Direct detection of dark matter in the minimal supersymmetric standard model with non-universal Higgs boson masses

We calculate dark matter scattering rates in the minimal supersymmetric extension of the standard model (MSSM), allowing the soft supersymmetry-breaking masses of the Higgs multiplets, $m_{1,2},$ to be nonuniversal (NUHM). Compared with the constrained MSSM (CMSSM) in which $m_{1,2}$ are required to be equal to the soft supersymmetry-breaking masses $m_0$ of the squark and slepton masses, we find that the elastic scattering cross sections may be up to two orders of magnitude larger than values in the CMSSM for similar lightest supersymmetric particle masses. We find the following preferred ranges for the spin-independent cross section, ${10}^{-6}\mathrm{pb}\gtrsim {\sigma }_{\mathrm{SI}}\gtrsim {10}^{-10}\mathrm{pb},$ and, for the spin-dependent cross section, ${10}^{-3}\mathrm{pb}\gtrsim {\sigma }_{\mathrm{SD}},$ with the lower bound on ${\sigma }_{\mathrm{SI}}$ dependent on using the putative constraint from the muon anomalous magnetic moment. We stress the importance of incorporating accelerator and dark matter constraints in restricting the NUHM parameter space, and also of requiring that no undesirable vacuum appear below the grand unified theory (GUT) scale. In particular, values of the spin-independent cross section another order of magnitude larger would appear to be allowed, for small $\tan \beta ,$ if the GUT vacuum stability requirement were relaxed, and much lower cross-section values would be permitted if the muon anomalous magnetic moment constraint were dropped.