Two-Higgs-Doublet type-II and -III models and $t\to c h$ at the LHC

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 $\chi$-square fitting approach by including theoretical and experimental constraints, such as 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 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 the $h\to Z\gamma$ can be of ${\cal O}(10\%)$. 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 $Br(t\to c(h, H) )<10^{-3}$ for $m_h=125.36$ and $m_H=150$ GeV and $Br(t\to cA)$ slightly exceeds $10^{-3}$ for $m_A =130$ GeV.


I. 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 following channels: γγ, W W * , ZZ * 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][4][5][6][7] indicate the possible deviations from the standard model (SM) predictions. Although the errors of current data are still somewhat large, the new physics signals may become clear in the second run of the LHC at [13][14] 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 [8,9]. Furthermore, e + e − Linear Collider (LC) would be able to measure the Higgs couplings at the percent level [10]. 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 * , ZZ * , 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 → Zγ and t → ch.
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 on the 2HDMs are shown elsewhere [15].
After scalar particle of 125 GeV is discovered, the implications of the observed h → γγ in the type-I and II models are studied [21] and the impacts on h → γZ are given [22,23]. As known that 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 [16]. For instance, the large tan β ∼ m t /m b 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, γγ, W W, ZZ and h → Zγ decays in the framework of the 2HDM type-III. We will show what is the most favored regions of the type-III parameter space when theoretical and experimental constraints are considered simultaneously. FCNCs of heavy quark such as t → qh have been intensively studied both from the experimental and theoretical point of view [24]. 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 [25]. If this decay t → ch is observed, it would be an indisputable sign of new physics. Since the tree-level FCNCs appear in the type-III model, we explore if the Br(t → ch) reaches the order of 10 −5 -10 −4 [26,27], the sensitivity which is expected by the integrated luminosity of 3000 fb −1 .
The paper is organized as follows. In section II, we introduce the scalar potential and the Yukawa interactions in the 2HDM type-III. The theoretical and experimental constraints are described in section III. We set up the free parameters and establish the χ-square for the best-fit approach in section VI. In the same section, we discuss the numerical results when all theoretical and experimental constraints are taken into account. The conclusions are given in section V.

II. 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 [32] where the doublets Φ 1,2 have weak hypercharge Y = 1, the corresponding VEVs are v 1 and v 2 , and λ i and m 2 12 are real parameters. After electroweak symmetry breaking, three of the eight degrees of freedom in the two Higgs doublets are the Goldstone bosons (G ± , G 0 ) and the remaining five degrees of freedom become the physical Higgs bosons: 2 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: (λ i ) i=1,...,7 , m 2 12 , and tan β ≡ v 2 /v 1 . Equivalently, we can use the masses as the independent parameters; therefore, the set of free parameters can be chosen to be 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 with ζ = 1(0) for λ 5 > (<)0 [32]. It has been known that by assuming neutral flavor conservation at the tree-level [28], 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 [15,29,30]. Thus, the Yukawa interactions for quarks are written as where the flavor indices are suppressed, Q T L = (u L , d L ) is the left-handed quark doublet, Y k andỸ k denote the 3×3 Yukawa matrices,φ k = iσ 2 φ * k , and k is the doublet number. Similar formulas could be applied to the lepton sector. Since the mass matrices of quarks are combined by Y 1 (Ỹ 1 ) and Y 2 (Ỹ 2 ) for down (up) type quarks and Y 1,2 (Ỹ 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, B q −B q and D −D at the tree-level. To get naturally small FCNCs, one can use the ansatz formulated [29,30]. After spontaneous symmetry breaking, the scalar couplings to fermions can be expressed as [31] where and χ q ij are the free parameters. By above formulation, if the FCNC effects are ignored, the results are returned to the case of the 2HDM type-II, given by For the couplings of other scalars to fermions, the can be found elsewhere [31]. It can be seen clearly that if χ u,d ij 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 h and H to 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 m h m H , m A , m H± are satisfied [32]. From Eqs. (5) and (6), one can also find that in the decoupling limit, the h couplings to quarks are returned to the SM case.
In this analysis, since we take α in the range −π/2 ≤ α ≤ π/2, sin α will have both positive and 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 worthy to mention that sin α in minimal supersymmetric SM (MSSM) is negative unless some extremely large radiative corrections flip its sign [32]. 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 by the wrong sign Yukawa coupling in the literature [32,33].
Later we will explain if the type-III model would favor such wrong sign scenario or not.

