Predictions of neutralino dark matter event rates in minimal supergravity unification

A detailed analysis of dark matter event rates in minimal supergravity models (MSGM's) is given. It is shown analytically that the lightest neutralino ${\tilde{Z}}_1$ is the LSP over almost all of the parameter space, and hence the natural candidate for cold dark matter (CDM). The radiative breaking of SU(2)×U(1) constraints is shown to be crucial in determining the expected event rates. Approximate analytic formulas are obtained to determine the gaugino-Higgsino content of the ${\tilde{Z}}_1$ particle. From this one can deduce the behavior of the event rates as one varies the SUSY soft breaking parameters and $tan\beta$. The constraint on the event rates due to the recently measured $b\to s+\gamma$ decay is calculated. It is seen that these data eliminate most of the parameter space where $\mu$ (the Higgs mixing parameter) and $A_t$ (the $t$-quark cubic soft breaking parameter) have the same sign. Since the $t$ quark is close to its Landau pole, $A_t$ is restricted to be mostly positive, and so most of the $\mu >0\mathrm{}$ part of the parameter space is eliminated. However, for $\mu <0\mathrm{}$, one finds large regions of parameter space where the event rate is large and exceeds 0.01 events/kg day. The importance of proper treatment of the $s$-channel $Z$ and Higgs poles in calculating the relic density is stressed. The implications of the recent new experiments (SMC and E143) on the quark polarizabilities are analyzed and it is seen that uncertainties in these generally produce only small uncertainties in the event rates. A discussion is also given of the sensitivity of the expected event rates to changes in the allowed range of ${\tilde{Z}}_1$ relic density.