The fine-tuning price of neutralino dark matter in models with non-universal Higgs masses

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We study the amounts of fine-tuning of the parameters of the MSSM with non-universal soft supersymmetry-breaking contributions to the Higgs masses (the NUHM) that would be required for the relic neutralino density to lie within the range favoured by WMAP and other astrophysical and cosmological observations. Such dark matter fine-tuning is analogous to the commonly studied electroweak fine-tuning associated with satisfying the electroweak symmetry breaking conditions, which we also study for completeness. We identify several distinct regions of the NUHM parameter space: a bulk region, a $\stau-\neut$ coannihilation region, a pseudoscalar Higgs funnel region, a focus-point bino/higgsino region and a $\sneut-\neut$ coannihilation region. Within each region, we analyse specific representative points for which we provide breakdowns of the contributions to the dark matter fine-tuning associated with the different NUHM parameters. In general, the NUHM offers points with both both smaller and larger amounts of dark matter fine-tuning than points in the corresponding regions of the CMSSM. Lower amounts of dark matter fine-tuning typically arise at points where several different (co)annihilation processes contribute, e.g., at junctions between regions with different dominant processes. We comment on the prospects for using collider measurements to estimate the likely dark matter density within the NUHM framework.