# NMSSM with exotic higgs decay to fermions

While both the R- and the PQ-limit lead to a light pseudoscalar as discussed elsewhere, the PQ-limit with mh = 125  GeV typically leads to different exotic Higgs decay phenomenology, in which decays to fermions can be as or more important than decays to scalars [1,2].
When vs >> vu, vd, the dominant tree-level contributions to the masses of the singlet-like scalars and singlino-like fermion ~S are [3,4,1]

(1)

The pseudoscalar a is light in both the R- and PQ-limits, but in the PQ-limit s and ~S must be light as well. This cannot be realized in the R-limit, since vacuum stability for small κ requires Aλ  ∼ μtanβ, strongly breaking R-symmetry.
This abundance of possible light singlet-like states opens up many different exotic Higgs decays, giving phenomenology that is qualitatively unlike the decays in the R-limit. In the R-limit, the coupling of the SM-like Higgs to the R-axion eigenstate is gh a a ∼ O (mh2/vS2) ×v [5,6], and vs as large as 10 mh can still yield a sizeable branching fraction Br(h→aa) ∼ 0.1.
The corresponding couplings in the PQ-limit instead scale as [1,2]

(2)

where

(3)

is required by vacuum stability (avoiding a runaway in the S-direction). For a given μeff, small λ corresponds to small singlet-doublet mixing and mostly SM-like Higgs phenomenology. Correspondingly, parameter scans using NMSSMTools [7,8,9,10] indicate that λ <~0.3 dominates the surviving parameter space in the PQ-limit (κ << λ) (see App. ). It is thus common in the PQ-limit to obtain ghaa, ghss << v, suppressing exotic Higgs decays to (pseudo-)scalars. However, the PQ-limit allows the SM-like Higgs boson to decay into a pair of light neutralinos h → χiχj. The relevant vertex couplings for a singlino-like χ1 and a bino-like χ2 are

(4)

For mχ2 <~100 and mχ1  ∼ O(1−10 GeV) the off-diagonal decay h → χ1 χ2 can be kinematically accessible with an O(0.1) branching fraction. The purely invisible decay h → χ1 χ1 is suppressed by a factor of  ∼ λ/(g1 tanβ) relative to the off-diagonal decay, ignoring phase space factors. Meanwhile, Higgs decay to a pair of bino-like χ2 also scales as a single factor of the bino-Higgsino mixing angle, C2χ2 ∼ O (g1 /λ) C1χ2 and if h→χ2χ2 is kinematically available, this branching fraction can be important.
For mχ2−mχ1 > min {ms, ma}, the heavier neutralino can decay via χ2→χ1 a or χ2→χ1s [1,2]. This leads to a plethora of possible h→ (xx) + MET or h → (xx)(yy) + MET decays, where x, y are SM partons (most likely b, τ, or light jets, see §) that reconstruct the singlet boson mass a or s. If mχ2 − mχ1 < min {ms, ma }, the principal decay mode of χ2 is the three-body decay χ2→(a,s)*χ1 → (xx) χ1, while the radiative mode χ2 →χ1 γ may become significant, with Br(h → χ1 χ1γ) as high as O(0.1). On-shell χ2 → χ1Z does not occur until mχ2 − mχ1 > mZ. Given that we require mχ2 − mχ1 < mh−2 mχ1, these points are sparse. Fig. 1 shows the corresponding exotic decay topologies.

Figure 1: Two significant fermionic decay topologies of the SM-like Higgs boson in the
PQ symmetry limit. Left (a): depending on whether min{ms, ma} exceeds mχ2 − mχ1, a(s) may or may not be on shell. Right (b): to be non-negligible, the radiative χ2 decay requires min{ms, ma} > mχ2 − mχ1.)

Summary:
The PQ-limit of the NMSSM yields semi-invisible exotic Higgs decays into pairs of light neutralinos, most typically h→ χ2χ1 or h→ χ2χ2, with χ2 → χ1 a, χ1 s, and a,s→ (ff, gg, γγ). This yields final states of the form (bb)+MET, (ττ)+MET, (bb) (bb)+MET, (ττ)(ττ))+MET, and the rarer but cleaner γ+MET, (2,4)μ+MET, (μμ)(bb)+MET. Depending on the spectrum, the visible particles may be collimated or isolated. Current experimental constraints and future prospects for a subset of these decays are discussed on the γ+MET, bb+MET, 2γ+MET, ττ+MET, and collimated/resonant leptons pages.

## References

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