MATOS, LUIS,FILIPE,PINTO,T.,A. (2010) *Supersymmetry Breaking: Models of Gauge Mediation with Gauge Messengers.* Doctoral thesis, Durham University.

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## 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.

Item Type: | Thesis (Doctoral) |
---|---|

Award: | Doctor of Philosophy |

Faculty and Department: | Faculty of Science > Physics, Department of |

Thesis Date: | 2010 |

Copyright: | Copyright of this thesis is held by the author |

Deposited On: | 11 Jan 2011 10:02 |