Aspects of Heavy Supersymmetry
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The recent discovery of a Higgs boson with a mass around 125 GeV, taken together with experimental results from flavor factories, dark matter direct detection, and searches for SUSY particles in the LHC suggest that supersymmetric particles could be heavy in the range of multi-TeV beyond the reach of LHC. In typical supersymmetry breaking models, supersymmetry breaking in the hidden sector is parametrised by a single spurion field mediated at a specific scale, which we call single scale breaking. Although in this case, heavy-scale SUSY breaking models have very large fine-tuning, they are simultaneously economic from the phenomenological perspective. In a typical heavy-scale SUSY model, the gauginos and higgsinos are still around the TeV scale since they can be protected by chiral symmetry, and contain a dark matter candidate. The heavy sfermions relax bounds coming from flavor changing processes and CP violation, and also increase the radiative corrections to the Higgs mass. The aim of the thesis is to study the implications of the heavy supersymmetry while relaxing the assumption of single scale mediation for supersymmetry breaking. In the first study of this thesis, we consider MSSM with N_HS sequestered hidden sectors at a high scale, contributing to supersymmetry breaking. Each hidden sector communicates supersymmetry breaking to the visible (MSSM) sector through effective interactions. Considering a random distribution for the spurion parameters leads a normal distribution for the soft parameters with mean values and standard deviations that are analytically computable. We study the probability of getting Higgs mass in the correct range while having successful electroweak symmetry breaking. We show that the probability distribution is peaked when the quanta of supersymmetric breaking is around m ̃=220 GeV for the parametrisation of the spurion fields we have considered. For these regions we study the supersymmetric spectrum. In the next work, we study fine-tuning, where each of the spurion's contribution is parametrised as m ̃M_Pl c_α. We treat each spurion field as an independent source of supersymmetry breaking. Requiring minimal fine tuning from each sector, gives C_r^((2N_HS-1) ) solutions. In fact, we find there is only one solution independent of all the RG coefficients, where all the sectors contribute coherently. The fine-tuning becomes almost negligible even with a small number of hidden sectors, N_HS=20. The coherent SUSY framework also has a well-tempered dark matter region due to high cancellation in gaugino soft terms. It also has regions of coannihilation with charginos. A concrete realisation with a large number of hidden sectors is presented in the next chapter, where we consider a Stringy landscape like scenario inspired by Bousso-Polchinski's solution to the cosmological constant problem. The spurion fields are given in terms of quantized four form fluxes whose vacuum expectation values set the supersymmetry breaking scales. Coupled to supergravity, we compute the soft spectrum in this framework assuming a uniform distribution for the quantized flux charges. We have shown that this framework naturally leads to a suppression of the flavor violating entries as 1/√(N_HS ) There is further suppression due to the renormalisation group running at the weak scale, especially for the hadronic mass insertions. In the last part of the thesis, we consider single scale supersymmetry breaking and study the implications of the heavy spectrum in the context of SUSY GUT. We consider SUSY SU(5) with a novel decoupling scenario named flavored 'split-generation', where O(1) flavor violation can be present in the model. In this scenario, first and second generation of sfermions are assumed to be heavy (order of 10s of TeV) and the remaining SUSY spectrum lies around a few TeV. Two codes have been developed for this work. 1) A modified version of SuSeFLAV has been developed where we calculate the full two-loop $\beta-$coefficients and one-loop threshold at the two different scales. 2) A code for full SUSY SU(5) proton decay analysis. In this work, we study gauge coupling unification and the two dominant proton decay channels ( p→e^+ π^0 and p→K^+ ν ̅) both with and without flavor mixing in a heavy and light (third) generation. The flavored ‘split-generation' scenario leads to peculiar cancellations in the amplitudes. The rate of p→e^+ π^0 is highly sensitive to amount of flavor violation present as it opens the gluino contribution to the amplitudes. On the other hand, we find that sensitivity of the rates of p→K^+ ν ̅ is related to the flavor of the neutrino emitted. The implications for future proton decay experiments like Hyper-K, DUNE and JUNO are reported.