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.
Highlights
Broken supersymmetry alleviates the electroweak hierarchy problem [1,2]
In the minimal supersymmetric extension of the Standard Model (MSSM) the Higgsino mass parameter μ appears both in the masses of the Higgs bosons and in the neutralino mass matrix
We show that current direct search limits impose a strong lower bound on jμj, in particular for μ > 0 or if the masses of the heavy Higgs bosons of the MSSM are near their current limit from LHC searches; these bounds on jμj are typically much stronger than the ones from collider physics
Summary
Broken supersymmetry alleviates the electroweak hierarchy problem [1,2]. In supersymmetric theories there are no quadratically divergent radiative corrections to the masses of Higgs bosons. If jμj ≃ M1 the LSP has sizable Higgsino and bino components, and generically sizable couplings to the neutral Higgs bosons of the MSSM Such mixed neutralinos tend to have rather large scattering cross sections on matter, in potential conflict with strong lower bounds on this quantity from direct dark matter searches [3]. This is true in particular for the so-called “well-tempered neutralino” [14], a bino-Higgsino mixture with the correct relic density in minimal cosmology.
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