# Two Higgs-Doublet Dark Matter Model with Pseudoscalar Mediator¶

Preliminary/work in progress study of this model , see also [95], also studied in [14].

Parameters (as described in the model README file):

• There are four Higgs bosons. $$h_1$$ is identified with the SM Higgs. Then there is a heavy scalar Higgs $$h_2 = H$$, a charged Higgs $$h_c = h^\pm$$, a CP-odd Higgs $$h_3 = A$$, and a pseudoscalar Higgs $$h_4 = a$$, which plays the role of the DM mediator. Unless stated otherwwise, the masses of the $$H, A$$ and $$h^\pm$$ are set equal to each other.
• The fermionic DM candidate has mass default $$M_{X_d} = 10$$ GeV.
• $$\sin(\beta-\alpha)$$ is the sine of the difference of the mixing angles in the scalar potential containing only the Higgs doublets, default = 1.0 (aligned limit).
• $$g^\prime_{X_d}$$ is the coupling of $$a$$ to DM. Default = 1.0.
• $$\tan\beta$$ is the ratio of the vacuum expectation values $$\tan \beta = \frac{v_2}{v_1}$$ of the Higgs doublets. Default = 1.0.
• $$sin \theta$$ is the sine of the mixing angle between the two neutral CP-odd weak eigenstates, as defined in Section 2.1 of [95]. Default = 0.35.
• $$\lambda_3$$. Default = 0.0.
• $$\lambda_{P1}$$ = The quartic coupling between the scalar doublet $$H_1$$ and the pseudoscalar $$P$$. Default = 0.0.
• $$\lambda_{P2}$$ = The quartic coupling between the scalar doublet $$H_2$$ and the pseudoscalar $$P$$. Default = 0.0.

## Comparison to ATLAS summaries¶

See the Les Houches wiki for some significant progess on understanding all this.

The ATLAS summary [48] / [14] shows, in Fig.15a, a scan in $$M_A = M_{h^\pm,} = M_H$$ and the mass of the pseudoscalar mediator $$M_a$$, and in Fig.15b a scan in $$\tan\beta$$ and $$M_a$$ for $$M_A = M_{h^\pm,} = M_H = 600$$ GeV. Similar scans are shown below. Note that, as specified in Table 6 of [48], the values of $$\lambda_3, \lambda_{P1}, \lambda_{P2}$$ are all changed from the model default of zero, and set to 3.

This is all in the “aligned limited” ie $$\sin(\beta-\alpha) = 1.0, \cos(\beta-\alpha) = 0.0$$ so the lightest Higgs has the branching factiors and couplings of the SM Higgs.

Figure 19a, a scan in $$M_A = M_{h^\pm,} = M_H$$ and the mass of the pseudoscalar mediator $$M_a$$. (Updated to Rivet 2.7.x 7/6/2019.)

The Contur sensitivity at $$800 < M_A < 1400$$ GeV is worse that the ATLAS searches, because the measurements available in Rivet include very few $$E_{T}^{\rm miss} + X$$ cross sections, and no $$E_{T}^{\rm miss} + H(b\bar{b})$$ at all, where most of the ATLAS sensitvity comes from. One of the few exceptions is the $$l^+l^- + E_T^\mathrm{miss}$$ measurement in 7 TeV, where the heatmap is shown below, shadowing a subset of the ATLAS search sensitivity in the same final state, which has more luminosity and higher beam energy than the measurement available to Contur.

The band of sensitivity at $$M_A < 600$$ GeV is not present in the ATLAS searches, however. This comes from various measurements, most especially the CMS 8 TeV $$h \rightarrow WW$$ measurement (the Higgs transverse momentum differential cross section) [211] . The contributions to this fiducial cross section seem to come not from genuine SM Higgs events, but from the copious W boson production via charged Higgs decays to, and associated production with, top quarks. In general multiple exotics Higgs channels contribute. An example is given below right, for $$M_A = 272$$ GeV, $$M_a = 357$$ GeV.

(The theory prediction from the CMS paper is also shown, in green, for illustration.) For this parameter point the charged Higgs decays dominantly to to $$tb$$, and there is also a 5% branching of the pseudoscalar ($$a$$) to $$t\bar{t}$$. For 8 TeV collisions, Herwig calculates the production cross section for $$gb \rightarrow t h^-$$ (+ c.c.) as 840fb, for example, with several other relevant processes also having a significant cross section.

Similar but less significant contributions are seen in other ATLAS and CMS measurements of W+jets, top, and WW production.

Figure 19b a scan in $$\tan\beta$$ and $$M_a$$ for $$M_A = M_{h^\pm,} = M_H = 600$$ GeV. (Updating to Rivet 2.7.x 8/6/2019.)

There is good sensitivity via for $$M_A < 600$$ GeV and $$\tan\beta < 1$$ or so regardless of $$M_a$$, generally coming from processes involving the production and decay of the new heavy Higgs bosons, contributing to final-state signatures not considered in [14]. The signatures mostly involve top quarks, although not the four-top signature which was considered in [14].

See the Les Houches wiki for some significant progess on understanding all this.

## Other Variants¶

Moving away from the aligned limit, the decays of the Higgs bosons change, and for large enough $$\cos(\beta-\alpha)$$ the decays of the SM-like Higgs will change enough to be inconsistent with measurements. However, small misalignments are still possible. The figure below (made for fixed $$M_a = 300$$ GeV) shows that the Contur limit is quite stable against such changes - as some decays become less common, others (for example the four-lepton channel, shown as an example) begin to contribute.

Note that for values of $$\cos(\beta-\alpha)$$ higher than those in this plot, the SM Higgs branchings are substantially modified, and the SM Higgs measurements would exclude those scenarios anyway.

Same scan as Fig 19a of [14] in $$M_A = M_{h^\pm} = M_H$$ and the mass of the pseudoscalar mediator $$M_a$$, but with $$\sin\theta = 0.7$$. (Updated to Rivet 2.7.x 9/6/2019.)

This exclusion still be understood.