Limits on Sparticle Dark Matter

Arguments are given that the lightest supersymmetric particle should be a neutralino χ. Minimizing the fine tuning of the gauge hierarchy favours Ωχh 2 ∼ 0.1. There are important constraints on the parameter space os the MSSM from the stability of the electroweak vacuum. Co-annihilation with the next-to-lightest supersymmetric particle is potentially significant. Incorporating the latest accelerator constraints from LEP and elsewhere, we find that 50 GeV <∼ mχ <∼ 600 GeV and tanβ >∼ 2.5, if soft supersymmetry breaking parameters are assumed to be universal. THE LIGHTEST SUPERSYMMETRIC PARTICLE IN THE MSSM The motivation for supersymmetry at an accessible energy is provided by the gauge hierarchy problem [1], namely that of understanding why mW ≪ mP , the only candidate for a fundamental mass scale in physics. Alternatively and equivalently, one may ask why GF ∼ g2/m2W ≫ GN = 1/m2P , where MP is the Planck mass, expected to be the fundamental gravitational mass scale. Or one may ask why the Coulomb potential inside an atom is so much larger than the Newton potential, which is equivalent to why e = O(1) ≫ mpme/m2P , where mp,e are the proton and electron masses. One might think it would be sufficient to choose the bare mass parameters: mW ≪ mP . However, one must then contend with quantum corrections, which are quadratically divergent: