Two-Higgs-doublet type-II and -III models and \(t\rightarrow c h\) at the LHC

The European Physical Journal C, Jun 2016

We study the constraints of the generic two-Higgs-doublet model (2HDM) type-III and the impacts of the new Yukawa couplings. For comparisons, we revisit the analysis in the 2HDM type-II. To understand the influence of all involving free parameters and to realize their correlations, we employ a \(\chi \)-square fitting approach by including theoretical and experimental constraints, such as the S, T, and U oblique parameters, the production of standard model Higgs and its decay to \(\gamma \gamma \), \(WW^*/ZZ^*\), \(\tau ^+\tau ^-\), etc. The errors of the analysis are taken at 68, 95.5, and \(99.7~\%\) confidence levels. Due to the new Yukawa couplings being associated with \(\cos (\beta -\alpha )\) and \(\sin (\beta -\alpha )\), we find that the allowed regions for \(\sin \alpha \) and \(\tan \beta \) in the type-III model can be broader when the dictated parameter \(\chi _F\) is positive; however, for negative \(\chi _F\), the limits are stricter than those in the type-II model. By using the constrained parameters, we find that the deviation from the SM in \(h\rightarrow Z\gamma \) can be of \(\mathcal{O}(10~\%)\). Additionally, we also study the top-quark flavor-changing processes induced at the tree level in the type-III model and find that when all current experimental data are considered, we get \(Br(t\rightarrow c(h, H) )< 10^{-3}\) for \(m_h=125.36\) and \(m_H=150\) GeV, and \(Br(t\rightarrow cA)\) slightly exceeds \(10^{-3}\) for \(m_A =130\) GeV.

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Two-Higgs-doublet type-II and -III models and \(t\rightarrow c h\) at the LHC

Eur. Phys. J. C Two-Higgs-doublet type-II and -III models and t → ch at the LHC A. Arhrib 1 2 R. Benbrik 0 5 Chuan-Hung Chen 4 Melina Gomez-Bock 3 Souad Semlali 0 0 LPHEA, Semlalia, Cadi Ayyad University , Marrakech , Morocco 1 Physics Division, National Center for Theoretical Sciences , Hsinchu 300 , Taiwan 2 Département de Mathématiques, Faculté des Sciences et Techniques, Université Abdelmalek Essaadi , B. 416, Tangier , Morocco 3 DAFM, Universidad de las Américas Puebla, Ex. Hda. Sta. Catarina Mártir , 72810 Cholula, PUE , Mexico 4 Department of Physics, National Cheng-Kung University , Tainan 70101 , Taiwan 5 MSISM Team, Faculté Polydisciplinaire de Safi, Sidi Bouzid , B.P 4162, 46000 Safi , Morocco We study the constraints of the generic twoHiggs-doublet model (2HDM) type-III and the impacts of the new Yukawa couplings. For comparisons, we revisit the analysis in the 2HDM type-II. To understand the influence of all involving free parameters and to realize their correlations, we employ a χ -square fitting approach by including theoretical and experimental constraints, such as the S, T, and U oblique parameters, the production of standard model Higgs and its decay to γ γ , W W ∗/Z Z ∗, τ +τ −, etc. The errors of the analysis are taken at 68, 95.5, and 99.7 % confidence levels. Due to the new Yukawa couplings being associated with cos(β − α) and sin(β − α), we find that the allowed regions for sin α and tan β in the type-III model can be broader when the dictated parameter χF is positive; however, for negative χF , the limits are stricter than those in the type-II model. By using the constrained parameters, we find that the deviation from the SM in h → Z γ can be of O(10 %). Additionally, we also study the top-quark flavor-changing processes induced at the tree level in the type-III model and find that when all current experimental data are considered, we get Br (t → c(h, H )) < 10−3 for mh = 125.36 and m H = 150 GeV, and Br (t → c A) slightly exceeds 10−3 for m A = 130 GeV. 1 Introduction A scalar boson around 125 GeV was observed in 2012 by ATLAS [1] and CMS [2] at CERN with more than 5σ significance. The discovery of such particle was based on the analyses of the following channels: γ γ , W W ∗, Z Z ∗ and τ +τ − with errors of order of 20–30 % and bb¯ channel with an error of order of 40–50 %. The recent updates from ATLAS and CMS with 7 ⊕ 8 TeV data [3–7] indicate the possible deviations from the standard model (SM) predictions. Although the errors of the current data are still somewhat large, the new physics signals may become clear in the second run of the LHC at 13–14 TeV. It is expected that the Higgs couplings to gauge bosons (fermions) at the LHC indeed could reach 4–6 % (6–13 %) accuracy when the collected data are up to the integrated luminosity of 300 fb−1 [8–11]. Furthermore, the e+e− Linear Collider (LC) would be able to measure the Higgs couplings at the percent level [12]. Therefore, the goals of LHC at run II are (a) to