Lepton flavour violating heavy Higgs decays within the νMSSM and their detection at the LHC

Within the νMSSM, a Minimal Supersymmetric neutrino See-saw Model, Lepton Flavour Violating Higgs couplings are strongly enhanced at large tanβ (≥30), which can lead to BR(H0/A0→τμ)≅O(10-4), for MH0/A0≥160 GeV. Enhancements on the production of Higgs bosons, through the gluon fusion mechanism, gg→H0/A0, and the associated production channel gg,qq-bar →bb-bar H0/A0, whose rates grow with tanβ, as well as the mass degeneracy that occurs between the H0 and A0 states in this regime, also contribute to further the possibilities to detect a heavy Higgs signal into τμ pairs. We show that the separation of τμ Higgs events from the background at the upcoming CERN Large Hadron Collider could be done for Higgs masses up to about 600 GeV for 300 fb-1 of luminosity, for large tanβ values. However, even with as little as 10 fb-1 one can probe H0/A0 masses up to 400 GeV or so, if tanβ=60. Altogether, these processes then provide a new Higgs discovery mode as well as an independent test of flavour physics.