PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

where ˆΦ is the MSSM chiral superfield which transforms non-trivially under the gauge
group with gauge coupling constant g. With all these particle contents the MSSM superpotential
is given by,
W = W MSSM +W̸Rp−MSSM, (1.25)
where W MSSM and W̸Rp−MSSM are respectively the following,
and
W MSSM = Y e Ĥ dˆLÊ c +Y d Ĥ d ˆQˆDc −Y u Ĥ u ˆQÛ c +µĤuĤd, (1.26)
W̸Rp−MSSM = −ǫĤuˆL+λˆLˆLÊc +λ ′ˆLˆQˆDc +λ ′′ Û c ˆDc ˆDc . (1.27)
The superpotential W̸Rp−MSSM violates a discrete symmetry known as R-parity or matter
parity. The R-parity or matter parity is defined as (−1) 3(B−L)+2S , where B, L are the
baryon, lepton number of the particle and S is the spin. Each of the standard model
particle is R-parity even and their superpartners are odd under R-parity. In other words,
the matter chiral superfield has R-parity −1 and the Higgs chiral superfield has R-parity
+1.
Since, supersymmetry predictsequality between themasses oftheparticlesandtheir
superpartners and till date no superpartners of the standard model particles have been
observed, hence supersymmetry must be broken. In the minimal supersymmetric standard
model the supersymmetry is broken explicitly and softly to avoid any dimensionless
quartic scalar coupling in the explicitly supersymmetry breaking Lagrangian. The soft
supersymmetry breaking Lagrangian of MSSM is,
−L soft
MSSM = (m2˜Q )ij ˜Q† ˜Q i j +(m 2 ũ c)ij ũ c∗
i ũc j +(m2˜dc) ij ˜dc ∗
i
˜d c j )ij˜L† +(m2˜L ˜L i j
+ (mẽ 2 c)ij ẽ c∗
i ẽ c j +m 2 H d
H † d H d +m 2 H u
H uH † u +(bH u H d +h.c.)
[
+ −A ij
u H ˜Q u i ũ c j +Aij d H ˜Q
]
d i˜dc j +A ij
e H d˜L i ẽ c j +h.c.
+ 1 (
M 3˜g˜g )
+M 2˜λi˜λi +M 1˜λ0˜λ0 +h.c. . (1.28)
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 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 .
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