PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

Appendix
A: Soft supersymmetry breaking lagrangian of MSSM
The soft supersymmetry breaking Lagrangian of this model is given by,
L soft = L soft
MSSM +L soft
Σ ,
(A1)
where L soft
Σ has been written in Eq. (4.12) and the MSSM soft supersymmetry breaking
lagrangian has the following form,
−L soft
MSSM = (m 2˜Q) ij ˜Q† ˜Q i j +(m 2 ũ c)ij ũ c∗
i ũ c j +(m 2˜dc) ij ˜dc ∗
i
˜d c j +(m
ij˜L†
2˜L) ˜L i j
+ (m 2 ẽ c)ij ẽ c∗
i ẽc j +m2 H d
H † d H d +m 2 H u
H u † H u +(bH u H d +H.c.)
[
+ −A ij
uH u ˜Qi ũ c j +A ij
d H ˜Q
]
d i˜dc j +A ij
e H d˜Li ẽ c j +H.c.
+ 1 (
M 3˜g˜g )
+M 2˜λi˜λi +M 1˜λ0˜λ0 +H.c. . (A2)
2
where i and j are generation indices, m 2˜Q, m 2˜L and other terms in the first two lines of
the above equation represent the mass-square of different squarks, slepton, sneutrino 5 and
Higgs fields. In the third line the trilinear interaction terms have been written down and
in the fourth line M 3 , M 2 and M 1 are respectively the masses of the gluinos ˜g, winos
˜λ 1,2,3 and bino ˜λ 0 .
B: Gaugino-lepton-slepton mixing
In this section we write down explicitly all the interaction terms generated from W Σ , as
well as the gaugino-triplet leptons-triplet sleptons interaction terms originating from L k Σ .
As has already been discussed in section 2, W Σ is given by
W Σ = −Y Σi Ĥ T u (iσ 2)ˆΣ c R ˆL i + M 2 Tr[ˆΣ c RˆΣ c R ].
(B1)
W Σ = Y Σ
√ i
ĤuˆΣ 0 0c
Rˆν L i
+Y Σi ĤuˆΣ 0 −cˆl
− Y
R i + √
Σi
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 .
(B2)
In Table. 4.4 we show all the trilinear interaction terms generated from Y Σi Ĥ uˆΣc R ˆLi .
5 m2˜ν represents the mass square of the superpartner of the standard model neutrino and m2˜ν =m2˜L.
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