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Constraints on Supersymmetry from Relic Density compared with future Higgs Searches at the LHC

Among the theories beyond the Standard Model (SM) of particle physics Supersymmetry (SUSY) provides an excellent dark matter (DM) candidate, the neutralino. One clear prediction of cosmology is the annihilation cross section of DM particles, assuming them to be a thermal relic from the early universe. In most of the parameter space of Supersymmetry the annihilation cross section is too small compared with the prediction of cosmology. However, for large values of the tan beta parameter the annihilation through s-channel pseudoscalar Higgs exchange yields the correct relic density in practically the whole range of possible SUSY masses up to the few TeV range. The required values of tan beta are typically around 50, i.e. of the order of top and bottom mass ratio, which happens to be also the range allowing for Yukawa unification in a Grand Unified Theory with gauge coupling unification. For such large values of tan beta the associated production of the heavier Higgses, which is enhanced by tan beta squared, becomes three orders of magnitude larger than the production of a simlar SM-like Higgs and could be observable as one of the first hints of new physics at the LHC.