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Lepton flavour violating Higgs Boson decays, tau --> mu gamma and B(s) --> mu+mu- in the constrained MSSM+NR with large tan beta

Realistic predictions are made for the rates of lepton flavour violating Higgs boson decays, tau --> mu gamma, mu --> e gamma, Bs --> mu+mu-, Bs --> tau mu and tau --> 3mu, via a top-down analysis of the Minimal Supersymmetric Standard Model(MSSM) constrained by SU(5) unification with right-handed Neutrinos and large tan beta. The third family neutrino Yukawa coupling is chosen to be of order 1, in this way our model bares a significant resemblance to supersymmetric SO(10). In this framework the large PMNS mixings result in potentially large lepton flavour violation. Our analysis predicts tau --> mu gamma and mu --> e gamma rates in the region (10^{-8}-10^{-6}) and (10^{-15}-10^{-14}) respectively. We also show that the rates for lepton flavour violating Higgs decays can be as large as 10^{-7}. The non-decoupling nature of H --> tau mu is observed which leads to its decay rate becoming comparable to that for tau --> mu gamma for large values of m_0 and M_1/2. We also find that the present bound on Bs --> mu+mu- is an important constraint on the rate of lepton flavour violating Higgs decays. The recently measured Bs-Bsbar mixing parameter Delta Ms is also investigated.