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 significanlty the discovery possibilities of the lightest Higgs at the LHC. We show that due to these decays, there exist regions of the $M_2-\mu$ space where the B.R. $(h\to \gamma \gamma )$ becomes dangerously low even after imposing the LEP constraints on the sparticle masses, implying a possible preclusion of its discovery in the $\gamma \gamma$ channel. We find that there exist regions in the parameter space with acceptable relic density and where the ratio ${B.R. (h \to \gamma \gamma){SUSY} \over B.R. (h \to \gamma \gamma){SM}}$ falls below 0.6, implying loss of signal in the $\gamma \gamma$ channel. These regions correspond to ${\tilde{\chi }}_1^{+},{\tilde{\chi }}_2^0$ 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 $M_1$ independently of $\mu ,\tan \beta$ and $m_0$.