pin down the nature of the observed scalar and see if it is the SM Higgs boson or a new scalar boson; (b) to reveal the existence of new physics effects, such as the measurement of flavor-changing neutral currents (FCNCs) at the top-quark decays, i.e. t → qh. Motivated by the observations of the diphoton, W W ∗, Z Z ∗, and τ +τ − processes at the ATLAS and CMS, it is interesting to investigate what sorts of models may naturally be consistent with these measurements and what the implications are for other channels, e.g. h → Z γ and t → ch. Although many possible extensions of the SM have been discussed [13–19], it is interesting to study the simplest extension from a one-Higgs doublet to a two-Higgs-doublet model (2HDM) [20–47]. According to the situation of Higgs fields coupling to fermions, the 2HDMs are classified as type-I, II, and -III models, lepton specific model, and flipped model. The 2HDM type-III is the case where both Higgs doublets couple to all fermions; as a result, FCNCs at the tree level appear. The detailed discussions of the 2HDMs are shown elsewhere [23]. After the scalar particle of 125 GeV was discovered, the implications of the observed h → γ γ in the type-I and -II models were studied [48–54] and the impacts on h → γ Z are given [55–57]. As is well known, the tan β and angle α are important free parameters in the 2HDMs, where the former is the ratio of two vacuum expectation values (VEVs) of Higgses and the latter is the mixing parameter between the two CP-even scalars. It is found that the current LHC data put rather severe constraints on the free parameters [24–29]. For instance, the large tan β ∼ mt /mb scenario in the type-I and -II is excluded except if we tune the α parameter to be rather small, α < 0.02. Nevertheless, both type-I and type-II models can still fit the data in some small regions of tan β and α. In this paper, we will explore the influence of new Higgs couplings on the h → τ +τ −, h → gg, γ γ , W W, Z Z , and h → Z γ decays in the framework of the 2HDM type-III. We will show what is the most favored regions of the typeIII parameter space when theoretical and experimental constraints are considered simultaneously. FCNCs of the heavy quark such as t → qh have been intensively studied both from the experimental and the theoretical points of view [58]. Such processes are well established in the SM and are excellent probes for the existence of new physics. In the SM and 2HDM type-I and -II, the top-quark FCNCs are generated at one-loop level by charged currents and are highly suppressed due to the GIM mechanism. The branching ratio (BR) for t → ch in the SM is estimated to be 3 × 10−14 [59]. If this decay t → ch is observed, it would be an indisputable sign of new physics. Since the tree-level FCNCs appear in the typeIII model, we explore if the Br (t → ch) reaches the order of 10−5–10−4 [60–62], the sensitivity which is expected by the integrated luminosity of 3000 fb−1. The paper is organized as follows. In Sect. 2, we introduce the scalar potential and the Yukawa interactions in the 2HDM type-III. The theoretical and experimental constraints are described in Sect. 3. We set up the free parameters and establish the χ -square for the best-fit approach in Sect. 6. In the same section, we discuss the numerical results when all theoretical and experimental constraints are taken into account. The conclusions are given in Sect. 7. 2 Model In this section we define the scalar potential and the Yukawa sector in the 2HDM type-III. The scalar potential in SU ( 2 )L ⊗ U ( 1 )Y gauge symmetry and CP invariance is given by [69] V ( 1, 2 ) = m21 †1 1 + m22 †2 2 − (m122 1 2 + h.c.) † + 21 λ1( 1† 1)2 + 21 λ2( 2† 2)2 + λ3( 1† 1)( 2† 2) + λ4( 1† 2)( 1† 2) + λ25 ( 1† 2)2 + λ6 1† 1 + λ7 2† 2 † 1 2 + h.c. , (1) where the doublets 1,2 have a weak hypercharge Y = 1, the corresponding VEVs are v1 and v2, and λi and m212 are real parameters. After electroweak symmetry breaking, three of the eight degrees of freedom in the two Higgs doublets are the Goldstone bosons (G±, G0) and the remaining five degrees of freedom become the physical Higgs bosons: two CP-even h, H , one CP-odd A, and a pair of charged Higgs H ±. After using the minimized conditions and the W mass, the potential in Eq. ( 1 ) has nine parameters, which will be taken as (λi )i=1,...,7, m212, and tan β ≡ v2/v1. Equivalently, we can use the masses as the independent parameters; therefore, the set of free parameters can be chosen to be ( 2 ) {mh , m H , m A, m H± , tan β, α, m122}, where we only list seven of the nine parameters, the angle β diagonalizes the squared-mass matrices of CP-odd and charged scalars and the angle α diagonalizes the CP-even squared-mass matrix. In