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

*Jon Butterworth, Martin Habedank, Louie Corpe, Deepak Kar, Priscilla Pani, Andrius Vaitkus*

Two studies of this model ,
[77], which was also studied by ATLAS in [22], appear in [83] (*Sensitivity of LHC measurements to a two-Higgs-doublet plus pseudoscalar DM model* and *Determining sensitivity of future measurements to new physics signals*)

The key parameters (as also described in the model README file) are as follows.

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 [77]. 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¶

The ATLAS summary [22] shows, in Fig.19a, a scan in \(M_A = M_{h^\pm,} = M_H\) and the mass of the pseudoscalar mediator \(M_a\), and in Fig.19b a scan in \(\tan\beta\) and \(M_a\) for \(M_A = M_{h^\pm,} = M_H = 600\) GeV. We compare to these scans below.

Note that, as specified in Table 6 of [22], the values of \(\lambda_3, \lambda_{P1}, \lambda_{P2}\) are all changed from the model default of zero, and set to 3, and we are in the “aligned limited” ie \(\sin(\beta-\alpha) = 1.0, \cos(\beta-\alpha) = 0.0\) so the lightest Higgs has the branching fractions 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 3.1.x 6/2/2020, A. Vaitkus.*

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 exclusion heatmap (shown below and in the proceedings) shadows a subset of the ATLAS search sensitivity in the same final state. The ATLAS searches have more luminosity and higher beam energy than the measurement available to Contur. Repeating these measurements with higher energies and more integrated luminosity would be highly desireable.

The band of sensitivity at \(M_A < 600\) GeV is not present in the ATLAS searches, however.
This comes from various measurements, mostly involving \(W\) boson in the final state.
In general multiple exotics Higgs channels contribute, as discuss, and illustrated in Figure 3 of, the proceedings (**TODO** add link when available).

**Figure 19b** a scan in \(\tan\beta\) and \(M_a\) for \(M_A = M_{h^\pm,} = M_H = 600\) GeV.
*Updated to Rivet 3.1.x 6/2/2020, A. Vaitkus.*

There is good sensitivity 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 [22]. The signatures mostly involve top quarks, although not the four-top signature which was considered in [22].