How Finely Tuned is Supersymmetric Dark Matter?

Abstract

We introduce a quantification of the question in the title: the logarithmic sensitivity of the relic neutralino density Omega-hsquared to variations in input parameters such as the supersymmetric mass scales m_0, m_1/2 and A_0, tan beta and the top and bottom quark masses. In generic domains of the CMSSM parameter space with a relic density in the preferred range 0.1 < Omega-hsquared < 0.3, the sensitivities to all these parameters are moderate, so an interesting amount of supersymetric dark matter is a natural and robust prediction. Within these domains, the accuracy in measuring the CMSSM and other input parameters at the LHC may enable the relic density to be predicted quite precisely. However, in the coannihilation regions, this might require more information on the supersymetric spectrum than the LHC is able to provide. There are also exceptional domains, such as those where direct-channel pole annihilation dominates, and in the `focus-point' region, where the logarithmic sensitivity to the input parameters is greatly increased, and it would be more difficult to predict Omega-hsquared accurately.