Abstract
An analytical formalism, including RG running at two loop order, is used to link the supersymmetric and GUT spectra in any GUT model in which the three gauge couplings unify. In each specific GUT model, one can then fully explore the interplay between the pattern of supersymmetry breaking and the prediction for the proton lifetime. With this formalism at hand, we study three concrete GUT models: (i) Minimal SU(5) SUSY GUT, (ii) Missing Partner SU(5) SUSY GUT, and (iii) an orbifold SU(5) SUSY GUT. In each case we derive interesting conclusions about the possible patterns of the supersymmetric spectrum once the present limits on the proton lifetime are imposed, and vice versa, we obtain the predictions for the proton lifetime for specific viable choices of the SUSY spectrum.
Highlights
The D = 5 operators generated by the coloured Higgs exchange diagrams, may give a strong constraint on the colour triplet Higgs mass and low energy SUSY spectrum as well as the structure of the Higgs sector in the GUT models.this mode is highly model-dependent and several mechanisms have been constructed to eliminate the D = 5 operator contribution
The gauge coupling unification implies a non-trivial relation between SUSY and GUT spectra, which may lead to an interesting interplay between the signatures at collider and proton decay experiments
The formula is generic and applicable for any GUT models in which the SM gauge group is directly unified into a simple unified gauge group at some high energy scale
Summary
In this paper we assume that there is an underlying simple GUT group unifying the SM gauge couplings. The “Vanilla” SUSY scenario, shown in the left panel of figure 1, assumes a low energy gaugino mass ratio M3/M2 = 3. This ratio typically arises in the scenarios where the gaugino masses are unified around the GUT scale, e.g. in the Constrained MSSM (CMSSM) or in the Gauge Mediated SUSY Breaking (GMSB) scenario. We see in this plot that the current proton decay limit demands the sfermions to be heavier than 200 TeV for μ ∼ 1 TeV and heavier than 40 TeV for μ ∼ 103 TeV This means that the split SUSY scenarios with both Wino and Higgsino DM are consistent with the minimal SU(5) model. Wino or Higgsino DM models in minimal SU(5) predict a proton decay lifetime in the region that may be discovered by the generation experiments
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