Abstract
We show how the Higgs boson mass is protected from the potentially large corrections due to the introduction of minimal dark matter if the new physics sector is made supersymmetric. The fermionic dark matter candidate (a 5-plet of $SU(2{)}_{L}$) is accompanied by a scalar state. The weak gauge sector is made supersymmetric, and the Higgs boson is embedded in a supersymmetric multiplet. The remaining standard model states are nonsupersymmetric. Nonvanishing corrections to the Higgs boson mass only appear at three-loop level, and the model is natural for dark matter masses up to 15 TeV---a value larger than the one required by the cosmological relic density. The construction presented stands as an example of a general approach to naturalness that solves the little hierarchy problem which arises when new physics is added beyond the standard model at an energy scale around 10 TeV.
Highlights
We show how the Higgs boson mass is protected from the potentially large corrections due to the introduction of minimal dark matter if the new physics sector is made supersymmetric
Nonvanishing corrections to the Higgs boson mass only appear at three-loop level, and the model is natural for dark matter masses up to 15 TeV—a value larger than the one required by the cosmological relic density
The construction presented stands as an example of a general approach to naturalness that solves the little hierarchy problem which arises when new physics is added beyond the standard model at an energy scale around 10 TeV
Summary
Minimal dark matter (MDM) [1] is an attractive model because the stability of the dark matter (DM) candidate is not enforced by an additional ad hoc symmetry, and the coupling to ordinary matter is fixed and equal to that of the weak gauge interaction. The model contains one or more new particles belonging to multiplets in a representation of the weak SUð2ÞL gauge group that makes their coupling to standard model (SM) particles by means of renormalizable operators impossible, except for the gauge interaction itself. A fermionic multiplet with n 1⁄4 5 is singled out by the simultaneous requirements of containing a stable (neutral) state and preserving the perturbative running of the gauge coupling—that would be destroyed by too large a representation This model suffers a (mild) problem of naturalness [2] insofar as the mass of the DM candidate must be around 10 TeV to satisfy the current relic abundance constraint [3].
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