order to avoid generating spontaneous CP violation, we further require λ6v12 λ7v22 2 − 2 with ζ = 1(0) for λ5 > (<)0 [69]. It has been well known that by assuming neutral flavor conservation at the tree level [63], we have four types of Higgs couplings to the fermions. In the 2HDM type-I, the quarks and leptons couple only to one of the two Higgs doublets and the case is the same as the SM. In the 2HDM type-II, the charged leptons and down-type quarks couple to one Higgs doublet and the up-type quarks couple to the other. The lepton-specific model is similar to type-I, but the leptons couple to the other Higgs doublet. In the flipped model, which is similar to type-II, the leptons and up-type quarks couple to the same double. If the tree-level FCNCs are allowed, both doublets can couple to leptons and quarks and the associated model is called 2HDM type-III [23,64–66]. Thus, the Yukawa interactions for the quarks are written as ( 3 ) LY = Q¯ L Y k dR φk + Q¯ L Y˜ k u R φ˜k + h.c. where the flavor indices are suppressed, QTL = (u L , dL ) is the left-handed quark doublet, Y k and Y˜ k denote the 3 × 3 Yukawa matrices, φ˜k = i σ2φk∗, and k is the doublet number. Similar formulas could be applied to the lepton sector. Since the mass matrices of the quarks are combined by Y 1(Y˜ 1) and Y 2(Y˜ 2) for down- (up-) type quarks and Y 1,2(Y˜ 1,2) generally cannot be diagonalized simultaneously, as a result, the tree-level FCNCs appear and the effects lead to the oscillations of K − K¯ , Bq − B¯q and D − D¯ at the tree level. To get ( 4 ) naturally small FCNCs, one can use the ansatz formulated by Yikj , Y˜ikj ∝ √mi m j /v [64–66]. After spontaneous symmetry breaking, the scalar couplings to the fermions can be expressed as [67,68] L2YHDM-III = u¯ Li csoinsβα mvui δi j − co√s(2βsi−n βα) Xiuj u R j h + d¯Li − csoins αβ mvdi δi j + co√s2(βco−s βα) Xidj dR j h + u¯ Li + d¯Li − i u¯ Li + h.c., + i d¯Li − tan β mvdi δi j + √ ssiinn βα mvui δi j + si√n(2βsi−n βα) Xiuj u R j H cos α mdi δi j − √ sin(β − α) Xidj dR j H cos β v 2 cos β 1 mui δi j − √ tan β v Xiuj 2 sin β Xidj 2 cos β u R j A dR j A ( 5 ) ( 6 ) where v = χiqj are the free parameters. By the above formulation, if the FCNC effects are ignored, the results are returned to the case of the 2HDM type-II, given by v1 + v22, Xi j = √mqi mq j /vχiqj (q = u, d) and 2 q L2YHDM-II = u¯ Li cos α mui sin β v δi j u R j h sin α mdi + d¯Li − cos β v δi j dR j h + h.c. The couplings of the other scalars to fermions can be found elsewhere [67,68]. It can be seen clearly that if χiuj,d are of O(10−1), the new effects are dominated by heavy fermions and comparable with those in the type-II model. The couplings of the h and H to the gauge bosons V = W, Z are proportional to sin(β − α) and cos(β − α), respectively. Therefore, the SM-like Higgs boson h is recovered when cos(β − α) ≈ 0. The decoupling limit can be achieved if cos(β − α) ≈ 0 and mh m H , m A, m H± are satisfied [69]. From Eqs. ( 5 ) and ( 6 ), one can also find that in the decoupling limit, the h couplings to the quarks return to the SM case. In this analysis, since we take α in the range −π/2 ≤ α ≤ π/2, sin α will have both a positive and a negative sign. In the 2HDM type-II, if sin α < 0 then the Higgs couplings to up- and down-type quarks will have the same sign as those in the SM. It is worthwhile to mention that sin α in minimal supersymmetric SM (MSSM) is negative, unless some extremely large radiative corrections flip its sign [69]. If sin α is positive, then the Higgs coupling to down quarks will have a different sign with respect to the SM case. This is called the wrong sign Yukawa coupling in the literature [69–71]. Later we will explain whether the type-III model would favor such a wrong sign scenario or not. 3 Theoretical and experimental constraints The free parameters in the scalar potential defined in Eq. ( 1 ) could be constrained by theoretical requirements and the experimental measurements, where the former mainly includes tree-level unitarity and vacuum stability when the electroweak symmetry is broken spontaneously. Since the unitarity constraint involves a variety of scattering processes, we adopt the results [72–75]. We also force the potential to be perturbative by requiring that all quartic couplings of the scalar potential obey |λi | ≤ 8π for all i . For the vacuum stability conditions which ensure that the potential is bounded from below, we require that the parameters satisfy the conditions [76–78] ( 7 ) ( 8 ) λ1 > 0, λ2 > 0, λ3 + λ1λ2 > 0, λ1λ2 + λ3 + λ4 − |λ5| > 0, 1 2|λ6 + λ7| ≤ 2 (λ1 + λ2) + λ3 + λ4 + λ5. In the following we state the constraints from the experimental data. The new neutral and charged scalar bosons in 2HDM