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

2.4. ORIGINS OF SUPERSYMMETRY BREAKING
gaugino masses arise either by unification of gauge interactions or from a universal gauge
kinetic function for each factor of gauge symmetry. The fundamental parameters of this
model are :
m 0 , m 1/2 , A 0 , tan β, sign(µ), (2.85)
where m 0 is the common mass of the scalars, m 1/2 is the common gaugino mass, A 0 is the
universal proportionality constant between an a-term and the corresponding Yukawa coupling,
tan β is the ratio of the Higgs vacuum expectation ratios, as defined in section 2.2.1 which is
treated for the B-term after electroweak symmetry breaking, and sign(µ) is the sign of µ term,
whose magnitude is fixed by the Z-boson mass after electroweak symmetry breaking. It is
assumed that the universality of the parameters holds at the scale of grand unification rather
than at M P . The model is also called the CMSSM for constrained minimal supersymmetric
Standard Model rather than mSUGRA, since supergravity does not necessary lead to high
scale universality, in contrast to what was originally thought [102].
2.4.2 Hybrid Gauge-Gravity Mediation
The apparent unification of gauge couplings at the scale M GUT ≈ 10 16 GeV is a strong hint
for the paradigm of unification presented in the beginning of this chapter. The forces should
unify and be described by a simple gauge group. However, since now all particles have to form
multiplets of the larger gauge group, which is at least SU(5), one faces the problem of SU(3)-
triplet Higgs fields which lead to the proton decay via dimension-5 operators. Therefore, it
is assumed that Higgs multiplets are incomplete (split). The question why matter appears in
complete representations, while the Higgs multiplets are split, is one of the motivations for
grand unified theories on orbifolds.
In these models the usual space-time is augmented by compact extra dimensions. The
compact manifold M and the quantum-field theory under discussion are both thought to be
symmetric under a discrete group G. If the manifold possesses fixed-points under the nontrivial
action of the group, the physical shape of the extra dimensions is a quotient manifold
C = M/G which turns out to be an orbifold (orbit-manifold). It is not smooth, but has
singular points which are precisely the fixed points. The fields living on the orbifold (bulk
fields) have to obey special boundary conditions at the fixed points, which can differ from
fixed point to fixed point. The physical fields in the effective 4-dimensional theory are the zero
modes of the Kaluza-Klein expansion on the orbifold which respect all boundary conditions
and the fields living on the branes at the fixed-points. The effects of the orbifold construction
can be twofold: The gauge symmetry can be reduced from the full gauge group to a subgroup
either in the bulk or at the brane located at some fixed point, if not all gauge fields posses
zero modes. The same mechanism can lead to appearance of split multiplets in the case of
matter or Higgs fields.
Any incomplete multiplet, besides the Higgs, should have a mass near M GUT in order not
to spoil gauge coupling unification. They can obtain masses from SM singlet fields acquiring
vacuum expectation values of the order of M GUT . Since the incomplete multiplets are charged
under the SM gauge group, the singlets couple always to conjugate pairs i.e. to a “vector-like”
representation of the SM gauge group. Therefore, vector-like pairs of exotics obtain masses.
The number of such exotics in orbifold models can be large. If the singlets also obtain F-
term expectation values (break SUSY) from some dynamics, the vector-like fields will act
as messengers for gauge-mediated SUSY breaking. The resulting patter of SUSY-breaking
terms will be different from the usual low-scale gauge mediation scenarios sketched above,
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