Relation between heat kernel method and scattering spectral method

Taking into account the available accelerator and astrophysical constraints, the mass of the lightest neutral Higgs boson h in the minimal supersymmetric extension of the Standard Model with universal soft supersymmetry-breaking masses (CMSSM) has been estimated to lie between 114 and ??130?GeV. Recent data from ATLAS and CMS hint that m _h ??125?GeV, though m _h ??119?GeV may still be a possibility. Here we study the consequences for the parameters of the CMSSM and direct dark matter detection if the Higgs hint is confirmed, focusing on the strips in the (m _1/2,m ₀) planes for different tan?? and A ₀ where the relic density of the lightest neutralino ?? falls within the range of the cosmological cold dark matter density allowed by WMAP and other experiments. We find that if m _h ??125?GeV focus-point strips would be disfavoured, as would the low-tan?? ${tilde{tau}}$ ?C?? and ${tilde{t}}_{1} $ ?C?? coannihilation strips, whereas the ${tilde{tau}}$ ?C?? coannihilation strip at large tan?? and A ₀>0 would be favoured, together with its extension to a funnel where rapid annihilation via direct-channel H/A poles dominates. On the other hand, if m _h ??119?GeV more options would be open. We give parameterisations of WMAP strips with large tan?? and fixed A ₀/m ₀>0 that include portions compatible with m _h =125?GeV, and present predictions for spin-independent elastic dark matter scattering along these strips. These are generally low for models compatible with m _h =125?GeV, whereas the XENON100 experiment already excludes some portions of strips where m _h is smaller.