will affect the self-energy of W and Z bosons through the loop effects. Therefore, the involved parameters could be constrained by the precision measurements of the oblique parameters, denoted by S, T, and U [79]. Taking mh = 125 GeV, mt = 173.3 GeV, and assuming that U = 0, the tolerated ranges for S and T are found to be [80] S = 0.06 ± 0.09, T = 0.10 ± 0.07, where the correlation factor is ρ = +0.91, S = S2HDM − SSM, and T = T 2HDM − T SM, and their explicit expressions can be found [69]. We note that in the limit m H± = m A0 or m H± = m H0 , T vanishes [81,82]. The second set of constraints comes from B physics observables. It has been shown recently in Ref. [83] that Br (B → Xs γ ) gives a lower limit on m H± ≥ 480 GeV in the 2HDM type-II at 95 % CL. However, in 2HDM type-III the situation is slightly different. In fact, the charged Higgs– top-quark affects Br (B → Xs γ ) via the Wilson coefficients C7,8 at leading-order (LO) as well as at the next-to-next LO (NNLO). The Br (B → Xs γ ) constraint can get weakened in the 2HDM type-III because of the off-diagonal element that enters in the H +t b¯ coupling. This new term can lead to a destructive interference with the SM and then reduce the 2HDM contribution. It was pointed out that in 2HDM typeIII a light charged Higgs boson with a mass around 200 GeV is still allowed at NLO level by the measured Br (B → Xs γ ) within 2σ [84–86]. While in type-II, such light charged Higgs boson cannot be accommodated. By precision measurements of Z → bb¯ and Bq –B¯q mixing, the values of tan β < 0.5 have been excluded [87,88]. In this work we allow tan β ≥ 0.5. Except for some specific scenarios, tan β cannot be too large due to the requirement of perturbation theory. By the observation of a scalar boson at mh ≈ 125 GeV, the searches for Higgs boson at ATLAS and CMS can give strong bounds on the free parameters. The signal events in the Higgs measurements are represented by the signal strength, which is defined by the ratio of the Higgs signal to the SM prediction and is given by μif = σiSσMi((hh)) ·· BBrrS(hM (→h →f ) f ) ≡ σ¯i · μ f , where σi (h) denotes the Higgs production cross section by channel i and Br (h → f ) is the BR for the Higgs decay h → f . Since several Higgs boson production channels are available at the LHC, we are interested in the gluon fusion production (gg F ), t t¯h, vector boson fusion (VBF) and Higgs-strahlung V h with V = W /Z ; and they are grouped into μgfgF+tt¯h and μVf B F+V h . In order to consider the constraints from the current LHC data, the scaling factors which show the Higgs coupling deviations from the SM are defined as κV = κW = κZ ≡ gh2HVDVM , κ ghSVMV f ≡ yh2HffDM yhSMff , ( 9 ) ( 10 ) where ghV V and yh f f are the Higgs couplings to gauge bosons and fermions, respectively, and f stands for top, bottom quarks, and tau lepton. The scaling factors for the loopinduced channels are defined by κγ2 ≡ 2 κZγ ≡ (h → γ γ )2HDM (h → γ γ )SM (h → Z γ )2HDM (h → Z γ )SM , κg2 ≡ , κh2 ≡ (h → g g)2HDM (h → g g)SM (h)2HDM , (h)SM , ( 11 ) where (h → X Y ) is the partial decay rate for h → X Y . In this study, the partial decay width of the Higgs is taken from [89,90], where the QCD corrections have been taken into account. In the decay modes h → γ γ and h → Z γ , we have included the contributions of the charged Higgs and the new Yukawa couplings. Accordingly, the ratio of the cross section to the SM prediction for the production channels gg F + t t¯h and VBF+V h can be expressed as σ ggF+tt¯h = κg2σSM (gg F) + κt2σSM (tth) σSM (gg F) + σSM (tth) , σ V B F+V h = κV2 σSMσ(SVM B(VFB) +F)κ+ZhσσSSMM((ZZhh))++σκSV2Mσ(SZMh()Z+h)σ+SMκ(V2WσShM) (W h) , ( 12 ) ( 13 ) where σSM (Z h) is from the coupling of Z Z h and occurs at the tree level, and σSM (Z h) ≡ σSM (gg → Z h) represents the effects of the top-quark loop. With mh = 125.36 GeV, 4 Parameter setting, global fitting, and numerical results 4.1 Parameters and global fitting After introducing the scaling factors for displaying the new physics in various channels, in the following we show the explicit relations with the free parameters in the type-III model. By the definitions in Eq. ( 10 ), the scaling factors for κV and κ f in the type-III are given by κV = sin(β − α), cos α cos(β − α) κU = κt = κc = sin β − χF √2 sin β , sin α cos(β − α) κD = κb = κτ = − cos β + χF √2 cos β . Although the FCNC processes give strict constraints on the flavor-changing couplings χifj with i = j , the constraints are applied to the flavor-changing processes in the K , D, and B meson systems. Since the couplings of the scalars to the light quarks have been suppressed by mqi /v, the direct limit on the flavor-conserved coupling χifi is mild. Additionally, since