III. 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 [34,35]. We also force the potential to be perturbative by requiring that all quartic couplings of the scalar potential obey |λ i | ≤ 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 as [36,37] In the following we state the constraints from 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 [38]. Taking m h = 125 GeV, m t = 173.3 GeV and assuming that U = 0, the tolerated ranges for S and T are found by [39] ∆S = 0.06 ± 0.09 , ∆T = 0.10 ± 0.07 , where the correlation factor is ρ = +0.91, ∆S = S 2HDM − S SM and ∆T = T 2HDM − T SM , and their explicit expressions can be found [32]. We note that in the limit m H ± = m A 0 or m H ± = m H 0 , ∆T vanishes [40,41].
The second set of constraints comes from B physics observables. It has been shown recently in Ref. [42] that Br(B → X s γ) gives a lower limit on m H ± ≥ 480 GeV in the type-II at 95%CL. By the precision measurements of Z → bb and B q −B q mixing, the values of tan β < 0.5 have been excluded [43]. In this work we allow tan β ≥ 0.5. Except some specific scenarios, tan β can not be too large due to the requirement of perturbation theory.
By the observation of scalar boson at m h ≈ 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 Higgs signal to the SM prediction and given by where σ i (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 (ggF ), tth, vector boson fusion (VBF) and Higgs-strahlung V h with V = W/Z; and they are grouped to be µ f ggF +tth and µ f V BF +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 where g hV V and y hf 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 loop-induced channels are defined by where Γ(h → XY ) is the partial decay rate for h → XY . In this study, the partial decay width of the Higgs is taken from [44], where QCD corrections have been taken into account. In the decay modes h → γγ and h → Zγ, we have included the contributions of charged Higgs and new Yukawa couplings. Accordingly, the ratio of cross section to the SM prediction for the production channels ggF + tth and VBF+V h can be expressed as where σ SM (Zh) is from the coupling of ZZh and occurs at the tree level and σ SM (Zh) ≡ σ SM (gg → Zh) represents the effects of top-quark loop. With m h = 125.36 GeV, the scalar factor κ Zh can be written as [3] κ In the numerical estimations, we use m h = 125.36 GeV which is from LHC Higgs Cross Section Working Group [8] at √ s = 8 TeV. The experimental values of signal strengths are shown in

A. 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 κ V and κ f in the type-III are given by Although FCNC processes give strict constraints on flavor changing couplings χ f ij with i = j, however, the constraints are applied to the flavor changing processes in K, D and B meson systems.
Since the couplings of scalars to the light quarks have been suppressed by m q i /v, the direct limit on flavor-conserved coupling χ f ii is mild. Additionally, since the signals for top-quark flavor changing processes haven't been observed yet, the direct constraint on X u 3i = √ m t m q i /vχ u 3i is from the experimental bound of t → hq i . Hence, for simplifying the numerical analysis, in Eq. (15) we have set χ u 22 = χ u 33 = χ d 33 = χ 33 = χ F . Since X u 33 = m t /vχ F , it is conservative to adopt the vale of χ F to be O(1). In the 2HDM, the charged Higgs will also contribute to h → γγ decay and the associated scalar triplet coupling hH + H − is read by where we have used m h = 125.36 GeV and taken m H ± = 480 GeV. It is clear that the charged Higgs contribution to h → γγ and h → Zγ is small. In order to study the influence of 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 = γγ, W W * , ZZ * , τ τ , we define the χ 2 f as (18) whereμ f 1,2 ,σ 1,2 and ρ are the measured Higgs signal strengths, their one-sigma errors, and their correlation, respectively and their values could refer to Table I, the indices 1 and 2 in turn stand for ggF + tth and VBF + Vh, and µ f 1,2 are the results in the 2HDM. The global χ-square is defined by where the χ 2 ST is related to the χ 2 for S and T parameters, the definition can be obtained from Eq. (18) by replacing µ f 1 → S 2HDM and µ f 2 → T 2HDM , and the corresponding values can be found from Eq. (8). We do not include bb channel in our analysis because the errors of 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 LHC data, we require the calculated results in agreement with those shown in ATLAS Fig. 3 of Ref. [3] and in CMS Fig. 5 of Ref. [7].

