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

2.1. GLOBAL SUPERSYMMETRY
Supersymmetry breaking As stated already in the introduction to this chapter, supersymmetry
must be broken. The only interesting case is spontaneous breaking of supersymmetry,
in which case it is still a symmetry of the laws but not the symmetry of the vacuum state.
Supersymmetry is spontaneously broken if the variation of some fermionic field operator acquires
a vacuum expectation value (VEV). It is often stated that spontaneous SUSY breaking
is indicated by the vacuum expectation value of the Hamiltonian, but this is not the case,
since the Hamiltonian would be undefined if the Hamiltonian density would acquire a VEV.
In fact, the generators of the superalgebra cease to exist after the breaking of supersymmetry.
The explicit known models of SUSY breaking give vacuum expectation values either to a
D-term or to an F -term in the scalar potential. However, there are severe difficulties if the
are renormalizable tree-level couplings between the SUSY-breaking fields and quarks and leptons.
Either the obtained spectrum is unrealistic (F -term breaking due to supertrace rules),
or there are quantum anomalies (D-term breaking). Therefore, the idea is to decouple the
sector of supersymmetry breaking from the observable sector of quarks, leptons, and gauge
interactions. One refers to the former as a hidden sector. After the breaking, the information
must somehow reach the observable sector. Some of the models for this mechanism which are
used in the present work will be presented in the Section 2.4.
In phenomenological discussions one usually introduces explicit SUSY-breaking terms,
which do not introduce quadratic divergences and are therefore called soft. Augmented by
these terms supersymmetric models still solve the hierarchy problem. The allowed terms have
been classified and are remarkably simple:
• Scalar mass terms m 2 and b:
m 2 φ ∗ φ + bφ 2 + b ∗ φ ∗2 , (2.20)
where the first term treats the scalar and the pseudoscalar (real and imaginary part) of
the supermultiplet equivalently, whereas the other terms introduce a gap between them.
• Gaugino masses M a for each gauge group:
1
2 M a λ a λ a . (2.21)
• Trilinear scalar couplings a:
aφ 3 + a ∗ φ ∗3 . (2.22)
• Tadpole coupling t i , which can occur if one scalar is a singlet under all gauge groups:
t i φ i (2.23)
The terms presented above clearly break supersymmetry, because they involve only scalars
and gauginos but not their superpartners. Having established the techniques and notions of
supersymmetry, we summarize the features of the minimal extension of the Standard Model
introducing our notation.
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