Supersymmetry Breaking:
Models of Gauge Mediation with
Gauge Messengers

Abstract

With the start of the LHC, it becomes increasingly important to understand
the experimental signatures that discriminate different extensions
of the standard model.
Supersymmetry (SUSY), in particular the Minimal Supersymmetric
Standard Model (MSSM), is one such extension that is specially attractive
by its simplicity and elegance. However, if this symmetry is to be
realized in nature, it must be spontaneously broken.
In this work we will try to understand the most general way in
which SUSY breaking can happen in renormalizable field theories and
the implications that this has on the minimal extension of the standard
model (MSSM) mass spectrum.
The first two chapters are the introductory material: in chapter 1
we will introduce some of the key ideas necessary to understand supersymmetric
field theories, and in chapter 2 we will briefly describe the
the simplest supersymmetric version of the Standard Model.
In chapter 3 we will focus on understanding the role of R-Symmetry
breaking in determining the soft terms gauge mediation of supersymmetry
breaking (GMSB) can lead to. To do this we consider a model where
both R-symmetry and SUSY are spontaneously broken. One starts
with the model proposed by Intriligator, Seiberg and Shih (ISS) and
adds a (dangerous) marginal operator, which we call a meson deformation.
The inclusion of this operator leads to the spontaneous breaking
of R-symmetry in the vacuum. One then gauges the SU(5) of flavour
and identifies it with the MSSM GUT gauge group, thus implementing
GMSB. This was the second explicit example where R-symmetry was
spontaneously broken in the vacuum. As in the first, gaugino masses
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turned out to be smaller than naively expected so that a mild splitting
between scalar (squark and slepton) and gaugino masses exists.
After this, a general argument showed that in fact gaugino masses
are always significantly smaller than scalar masses if the universe is
perturbatively stable. This arguments suggests that any viable vacuum
should be (perturbatively) metastable, as had been previously noticed
by Murayama and Nomura.
In chapter 4, we try to explore alternatives to this scenario by considering
the possibility that the vacuum doesn’t break supersymmetry
by F-term vevs alone, but by a having simultaneously non-zero F and
D-terms.
It turns out that this does not happen in models where the Kahler
potential is canonical, and the superpotential is a cubic polynomial in
the fields, but it can happen if either of these constraints is violated.
This leads us to consider a particular example, where we study a
hidden sector model with SU(3) gauge group, two flavours of quarks
and one singlet. The superpotential is the most general consistent with
the tree-level symmetries. The R-symmetry is anomalous, however, but
one can still derive selection rules that constrain the form of the effective
superpotential. The only extra term that is allowed is an instanton
induced contribution. This term explicitly breaks the R-symmetry, but
the resulting low energy superpotential is not generic and SUSY is still
spontaneously broken.
While not a complete example of GMSB, this class of hidden sector
models is interesting as it does not require metastability: the tension
between the spontaneous breaking of an R-symmetry and the massless
R-axion is bypassed by the naturally non-generic superpotential. These
models usually have both F and D-term SUSY breaking, but these two
vevs are not independent: in non-Abelian theories, the D-term vevs can
only be induced by the F-term vevs of fields that are not gauge singlets.
The implementation of GMSB in scenarios where the F-terms are
not gauge singlets is then considered in both its direct and semi-direct
forms:
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In chapter 5 we deal with direct gauge mediation with gauge messengers.
In this version of gauge mediation, the spontaneously broken
gauge group is identified with the MSSM GUT gauge group and generically
leads to tachyonic squark or slepton masses. In the particular
case where the GUT gauge group is SU(5), we show that this problem
can be solved if there are two independent sectors where SUSY is spontaneously
broken or simply by using a solution of the doublet-triplet
splitting problem where the vev responsible for the spontaneous breaking
of the GUT symmetry is larger than the SUSY breaking scale. In
both cases the effects gauge and non-gauge messengers have to combine
if a viable spectrum is to be reached.
We then finish out study in chapter 6 by considering the semi-direct
version of gauge mediation with gauge messengers. As it is known,
gaugino masses are screened from messenger interactions, at leading
order in the SUSY breaking parameter F. Because of this, gaugino soft
masses will be suppressed with respect to scalar soft masses. This leads
to a scenario of mildly split SUSY, i.e. scalars are at least one or two
orders of magnitude heavier than gauginos. This generically leads to
some extra fine-tuning to get the EW breaking scale to occur at the
correct scale.