Abstract
We revisit the theory and phenomenology of scalar electroweak multiplet thermal dark matter. We derive the most general, renormalizable scalar potential, assuming the presence of the Standard Model Higgs doublet, H, and an electroweak multiplet Φ of arbitrary SU(2)L rank and hypercharge, Y. We show that, in general, the Φ-H Higgs portal interactions depend on three, rather than two independent couplings as has been previously considered in the literature. For the phenomenologically viable case of Y = 0 multiplets, we focus on the septuplet and quintuplet cases, and consider the interplay of relic density and spin-independent direct detection cross section. We show that both the relic density and direct detection cross sections depend on a single linear combination of Higgs portal couplings, λeff. For λeff ∼ mathcal{O} (1), present direct detection exclusion limits imply that the neutral component of a scalar electroweak multiplet would comprise a subdominant fraction of the observed DM relic density.
Highlights
Detection (DD) experiments and LHC searches place severe constraints on this possibility, though some room remains depending on the specific model realization
We show that both the relic density and direct detection cross sections depend on a single linear combination of Higgs portal couplings, λeff
We first observe that in the SM, there is no true phase transition between the electroweak symmetric phase and the broken phase, but the cross over is located at Tc = 159 ± 1 GeV [53]. This temperature, which can be translated to a critical dark matter mass Mc ≈ 3.2 TeV, electroweak symmetry is restored; W and Z bosons can be taken as massless particles; and triple scalar couplings go to zero as they are proportional to the vacuum expectation value of neutral component of the Higgs doublet
Summary
We consider the renormalizable Higgs portal interactions involving H and Φ for two illustrative cases. The scalar multiplet Φ of integer isospin can be either real or complex. Notice that a scalar multiplet Φ of half integer isospin is always complex since the realness condition Φ = Φ can not be fulfilled anymore. Under certain assumptions about the model parameters, the complex scalar multiplets may reduce to a pair of degenerate real multiplets, allowing for a two-component. We focus on the complex Y = 0 examples that, in principle, can embody two-component real multiplet DM scenarios. Which in general is a distinct invariant from (ΦΦ)0 except in special cases when Φ is a real scalar multiplet satisfying Φ = Φ. The classification of the Φ self-interactions is more involved, and it is most illuminating to consider them on a case-by-case basis
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