V. NUMERICAL RESULTS
In the following we present the limits of current LHC data based on the three kinds of CL introduced in last section. In our numerical calculations, we set the mass of SM Higgs to be m h = 125.36 GeV, and scan the involved parameters in the chosen regions as 480 GeV ≤ m H ± ≤ 1 TeV, 126 GeV ≤ m H ≤ 1 TeV, 100 GeV ≤ m A ≤ 1 TeV , The main difference in the scalar potential between type-II and type-III is that the λ 6,7 terms appear in the type-III model. With the introduction of λ 6,7 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 λ 6 and λ 7 . Since the masses of scalar bosons are regarded as free parameters, the relevant λ 6,7 effects in this study enters game through the triple coupling h-H + -H − that contributes to the h → γγ decay, as shown in Eq. (16) and the first line of Eq. (17). Since the contribution of the charged Higgs loop to the h → γγ decay is small, expectably the influence of λ 6,7 on the parameter constraint is not significant. To demonstrate that the contributions of λ 6,7 are not very important, we present the allowed ranges for tan β and sin α by scanning λ 6,7 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 χ F defined in Eq. (15), we also scan χ F = [−1, 1] in the plots. By comparing the results with the case of λ 6,7 1 and χ F = 1 which is displayed in the third plot of Fig. (2), it can be seen that only small region in the positive sin α is modified and the modifications happen only in the large errors of χ 2 ; the plot with ∆χ 2 = 2.3 has almost no change. Therefore, to simplify the numerical analysis and to reduce the scanned parameters, it is reasonable in this study to assume λ 6,7 1. Since the influence of |χ F | ≤ 1 should be smaller, to get the typical contributions from FCNC effects, we illustrate our studies by setting χ F = ±1 in the whole numerical analysis. With λ 6,7 1, we present the allowed regions for sin α and tan β in Fig. 2, where the left, middle and right panels stand for the 2HDM type-II, type-III with χ F = −1 and type-III with χ F = +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. [16,21] when the same conditions are chosen. By the plots, we see that in type-III with χ F = −1, , due to the sign of coupling being the same as type-II, the allowed values for sin α and tan β are further shrunk; especially sin α is limited to be less than 0.1. On the contrary, type-III with χ F = +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), therefore, the three plots in Fig. 2  In order to see the influence of the new effects of type-III, we plot the allowed κ g 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 χ F = −1 and type-III with χ F = +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 comparisons, we also put the results of 99.7% in Fig. 2 in each plot. By the analysis, we see that the deviations of κ g from DL in χ F = +1 are clear and significant while the influence of χ F = −1 is small. It is pointed out that a wrong sign Yukawa coupling to down type quarks could happen in type-II 2HDM [32,33]. For understanding the sign flip, we rewrite the κ D defined in Eq. (15) to be In the type-II case, we know that in the decoupling limit κ D = 1, but κ D < 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 χ F . For χ F = −1, even sin α < 0, κ D could be negative when the first term is smaller than the second term. For χ F = +1, if sin α > 0 and the first term is over the second term, κ D < 0 is still allowed. In order to understand the available values of κ D when the constraints are considered, we present the correlation of κ U and κ D in Fig. 4, where the panels from left to right stand for type-II, type-III with χ F = −1 and type-III with χ F = +1. In each plot, the results obtained by χ-square fitting are applied. The similar correlation of κ V and κ D is presented in Fig. 5. By these results, we find that comparing with type-II model, the negative κ D gets more strict limit in type-III, although a wider parameter space for sin α > 0 is allowed in type-III with χ F = +1.
Besides the scaling factors of tree level Higgs decays, κ D,U and κ V , it is also interesting to understand the allowed values for loop induced processes in 2HDM, e.g. h → γγ, gg, and Zγ, etc.
It is known that the differences in the associated couplings between h → γγ 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, FIG. 5: The legend is the same as that in Fig. 4, but for the correlation of κ V and κ D .
the main difference is from the W -loop in which the κ V involves. By using the χ-square fitting approach and with the inputs of the experimental data and theoretical constraints, the allowed regions of κ γ and κ g in type-II and type-III are displayed in Fig. 6, where the panels from left to right are type-II, type-III with χ F = −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 κ γ is allowed in type-II, the first two plots have similar results. The situation can be understood from Figs. 4 and 5, where the κ U in both models is similar while κ V in type-II could be smaller in the region of negative κ D ; that is, a smaller κ V will lead a smaller κ γ . In χ F = +1 case, the allowed values of κ γ and κ g are localized in a wider region.
It is known that except the different gauge couplings, the loop diagrams for h → Zγ and h → γγ are exact the same. One can understand the loop effects by the numerical form of Eq. (17). Therefore, we expect the correlation between κ Zγ and κ γ should behave like a linear relation. We present the correlation between κ γ and κ Zγ in Fig. 7, where the legend is the same as that for Fig. 6. From the plots, we see that in most region κ Zγ is less than the SM prediction. The type-III with χ F = −1 gets more strict constraint and the change is within 10%. For χ F = +1, the deviation of κ Zγ from unity could be over 10%. From run I data, the LHC has an upper bounds on h → Zγ, at run II this decay mode will be probed. We give the predictions at 13 TeV LHC for the signal strength µ γγ ggF +tth and µ Zγ ggF +tth in Fig. 8. Hence, with the theoretical and experimental constraints, µ Zγ ggF +tth is bounded and could be O(10%) away from SM at 68%CL.