the signals for top-quark flavor-changing processes have not been observed yet, the direct constraint on X3ui = √mt mqi /vχ3ui is from the experimental bound of t → hqi . Hence, for simplifying the numerical analysis, in u u d Eq. ( 15 ) we have set χ22 = χ33 = χ33 = χ33 = χF . Since X3u3 = mt /vχF , it is conservative to adopt the value of χF ( 15 ) to be O( 1 ). In the 2HDM, the charged Higgs will also contribute to h → γ γ decay and the associated scalar triplet coupling h H + H − reads λh H ± H ∓ 1 = 2m2W cos(α + β) sin 2β where we have used mh = 125.36 GeV and taken m H ± = 480 GeV. It is clear that the charged Higgs contribution to h → γ γ and h → Z γ is small. In order to study the influence of the new free parameters and to understand their correlations, we perform the χ -square fitting by using the LHC data for Higgs searches [1, 2, 4, 6]. For a given channel f = γ γ , W W ∗, Z Z ∗, τ τ , we define the χ 2f as χ 2f = 1 f f 2 1 f f 2 σˆ12(1 − ρ2) (μ1 − μˆ 1 ) + σˆ12(1 − ρ2) (μ2 − μˆ 2 ) 2ρ f f − σˆ1σˆ2(1 − ρ2) (μ1 − μˆ 1f )(μ2 − μˆ 2f ), f , σˆ1,2 and ρ are the measured Higgs signal where μˆ 1,2 strengths, their one-sigma errors, and their correlation, respectively, and for their values one may refer to Table 1. The indices 1 and 2 in turn stand for ggF + tth and VBF + Vh, f and μ1,2 are the results in the 2HDM. The global χ -square is defined by ( 16 ) → ( 17 ) ( 18 ) ( 19 ) χ 2 = χ 2f + χS2T , f where the χS2T is related to the χ 2 for S and T parameters, the definition can be obtained from Eq. ( 18 ) by replacing μ1f → S2H D M and μ2f → T 2H D M , and the corresponding values can be found from Eq. ( 8 ). We do not include the bb¯ channel in our analysis because the errors of the data are still large. In order to display the allowed regions for the parameters, we show the best fit at 68, 95.5, and 99.7 % confidence levels (CLs), that is, the corresponding errors of χ 2 are χ 2 ≤ 2.3, 5.99, and 11.8, respectively. For comparing with the LHC data, we require the calculated results in agreement with those shown by ATLAS (Fig. 3 of Ref. [3]) and by CMS (Fig. 5 of Ref. [7]). 5 Numerical results In the following we present the limits of the current LHC data based on the three kinds of CL introduced in the last section. In our numerical calculations, we set the mass of SM Higgs to be mh = 125.36 GeV, and we scan the involved parameters in the chosen regions as 480 GeV ≤ m H ± ≤ 1 TeV, 126 GeV ≤ m H ≤ 1 TeV, ( 20 ) 100 GeV ≤ m A ≤ 1 TeV, −1 ≤ sin α ≤ 1, 0.5 ≤ tan β ≤ 50, − (1000 GeV)2 ≤ m212 ≤ (1000 GeV)2. The main difference in the scalar potential between typeII and type-III is that the λ6,7 terms appear in the type-III model. With the introduction of the λ6,7 terms in the potential, not only the mass relations of scalar bosons are modified but also the scalar triple and quartic coupling receives contributions from λ6 and λ7. Since the masses of the scalar bosons are regarded as free parameters, the relevant λ6,7 effects in this study enter the game through the triple coupling h– H +– H −, which contributes to the h → γ γ decay, as shown in Eq. ( 16 ) and the first line of Eq. ( 17 ). Since the contribution of the charged Higgs loop to the h → γ γ decay is small, expectedly the influence of λ6,7 on the parameter constraint is not significant. To demonstrate that the contributions of λ6,7 are not very important, we present the allowed ranges for tan β and sin α by scanning λ6,7 in the region of [−1, 1] in Fig. 1, where the theoretical and experimental constraints mentioned earlier are included and the plots from left to right in turn stand for χ 2 = 11.8, 5.99, and 2.3, respectively. Additionally, to understand the influence of χF defined in Eq. ( 15 ), we also scan χF = [−1, 1] in the plots. By comparing the results with the case of λ6,7 1 and χF = 1, which is displayed in the third plot of Fig. 2, it can be seen that only a small region for positive sin α is modified and the modifications happen only in the large errors of χ 2; the plot with χ 2 = 2.3 shows almost no change. However, it can be seen from Fig. 1 (right panel) that for small χ 2 the values of positive sin α are excluded by LHC constraints on h → τ +τ −, which exceed a 20 % deviation from SM values, which is excluded by the LHC data. Therefore, to simplify the numerical analysis and to reduce the scanned parameters, it is reasonable in this study to assume λ6,7 1. Since the influence of |χF | ≤ 1 should be smaller, to get the typical contributions from the FCNC effects, we illustrate our studies by setting χF = ±1 in the whole numerical analysis. With λ6,7 1, we present the allowed regions for sin α and tan β in Fig. 2, where the left, middle, and right panels Fig. 2 The