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Because the Higgs mass is rather large for weak scale supersymmetry breaking, it is likely that the soft masses of the MSSM are well beyond the weak scale. A rather well motivated way of explaining this is found in models such as pure gravity mediation. The base component of pure gravity mediation is a non singlet which breaks supersymmetry. This forbids gravity mediated gaugino masses and the dominant contribution to the gaugino masses comes from anomalies. As it turns out, the simplest model of pure gravity mediation, with universal soft masses, can meet all experimental constraints. In this seminar, I will review the simplest model or pure gravity mediation and then discuss some interesting variations. The first variation I will discuss is non-universal soft Higgs masses. Non-universal Higgs soft masses opens up the parameter space significantly because the constraints on tan beta are relaxed. Also, if non-universal Higgs soft masses are allowed, pure gravity mediation can be made consistent with a Peccei-Quinn symmetry which can explain the size of theta QCD. The axion of this Peccei-Quinn symmetry can be the dark matter as well. Since pure gravity mediation models often give too little dark matter this may explain this short coming of the model. Another way to realize a viable dark matter candidate in these models is through the addition of vector states. These additional vector states will modify the gaugino masses in such away that the bino can be the LSP and can co-annihilate with other guaginos reducing the dark matter density to acceptable levels. These vectors states also generate a non-universality of the Higgs soft masses through running relaxing the constraints on tan beta even if the Higgs soft masses are universal at the GUT scale. Lastly, I will discuss proton decay in pure gravity mediation with non-universal Higgs soft masses. Because non-universal Higgs soft masses allow the other soft masses to be pushed lower, the proton decay of these models for a minimal SU(5) GUT could have a proton lifetime just beyond the reach of planned experiments.
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