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The CP-conserving 2HDM after the 8 TeV run

We confront the most common CP-conserving 2HDM with the LHC data analysed so far while taking into account all previously available experimental data. A special allowed corner of the parameter space is analysed - the so-called wrong-sign scenario where the Higgs coupling to down-type quarks changes sign relative to the Standard Model while the coupling to the massive vector bosons does not.


Introduction
The end of the 8 TeV run at the Large Hadron Collider (LHC) has confirmed the existence of a Higgs boson [1,2] that very much resembles the one predicted by the Standard Model (SM). Furthermore there are no hints of extra scalars in the data analysed so far. As many of the extension of the SM, the two-Higgs doublet model (2HDM) is being cornered into a SM-like region except for a few regions of the parameter space.
The 2HDM is an extension of the SM where one extra doublet is added to the particle content while keeping the SM symmetries. It appears in the literature in a variety of versions that depend mainly on the extra symmetries imposed on the Lagrangian and on how the SU(2) ×U(1) symmetry is broken to U (1). In this work we will focus on the CP-conserving 2HDM with a Z 2 discrete symmetry, softly broken in the potential by a dimension two term.
We will show the allowed parameter space of the model after the LHC 8 TeV run with all theoretical and experimental constraints taken into account. We will then study a region of the parameter space where the lightest CP-even Higgs (considered to be the SM-like Higgs throughout the paper) coupling to the down-type quarks changes sign relative to the SM.

The allowed parameter space of the 2HDM
The most general 2HDMs give rise to couplings corresponding to tree-level Higgs-mediated flavour-changing neutral currents (FCNCs), in clear disagreement with experimental data. A simple and natural way to avoid tree-level FCNCs is to impose a Z 2 symmetry on the scalar doublets, , and a corresponding symmetry on the quark fields. This leads to the well known four Yukawa model types I, II, Flipped (F) (or Y) and Lepton Specific (LS) (or X). The different Yukawa types are built such that only φ 2 couples to all fermions (type I), or φ 2 couples to up-type quarks and φ 1 couples to down-type quarks and leptons (type II), or φ 2 couples to uptype quarks and to leptons and φ 1 couples to down-type quarks (type F) or finally φ 2 couples to all quarks and φ 1 couples to leptons (type LS). See [3] for a comprehensive review on the 2HDM.
The scalar potential in a softly broken Z 2 symmetric 2HDM can be written as where Φ i , i = 1, 2 are complex SU(2) doublets. We will focus on a specific realisation of the 2HDM, the usual 8-parameter CP-conserving potential where the potential parameters and the VEVs are all real. In this model we choose as free parameters, the four masses, the rotation angle in the CP-even sector, α, the ratio of the vacuum expectation values, tan β = v 2 /v 1 , and the soft breaking parameter m 2 12 . By convention, we take 0 ≤ β ≤ π/2 and −π/2 ≤ α ≤ π/2. The 2HDM parameters are chosen such that electric charge is conserved while neutral Higgs fields acquire real vacuum expectation values. Note that the existence of a tree-level scalar potential minimum that breaks the electroweak symmetry but preserves both the electric charge and CP symmetries, ensures that no additional tree-level potential minimum that spontaneously breaks the electric charge and/or CP symmetry can exist [4]. Further, we force the CP-conserving minimum to be the global one [5].
In order to find the 2HDM parameter space that is still allowed after the 8 TeV run we have used ScannerS [6] interfaced with SusHi [7] and HDECAY [8,9] for Higgs production and decays, cross-checked with HIGLU [10] and 2HDMC [11]. The remaining Higgs production cross sections were taken from [12]. All collider data was taken into account with HiggsBounds [13] and HiggsSignals [14]. The remaining constraints (see [15]), theoretical, electroweak precision and B-physics constraints are coded in ScannerS.
We have performed a scan in the 2HDM parameter space in the following range: m h = 125.9 GeV, m h + 5 GeV < m H , m A < 1 TeV, 100 GeV < m H ± < 1 TeV, 1 < tan β < 30, |α| < π/2 and −(50 GeV) 2 < m 2 12 < (500 GeV) 2 . In figure 1 we present the allowed parameter space af- ter the 8 TeV run at 1σ , 2σ and 3σ with all experimental and theoretical constraints taken into account. There are some interesting features worth mentioning. First, the bounds on sin(β − α) range from about 0.5 in type II to about 0.7 in type LS at 3σ . Second, that large values of tan β require sin(β − α) close to 1 except for the type I model. Note that although the Higgs couplings to quarks are equal in types I and LS, the couplings to leptons are different. As a result, the measurement of pp → h → τ + τ − affects considerably more the parameter space of type LS than that of type I [16]. Finally, it is clear from the figure that in models type II and Flipped, the allowed points are centred around two lines. The line on the right corresponds to the SM-like limit, that is sin(β − α) = 1. In this limit, the lightest Higgs couplings to gauge bosons and to fermions are the SM ones. The line on the left corresponds to the limit sin(β + α) = 1. In type II and with our conventions, it corresponds to the limit where the Higgs coupling to down-type quarks changes sign relative to the SM while couplings to up-type quarks and massive gauge bosons are the same. This is called the wrong-sign limit [17] (see also [18,19] . Note that this limit is imposed only at tree-level.

