˜Σ c R˜L i +h.c), (4.12)
˜Σ c R = √ 1 (
√ ˜Σ0c R
2 2˜Σ+c
R
√ 2˜Σ−c R
−˜Σ 0c
R
)
. (4.13)
We explicitly show in the Appendix A all the possible trilinear terms which will be generated
from Eq. (4.9) and the interaction terms between gauginos and SU(2) triplet fermion
and sfermion coming from Eq. (4.10). In the next section we analyze the neutral component
of the potential and discuss spontaneous R-parity violation through ˜Σ R and ˜ν L i
0c
vacuum expectation values.
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