allowed regions in (sin α, tan β) constrained by theoretical and current experimental inputs, where we have used mh = 125.36 GeV, the left, middle, and right panels stand for the 2HDM type-II, type-III with χF = −1 and type-III with χF = +1, respectively. The errors for the χ-square fit are 99.7 % CL (black), 95.5 % CL (red), and 68 % CL (green) stand for the 2HDM type-II, type-III with χF = −1 and type-III with χF = +1, respectively, and in each plot we show the constraints at 68 % CL (green), 95.5 % CL (red), and 99.7 % CL (black). Our results in type-II are consistent with those obtained by the authors in Refs. [24–29,48–54] when the same conditions are chosen. By the plots, we see that in type-III with χF = −1, due to the sign of the coupling being the same as type-II, the allowed values for sin α and tan β are further shrunk; especially sin α is limited values less than 0.1. On the contrary, for type-III with χF = +1, the allowed values of sin α and tan β are broad. As discussed before, the decoupling limit occurs at α → β − π/2, i.e. sin α = − cos β < 0. Since we regard the masses of new scalars as free parameters and scan them in the regions shown in Eq. ( 20 ), the three plots in Fig. 2 cover lower and heavier mass of charged Higgs. We further check that sin α > 0 could be excluded at 95.5(99.7) % CL when m H± ≥ 585(690) GeV. The main differences between typeII and type-III are the Yukawa couplings as shown in Eq. ( 5 ). In order to see the influence of the new effects of type-III, we plot the allowed κg as a function of sin α and tan β in Fig. 3, where the three plots from left to right correspond to type-II, type-III with χF = −1, and type-III with χF = +1, the solid, dashed, and dotted lines in each plot stand for the decoupling limit (DL) of SM, 15 % deviation from DL and 20 % deviation from DL, respectively. For comparison, we also put the results of 99.7 % in Fig. 2 in each plot. By the analysis, we see that the deviations of κg from DL in χF = +1 are clear and significant, while the influence of χF = −1 is small. It is pointed out that a wrong sign Yukawa coupling to down-type quarks could happen in type-II 2HDM [69–71]. For understanding the sign flip, we rewrite the κD defined in Eq. ( 15 ), sin α κD = − cos β 1 − χF sin β √2 + χF cos α √2 In the type-II case, we know that in the decoupling limit κD = 1, but κD < 0 if sin α > 0. According to the results in the left panel of Fig. 2, sin α > 0 is allowed when the errors of best fit are taken by 2σ or 3σ . The situation in type-III is more complicated. From Eq. ( 21 ), we see that the factor in the brackets is always positive, therefore, the sign of the first term should be the same as that in type-II case. However, due to α ∈ [−π/2, π/2], the sign of the second term in Eq. ( 21 ) depends on the sign of χF . For χF = −1, even sin α < 0, κD could be negative when the first term is smaller than the second term. For χF = +1, if sin α > 0 and the first term is over the second term, κD < 0 is still allowed. In order to deviation from DL and 20 % deviation from DL, respectively. The dotted points are the allowed values of parameters resulting from Fig. 2 understand the available values of κD when the constraints are considered, we present the correlation of κU and κD in Fig. 4, where the panels from left to right stand for type-II, type-III with χF = −1 and type-III with χF = +1. In each plot, the results obtained by χ -square fitting are applied. The similar correlation of κV and κD is presented in Fig. 5. By these results, we find that comparing with type-II model, the negative κD gets a stricter limit in type-III, although a wider parameter space for sin α > 0 is allowed in type-III with χF = +1. Besides the scaling factors of tree-level Higgs decays, κD,U and κV , it is also interesting to understand the allowed values for loop-induced processes in 2HDM, e.g. h → γ γ , gg, and Z γ , etc. It is well known that the differences in the associated couplings between h → γ γ and gg are the colorless W -, τ -, and H ±-loop. By Eq. ( 17 ), we see that the contributions of τ and H ± are small, therefore, the main difference is from the W -loop in which the κV is involved. By using the χ -square fitting approach and with the inputs of the experimental data and theoretical constraints, the allowed regions of κγ and κg in type-II and type-III are displayed in Fig. 6, where the panels from left to right are type-II, type-III with χF = −1 and +1; the green, red, and black colors in each plot stand for the 68, 95.5, and 99.7 % CL, respectively. We find that except a slightly lower κγ is allowed in type-II, the first two plots have similar results. The situation can be Fig. 8 Correlation between