Lepton flavour violating Higgs boson decays, τ→μγτ→μγ and Bs→μ+μ−Bs→μ+μ− in the constrained MSSM+νRMSSM+νR with large tanβtanβ

Realistic predictions are made for the rates of lepton flavour violating Higgs boson decays, τ→μγτ→μγ, μ→eγμ→eγ, Bs0→μμ, Bs0→τμ and τ→3μτ→3μ, via a top–down analysis of the minimal supersymmetric Standard Model (MSSM) constrained by SU(5)SU(5) unification with right-handed neutrinos and large tanβtanβ. 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)SO(10). In this framework the large PMNS mixings result in potentially large lepton flavour violation. Our analysis predicts τ→μγτ→μγ and μ→eγμ→eγ 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 H0→τμH0→τμ is observed which leads to its decay rate becoming comparable to that for τ→μγτ→μγ for large values of m0m0 and M1/2M1/2. We also find that the present bound on Bs→μμBs→μμ is an important constraint on the rate of lepton flavour violating Higgs decays. The recently measured BsBs–B¯s mixing parameter ΔMsΔMs is also investigated.