Constraints on the parameter space in an inert doublet model with two active doublets

Published for SISSA by Springer Received: November 21, 2019 Revised: March 2, 2020 Accepted: March 5, 2020 Published: March 19, 2020 Marco Merchand and Marc Sher High Energy Theory Group, College of William & Mary, Williamsburg, VA 23187, U.S.A. E-mail: , Abstract: We study a three Higgs doublet model where one doublet is inert and the other two doublets are active. Flavor changing neutral currents are avoided at tree-level by imposing a softly broken Z20 symmetry and we consider type I and type II Yukawa structures. The lightest inert scalar is a viable Dark Matter (DM) candidate. A numerical scan of the free parameters is performed taking into account theoretical constraints such as positivity of the scalar potential and unitarity of 2 → 2 scattering amplitudes. The model is further constrained by experimental results such as B physics lower limits on charged Higgs masses, Electroweak Precision Observables, LEP II, LHC Higgs measurements, Planck measurement of the DM relic abundance and WIMP direct searches by the LUX and XENON1T experiments. The model predictions for mono-jet, mono Z and mono Higgs final states are studied and tested against current LHC data and we find the model to be allowed. We also discuss the effects of abandoning the “dark democracy” assumption common in studies of inert models. Projected sensitivities of direct detection experiments will leave only a tiny window in the DM mass versus coupling plane that is compliant with relic density bounds. Keywords: Jets, Phenomenological Models ArXiv ePrint: 1911.06477 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP03(2020)108 JHEP03(2020)108 Constraints on the parameter space in an inert doublet model with two active doublets Contents 2 2 Model description 2.1 The inert plus two doublet model 2.2 Mass eigenstates 3 3 5 3 Theoretical constraints 3.1 Positivity of the potential 3.2 Unitarity 6 6 6 4 Experimental constraints 4.1 B physics constraints 4.2 Electroweak precision observables 4.3 Constraints from LEP 4.4 LHC Higgs data 4.5 Relic density 4.6 Direct detection experiments 7 7 8 8 9 9 10 5 Comparison with superposition of IDM + 2HDM 10 6 Numerical scan of parameter space 11 7 Model predictions 7.1 Mono jet 7.2 Mono Z 7.3 Mono-Higgs 7.4 Discussion 15 16 18 19 21 8 Dark democracy lifted 22 9 Heavy Higgs decays 23 10 Conclusions 25 A 2HDM parameters 26 B EWPO formulas 27 –1– JHEP03(2020)108 1 Introduction 1 Introduction –2– JHEP03(2020)108 The nature of dark matter remains one of the biggest mysteries in physics. While evidence for the existence of DM has been very well established over the last decades, the Standard Model (SM) lacks a good DM candidate. It is therefore necessary to consider theories beyond the SM to address this issue. One of the most conspicuous examples of a DM candidate is the so called WIMP whose mass is expected to be of order the electroweak scale mχ ≈ 100 GeV in order to give the correct annihilation cross section for DM depletion. Models with WIMP candidates exist in abundance in the literature. Perhaps the most famous example is the Minimal Supersymmetric Standard Model (MSSM), however the lack of evidence at the LHC for superpartners has prompted the physics community to look for alternative scenarios. The inert two Higgs doublet model (IDM) stands as a well motivated non supersymmetric extension of the SM that has within it a viable DM candidate and is still consistent with theoretical and experimental bounds. Like other WIMP models, it predicts monojet, mono-Z, mono-Higgs and vector boson fusion plus missing transverse energy signals at the LHC [1]. However the parameter space of the IDM will become more constrained as the LHC program continues improving on its precision measurements of the electroweak sector and as more stringent bounds are placed on the annihilation cross section of DM by direct detection experiments in the upcoming future. Thus it is interesting to consider extensions of the IDM which predict additional phenomena but might evade some of these constraints. The fact that the IDM doesn’t allow CP violation in the scalar sector was one of the main motivations for Grzadkowski, Ogreid and Osland, ref. [2] to extend the IDM by adding an extra active SU(2)L Higgs doublet. They called it the IDM2 and scanned its parameter space imposing theoretical and experimental constraints to determine where DM abundance is acceptable and CP is violated. Although the issue of electroweak baryogenesis was not addressed by the authors they used the difference between the average and the maximal values of the electron electric dipole moment and the basis-independent invariants, introduced by Gunion and Haber in [3], to provide a measure of the amount of CP violation. The same model was further studied by some of the same authors in refs. [4, 5]. In [4] the authors refined the basis invariants used in [2] to include the effect from the extra inert doublet and include DM direct detection constraints in their study. In ref. [5] the phenomenology of charged scalars at the LHC was studied. Another interesting scenario that allows for CP violation is that of a 2HDM plus an inert gauge singlet scalar [6]. This model has fewer parameters and the DM is more inert, i.e. it doesn’t have gauge interactions. In this model there are two independent portal couplings that allow decoupling between DM annihilation and scattering off nucleons and thus one has to take into account isospin violation i.e. the effective couplings of DM to the proton and the neutron are different and one has to rescale the experimental cross sections. The CP conserved version of the IDM2 was studied in ref. [7] by Moretti and Yagyu, together with a model with 2 inert and one active doublet. They referred to these models as I(1+2)HDM and I(2+1)HDM respectively. They studied the constraints on the parameter 2 2.1 Model description The inert plus two doublet model The I(1+2)HDM has two active SU(2)L Higgs doublets that we parametrize as follows ! ! + ϕ+ ϕ 1 2 √ √ Φ1 = , Φ2 = , (2.1) (v1 + ρ1 + iχ1 )/ 2 (v2 + ρ2 + iχ2 )/ 2 –3– JHEP03(2020)108 space from perturbative unitarity by calculating all possible scalar boson 2 → 2 elastic scatterings. They also included constraints from electroweak precision observables (EWPO) and provided the relevant formulas for the Peskin-Takeuchi S, T and U for both models. The results of this paper were used in the I(1+2)HDM by Moretti, Rojas and Yagyu in [8] to calculate the one loop induced H ± W ∓ Z vertex and study the parameter space where the branching fraction H ± → W ∓ Z can be of order 10% when the charged scalar is lighter than the top quark. The I(2+1)HDM [9–11] has two inert doublets and thus can alleviate the tension with direct detection experiments in the low mass region. In the high mass region, it can bring the model to testable territory by decreasing the mass or increasing the Higgs DM co (...truncated)