μγggγF+tth and μgZgγF+tth at √s = 13 TeV after imposing theoretical and experimental constraints. Left, middle, and right panels represent the allowed values in type-II, type-III with χF = −1 and type-III with χF = +1, respectively, and the results in Fig. 2 obtained by χ -square fitting are applied understood from Figs. 4 and 5, where the κU in both models is similar, while κV in type-II could be smaller in the region of negative κD ; that is, a smaller κV will lead to a smaller κγ . In the χF = +1 case, the allowed values of κγ and κg are localized in a wider region. It is well known that except for the different gauge couplings, the loop diagrams for h → Z γ and h → γ γ are exactly the same. One can understand the loop effects by the numerical form of Eq. ( 17 ). Therefore, we expect the correlation between κZ γ and κγ should behave like a linear relation. We present the correlation between κγ and κZ γ in Fig. 7, where the legend is the same as that for Fig. 6. From the plots, we see that in most of the region κZ γ is less than the SM prediction. The type-III with χF = −1 gets a stricter constraint and the change is within 10 %. For χF = +1, the deviation of κZ γ from unity could be over 10 %. From run I data, the LHC has an upper bound on h → Z γ , at run II this decay mode will be probed. We give the predictions at 13 TeV LHC for the signal strength μγggγF+tth and μgZgγF+tth in Fig. 8. Hence, with the theoretical and experimental con Z γ straints, μgg F+tth is bounded and could be O(10 %) away from SM at 68 % CL. In this section, we study the flavor-changing t → ch process in the type-III model. Experimentally, there have been intensive activities to explore the top FCNCs. The CDF, D0, and LEPII collaborations have reported some bounds on top FCNCs. At the LHC with rather large top cross section, ATLAS and CMS search for top FCNCs and put a limit on the branching fraction, which is Br (t → ch) < 0.82 % for ATLAS [60,61] and Br (t → ch) < 0.56 % for CMS [62]. Note that the CMS limit is slightly better than the ATLAS limit. CMS search for t → ch in different channels: h → γ γ , W W ∗, Z Z ∗, and τ +τ −, while ATLAS used only a diphoton channel. With the high luminosity option of the LHC, the above limit will be improved to reach about Br (t → ch) < 1.5 × 10−4 [60,61] for the ATLAS detector. From the Yukawa couplings in Eq. ( 5 ), the partial width for the t → ch decay is given by (t → ch) = cos(β − α)X2u3 sin β 2 mt 32π (xc + 1)2 − xh 2 × 1 − (xh − xc)2 1 − (xh + xc)2 ( 22 ) where xc = mc/mt , xh = mh /mt , and X2u3 is a free parameter and dictates the FCNC effect. It is clear from the above expression that the partial width of t → ch is proportional to cos(β −α). As seen in the previous section, in the case where h is SM-like, cos(β − α) is constrained by LHC data to be rather small and the t → ch branching fraction is limited. As we will see later in 2HDM type-II with flavor conservation the rate for t → ch is much smaller than type-III [92–95]. Since we assume that the charged Higgs is heavier than 400 GeV, the total decay width of the top contains only t → ch and t → bW . With mh = 125.36 GeV, mt = 173.3 GeV, and mc = 1.42 GeV, the total width can be written t = tSM + 0.0017 cos(β − α)X2u3 2 sin β GeV ( 23 ) where tSM is the partial decay rate for t → W b, given by SM t G F mt3 = 8π √2 1 − m2W mt2 2 1 + 2 mt2 m2W × 1 − 2 αs3(πmt ) 2 π32 − 25 = 1.43 GeV, in which the QCD corrections have been included. By the above numerical expressions together with the current limit from ATLAS and CMS, the limit on the t ch FCNC coupling is foun: ( 24 ) in agreement with [96]. We perform a systematic scan over the 2HDM parameters, as depicted in Eq. ( 20 ), taking into account LHC and theoretical constraints. Although X2u3 is a free parameter, in order to suppress the FCNC effects naturally, as stated earlier we adopt X2u3 = √mt mc/vχ2u3. Since the current experimental measurements only give an upper limit on t → hc, basically χ2u3 is limited by Eq. ( 24 ) and could be as large as O( 1 − 102 ), depending on the allowed value of cos(β − α). In order to use the constrained results which are obtained from the Higgs measurements and the selfconsistent parametrization X3u3 = mt /vχF , which was used u before, we assume χ23 = χF = ±1. In our numerical analysis, the results under the assumption should be conservative. In Fig. 9(left) we illustrate the branching fraction of t → ch in 2HDM-III as a function of cos(β − α). The LHC constraints within 1σ restrict cos(β − α) to be in the range [−0.27, 0.27]. The branching fraction for t → ch is slightly above 10−4. The actual CMS and ATLAS constraint on Br (t → ch) < 5.6 × 10−3 does not restrict cos(β − α). The expected