Gravitinos and hidden Supersymmetry at the LHC - Universität ...

2.4. ORIGINS OF SUPERSYMMETRY BREAKING
where G 0 is the expectation value of the Kähler function G. Writing the scalar potential as
V F = K i jF i F ∗j − 3e K/M 2 P W W ∗ /M 2 P , (2.81)
with F i defined in eq. (2.78), one sees that SUSY can be unbroken in spaces with negative
vacuum energy (AdS) and non-vanishing gravitino mass if G j vanishes.
If SUSY is broken, the potential (2.81) tells us that the vacuum can have an arbitrary
value of the cosmological constant. However, even if astrophysical observations imply a tiny
cosmological constant, the value is far too low to be associated with SUSY breaking, since
in general at the minimum V ≈ m 3/2 MP 2 . Therefore, it is usually assumed that the vacuum
energy vanishes. Why this is the case, is not understood. In the case of the vanishing
cosmological constant one finds:
〈
K
i
j F i F ∗j〉 = 3M 4 P e 〈G〉 , (2.82)
which leads to an equivalent formula for the gravitino mass:
〈 〉
K i
m 2 3/2 = j F iF ∗j
3M 2 P
2.4 Origins of Supersymmetry Breaking
. (2.83)
The MSSM, as presented in the previous sections, has a huge number of free parameters associated
with the breaking of supersymmetry. Therefore, the general MSSM is not a tractable
framework for phenomenological studies. Usually, the general features of the MSSM are associated
with the conservation of R-Parity, which leads to signatures involving missing transverse
energy from the lightest stable supersymmetric particle. However, even this prediction is not
robust, since R-parity might be violated. It is possible to obtain some hints about the structure
of the SUSY breaking terms from low energy experiments looking for flavor changing
neutral currents and violation of CP symmetry. Effects from arbitrary patterns (including
phases) of squark mass matrices would enter via loops into the low energy observables like the
mass difference between the long-lived and short-lived Kaons, or the electric dipole moment
of the neutron. The tight constraints on such effects suggest a pattern of universality in the
scalar mass terms. It is assumed that they are real, proportional to the identity matrix, and
degenerate in the first two generations. Usually, one takes the third family also to be degenerate
in mass with the first two. Additionally, the renormalization group evolution of the
gaugino masses is proportional to the evolution of the corresponding gauge couplings. Since
the gauge couplings should unify at the scale of grand unification, it is natural to assume that
also the masses of the gauginos unify at the GUT scale.
In order to obtain control over the huge parameter space of the MSSM, one has to make
assumptions on the structure of some underlying theory which is approximated by the MSSM
in the low energy regime. These assumptions are reflected in different phenomenological
models of supersymmetry which reduce the number of free parameters by exploiting the
hints presented above. In these models SUSY is broken at some high scale F ≫ MW
2 in a
hidden sector, whose dynamics is unimportant for phenomenology. The important part is
the nature of the agent, which is a superheavy particle of mass m X transmitting the SUSY
breaking to the fields of the observable sector. The coupling of the goldstino to the observable
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