Impact of the Bounds on the Direct Search for Neutralino Dark Matter on Naturalness

Abstract

In the Minimal Supersymmetric Extension of the Standard Model (MSSM) the higgsino mass parameter $\mu$ appears both in the masses of the Higgs bosons and in the neutralino mass matrix. Electroweak finetuning therefore prefers small values of $|\mu|$. On the other hand, bino--like neutralinos make a good dark matter candidate. We show that current direct search limits then impose a strong lower bound on $|\mu|$, in particular for $\mu > 0$ or if the masses of the heavy Higgs bosons of the MSSM are near their current limit from LHC searches. There is therefore some tension between finetuning and neutralino dark matter in the MSSM. We also provide simple analytical expressions which in most cases closely reproduce the numerical results.