limit from the ATLAS detector with high luminosity 3000 fb−1 is depicted as the dashed horizontal line. As one can see, the expected ATLAS limit is somehow similar to LHC constraints within 1σ . In the right panel, we show the allowed parameters space in the (sin α, tan β) plane where we apply the ATLAS expected limit Br (t → ch) < 1.5 × 10−4. This plot should be compared to the right panel of Fig. 2. It is then clear that this additional constraint only acts on the 3σ allowed region from the LHC data. In Figs. 10 and 11, we show the fitted branching fractions for t → ch (left), t → c H at m H = 150 GeV (middle), and t → c A at m A = 130 GeV (right) as a function of κU , where Fig. 10 is for χF = +1, while Fig. 11 is χF = −1. In the case of χF = +1 the fitted value for κU at the 3σ level is in the range [0.6, 1.18] and the branching fraction for t → ch, c H are less than 10−3, while Br (t → c A) slightly exceeds the 10−3 level. Similarly, for χF = −1 the fitted value for κU at the 3σ level is in the range [0.85, 1.25] and the branching fraction for t → ch, c H, c A are the same size as in the previous case. 7 Conclusions For studying the constraints of the 8 TeV LHC experimental data, we perform a χ -square analysis to find the most favorable regions for the free parameters in the two-Higgsdoublet models. For comparison, we focus on the type-II and type-III models, in which the latter model not only affects the flavor conserving Yukawa couplings but also generates the scalar-mediated flavor-changing neutral currents at the tree level. Although the difference between type-II and type-III is the Yukawa sector, however, since the new Yukawa couplings in type-III are associated with cos(β − α) and sin(β − α), the modified couplings t t h and bt H ± will change the constraint of the free parameters. In order to represent the influence of modified Yukawa couplings, we show the allowed values of sin α and tan β in Fig. 2, where the LHC updated data for pp → h → f with f = γ γ , W W ∗/Z Z ∗ and τ +τ − are applied and other bounds are also included. By the results, we see that sin α and tan β in type-III get an even stronger constraint if the dictated parameter χF = −1 is adopted; on the contrary, if we take χF = +1, the allowed values for sin α and tan β are wider. It has been pointed out that there exist Yukawa couplings to down-type quarks of the wrong sign in the type-II model, i.e. sin α > 0 or κD < 0. By the study, we find that except that the allowed regions of parameters are shrunk slightly, the situation in χF = −1 is similar to the type-II case. In χF = +1, although the κD < 0 is not excluded completely yet, the case has a strict limit by current data. We show the analyses in Figs. 4 and 5. In these figures, one can also see the correlations with a modified Higgs coupling to the top quark, κU , and to the gauge boson, κV . When the parameters are bounded by the observed channels, we show the influence on the unobserved channel h → Z γ by using the scaling factor κZ γ , which is defined by the ratio of the decay rate to the SM prediction. We find that the change of κZ γ in type-III with χF = −1 is less than 10 %; however, with χF = +1, the value of κZ γ could be lower from the SM prediction by over 10 %. We also show our predictions for the signal strengths μγ γ and μγ Z and their correlation at 13 TeV. The main difference between type-II and -III model is that the flavor-changing neutral currents in the former are only induced by loops, while in the latter they could occur at the tree level. We study the scalar-mediated t → c(h, H, A) decays in the type-III model and find that when all current experimental constraints are considered, Br (t → c(h, H )) < 10−3 for mh = 125.36 and m H = 150 GeV, and Br (t → c A) slightly exceeds 10−3 for m A = 130 GeV. The detailed numerical analyses are shown in Figs. 9, 10, and 11. Acknowledgments The authors thank Rui Santos for useful discussions. A.A would like to thank NCTS for warm hospitality where part of this work has been done. The work of CHC is supported by the Ministry of Science and Technology of R.O.C under Grant #: MOST103-2112-006-004-MY3. The work of M. Gomez-Bock was partially supported by UNAM under PAPIIT IN111115. This work was also supported by the Moroccan Ministry of Higher Education and Scientific Research MESRSFC and CNRST: “Projet dans les domaines prioritaires de la recherche scientifique et du développement technologique”: PPR/2015/6. 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A. Arhrib, R. Benbrik, Chuan-Hung Chen. Two-Higgs-doublet type-II and -III models and \(t\rightarrow c h\) at the LHC, The European Physical Journal C, 2016, 328, DOI: 10.1140/epjc/s10052-016-4167-9