Invisible decays of the supersymmetric Higgs and dark matter

We discuss effects of the light sparticles on decays of the lightest Higgs in a supersymmetric model with nonuniversal gaugino masses at the high scale, focusing on the 'invisible' decays into neutralinos. These can impact significantly the discovery possibilities of the lightest Higgs at the LHC. We show that due to these decays, there exist regions of the M2 - μ space where the B.R. (h → γγ) becomes dangerously low even after imposing the LEP constraints on the sparticle masses, implying a possible preclusion of its discovery in the γγ channel. We find that there exist regions in the parameter space with acceptable relic density and where the ratio B.R.(h→γγ)SUSY/B.R.(h→γγ)SM falls below 0.6, implying loss of signal in the γγ channel. These regions correspond to χ tilde1+, χ tilde20 masses which should be accessible already at the Tevatron. Further we find that considerations of relic density put lower limit on the U(1) gaugino mass parameter M1 independently of μ, tan β and m0. (author)