The wrong-sign scenario
We will now analyse the wrong-sign scenario in the light of the next run of the LHC. This scenario was first discussed in [20]. Let us start by defining which means that at tree-level κ i is just the ratio of couplings κ i = g 2HDM /g SM . In the SM-like limit, κ W (Z) = sin(β − α) = 1, implies κ U = κ D = κ L = 1, that is, the lightest Higgs couplings to up-type quarks (U), down-type quarks (D) and leptons (L), are the SM ones. The wrong-sign scenario can be defined as either κ D κ W < 0 or κ U κ W < 0 (κ L never plays a major role in the interference terms). We can further have κ D κ U < 0, in which case both κ g and κ γ can be affected or κ D κ U > 0 meaning that only κ γ can be affected. The wrong sign scenario is obtained in type II and F with As the constraints from B-physics and from the R b measurements force tan β to be above O(1) we will focus on the case κ D = −1. We will now discuss this scenario for the type II model (very similar to the type F case). Will the LHC be able to probe the wrong-sign scenario? We define the signal strength as where σ is the Higgs production cross section and BR(h → f ) is the branching ratio of the decay into some given final state f ; σ SM and BR SM (h → f ) are the expected values for the same quantities in the SM. We will not separate different LHC initial state production mechanisms and instead sum over all production mechanisms in computing the cross section. As a rough approximation of the precision with current data we require that the LHC's µ h f for the final states f = WW , ZZ, bb, γγ and τ + τ − are each consistent with unity within 20%. In order to understand how an increase in precision will affect the wrong-sign scenario we then require that all the µ h f are within 10% or 5% of the SM prediction. We now have to answer the following questions. First, why isn't this scenario excluded yet? Second, will it be probed at the LHC with high energy and high luminosity?
In the limit sin(β + α) → 1, κ D → −1 which implies that the main Higgs production mode, gluon-gluon fusion, is enhanced. The quark initiated modes are not modified relative to the SM because there are no interference terms (at LO). VBF and associated production do not suffer any significant change because sin(β − α) ≈ sin(β + α) for tan β 1. Therefore the scenario could in principle be probed at the production level in gg → h due to the interference between top and bottom loops. However, the uncertainties in the gluon fusion process advise not to use this production process to distinguish between the two scenarios [17,19].
Regarding the Higgs decays, it is clear that there is no difference between the two scenarios in the decay to fermions. Again, because sin(β − α) ≈ sin(β + α) for tan β 1, taking tan β = 8 the ratio of the wrong sign Γ(h → WW (ZZ)) decay width to the respective SM width is 0.94, which corresponds to a negligible effect in µ h WW due to the already discussed Higgs production cross section enhancement. Therefore, we have to turn into the decays where the interference between the different loop contributions occur, that is h → γγ and h → gg. In figure 2 we present κ γ (left) and κ g (right) as a function of κ D in type II with all rates within 20% (blue), 10% (green) and 5% (red) of the SM values. While it is understandable that a measurement of κ g could probe the wrong-sign scenario, the same is not true for κ γ . In fact, the decay h → γγ has not only the top and bottom loop contributions but also the W and charged-Higgs ones. Neglecting the charged-Higgs contribution, a change in the sign of κ D amounts to about a 1% difference in the width. Therefore it is the charged Higgs loop that is responsible for the more substantial reduction in Γ(h → γγ). This effect is due to the nondecoupling of the charged Higgs loop. As shown in [17] the charged-Higgs contribution to Γ(h → γγ) in the κ D < 0 case is approximately constant and always sufficiently significant as to eventually be observable at the LHC. However, the constraints coming from tree-level unitarity imply that the result is only perturbatively reliable for m H ± ∼ 650 GeV.
According to Table 1-20 of Ref. [21], the expected errors for κ g based on fittings are 6-8% for L = 300 fb −1 and 3-5% for L = 3000 fb −1 (for 14 TeV). The predicted accuracy for κ γ is 5-7% for an integrated luminosity of L = 300 fb −1 and 2-5% for L = 3000 fb −1 . Therefore there are good chances to probe the wrong-sign scenario in the 14 TeV LHC run. Also with the predicted accuracy for the International Linear Collider [22,23] the scenario could not only be probed by a measurement of κ g and κ γ but also in the process e + e − → Zh(→ bb). Finally one should mention that a thorough study of this scenario has to take into account the 2HDM electroweak corrections, some of which are already available [24,25].