Loop induced Higgs and Z boson couplings to Neutralinos and implications for collider and Dark Matter searches

We calculate the one-loop induced couplings of two gaugino-like neutralinos to the $Z$ and Higgs bosons in the Minimal Supersymmetric Standard Model. These couplings, which vanish at the tree level, can be generated through loops involving fermions and sfermions. We show that, while the neutralino contribution to the invisible $Z$ boson decay width remains small, the loop induced couplings to the lightest Higgs boson might be sufficiently large to yield a rate of invisible decays of this Higgs boson that should be detectable at future $e^+e^-$ colliders. We also study the implications of these couplings for direct searches of Dark Matter and show that they can modify appreciably the neutralino-nucleon elastic cross section for some parameter range.