VI. t → ch DECAY
In this section, we study the flavor changing t → ch process in type-III model.  [27]. Note that CMS limit is slightly better than ATLAS limit. CMS search for t → ch in different channels: h → γγ, W W * , ZZ * , and τ + τ − while ATLAS used only 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 [26] for ATLAS detector.
From the Yukawa couplings in Eq, (5), the partial width for t → ch decay is given by where x c = m c /m t , x h = m h /m t and X u 23 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 [47]. Since we assume that the charged Higgs is heavier than 400 GeV, the total decay width of the top contains  (23) where Γ SM t is the partial decay rate for t → W b and is given by 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 tch FCNC coupling is found by in agreement with [48].
We perform a systematic scan over 2HDM parameters, as depicted in Eq. (20), taking into account LHC and theoretical constraints. Although X u 23 is a free parameter, in order to suppress the FCNC effects naturally, as stated earlier we adopt X u 23 = √ m t m c /vχ u 23 . Since the current experimental measurements only give a upper limit on t → hc, basically χ u 23 is limited by Eq. (24) and could be as large as O(1 − 10 2 ), 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 self-consistent parametrisation X u 33 = m t /vχ F which was used before, we assume χ u 23 = χ F = ±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 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 (sin α, tan β) plan where we apply 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 act on the 3σ allowed region from LHC data.
In Fig. 10 and 11, we show the fitted branching fractions for t → ch (left), t → cH at m H = 150 GeV (middle) and t → cA at m A = 130 GeV (right) as a function of κ U , where Fig. 10 is for χ F = +1 while Fig. 11 is χ F = −1. In the case of χ F = +1 the fitted value for κ U at the 3σ level is in the range [0.6, 1.18] and the branching fraction for t → ch, cH are less than 10 −3 while

VII. CONCLUSIONS
For studying the constraints of 8 TeV LHC experimental data, we perform χ-square analysis to find the most favorable regions for the free parameters in the two-Higgs-doublet models. For comparisons, 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 tth and btH ± will change the constraint of free parameters.
In order to present 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 = γγ, W W * /ZZ * 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 gets even stronger constraint if the dictated parameter χ F = −1 is adopted; on the contrary, if we take χ F = +1, the allowed values for sin α and tan β are wider. It has been pointed out that there exist the wrong sign Yukawa couplings to down type quarks in the type-II model, i.e. sin α > 0 or κ D < 0. By the study, we find that except the allowed regions of parameters are shrunk slightly, the situation in χ F = −1 is similar to the type-II case. In χ F = +1, although the κ D < 0 is not excluded completely yet, but 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 modified Higgs coupling to top-quark κ U and to gauge boson κ V .
When the parameters are bounded by the observed channels, we show the influence on the unobserved channel h → Zγ by using the scaling factor κ Zγ , which is defined by the ratio of decay rate to the SM prediction. We find that the change of κ Zγ in type-III with χ F = −1 is less than 10%; however, with χ F = +1, the value of κ Zγ could be lower from SM prediction by over 10%.
We also show our predictions for signal strengths µ γγ and µ γZ and their correlation at 13 TeV.
The main difference between type-II and -III model is: 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 type-III model and find that when all current experimental constraints are considered, Br(t → c(h, H)) < 10 −3 for m h = 125.36 and m H = 150 GeV and Br(t → cA) slightly exceeds 10 −3 for m A = 130 GeV. The detailed numerical analyses are shown in Figs. 9, 10 and 11.