Study of the heavy CP-even Higgs with mass 125 GeV in two-Higgs-doublet models at the LHC and ILC

We assume that the 125 GeV Higgs discovered at the LHC is the heavy CP-even Higgs of the two-Higgs-doublet models, and examine the parameter space in the Type-I, Type-II, Lepton-specific and Flipped models allowed by the latest Higgs signal data, the relevant experimental and theoretical constraints. Further, we show the projected limits on tan β, sin(β − α), Hff¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ Hf\overline{f} $$\end{document} and HV V couplings from the future measurements of the 125 GeV Higgs at the LHC and ILC, including the LHC with integrated luminosity of 300 fb−1 (LHC-300 fb−1) and 3000 fb−1 (LHC-3000 fb−1) as well as the ILC at s=250\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s}=250 $$\end{document} GeV (ILC-250 GeV), s=500\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s}=500 $$\end{document} GeV (ILC-500 GeV) and s=1000\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s}=1000 $$\end{document} GeV (ILC-1000 GeV). Assuming that the future Higgs signal data have no deviation from the SM expectation, the LHC-300 fb−1, LHC-3000 fb−1 and ILC-1000 GeV can exclude the wrong-sign Yukawa coupling regions of the Type-II, Flipped and Lepton-specific models at the 2σ level, respectively. The future experiments at the LHC and ILC will constrain the Higgs couplings to be very close to SM values, especially for the HV V coupling.


Introduction
A 125 GeV Higgs boson has been discovered in the ATLAS and CMS experiments at the LHC [1,2]. A number of new measurements or updates of existing ones were presented in ICHEP 2014 [3,4]. Especially the diphoton signal strength is changed from 1.6 ± 0.4 to 1.17 ± 0.27 for ATLAS [5] and from 0.78 +0. 28 −0.16 to 1.12 +0.37 −0.32 for CMS [6]. There are some updates in the ZZ [7,8], W W [9,10], bb [11], ττ [12] decay modes, and the ttH events [13,14] from ATLAS and CMS, as well as an overall update from the D0 [15] since 2013. The properties of this particle with large experimental uncertainties agree with the Standard Model (SM) predictions. The two-Higgs-doublet model (2HDM) has very rich Higgs phenomenology, including two neutral CP-even Higgs bosons h and H, one neutral pseudoscalar A, and two charged Higgs H ± . There are four traditional types for 2HDMs, Type-I [16,17], Type-II [16,18], Lepton-specific, and Flipped models [19][20][21][22][23][24] according to their different Yukawa couplings, in which the tree-level flavor changing neutral currents (FCNC) are forbidden by a discrete symmetry. In addition, there is no tree-level FCNC in the 2HDM that allows both doublets to couple to the fermions with aligned Yukawa matrices [25]. The recent Higgs data have been used to constrain these 2HDMs over the last few months .
In this paper, we assume that the 125 GeV Higgs discovered at the LHC is respectively the heavy CP-even Higgs of the Type-I, Type-II, Lepton-specific and Flipped 2HDMs, and examine the parameter space allowed by the latest Higgs signal data, the non-observation of additional Higgs at the collider, and the theoretical constraints from vacuum stability, unitarity and perturbativity as well as the experimental constraints from the electroweak precision data and flavor observables. Further, we analyze how well 2HDMs can be distinguished from SM by the future measurements of the 125 GeV Higgs at the LHC and ILC, including the LHC with the center of mass energy √ s = 14 TeV and integrated luminosity of 300 fb −1 (LHC-300 fb −1 ) and 3000 fb −1 (LHC-3000 fb −1 ) as well as the ILC at √ s = 250 GeV (ILC-250 GeV), √ s = 500 GeV (ILC-500 GeV) and √ s = 1000 GeV  Table 1. The tree-level couplings of the heavy CP-even Higgs with respect to those of the SM Higgs boson. u, d and l denote the up-type quarks, down-type quarks and the charged leptons, respectively.
on 2HDMs from the future measurements of the 125 GeV Higgs at the LHC and ILC have been studied in [39,40]. Our work is organized as follows. In section II we recapitulate the two-Higgs-doublet models. In section III we introduce the numerical calculations. In section IV, we examine the implications of the latest Higgs signal data on the 2HDMs and projected limits on the 2HDMs from the future measurements of the 125 GeV Higgs at the LHC and ILC after imposing the theoretical and experimental constraints. Finally, we give our conclusion in section V.

Two-Higgs-doublet models
The Higgs potential with a softly broken Z 2 symmetry is written as [55] We focus on the CP-conserving model in which all λ i and m 2 12 are real. The two complex scalar doublets have the hypercharge Y = 1, Where the electroweak vacuum expectation values (VEVs) v 2 = v 2 1 + v 2 2 = (246 GeV) 2 , and the ratio of the two VEVs is defined as usual to be tan β = v 2 /v 1 . After spontaneous electroweak symmetry breaking, there are five mass eigenstates: two neutral CP-even h and H, one neutral pseudoscalar A, and two charged scalar H ± .
The tree-level couplings of the neutral Higgs bosons can have sizable deviations from those of SM Higgs boson. Table 1 shows the couplings of the heavy CP-even Higgs with respect to those of the SM Higgs boson in the Type-I, Type-II, Lepton-specific and Flipped models.

JHEP11(2014)085 3 Numerical calculations
Using the method taken in [56][57][58][59][60][61][62][63], we perform a global fit to the latest Higgs data of 29 channels (see tables I-V in [64]). The signal strength for the i channel is defined as with j denoting the partonic processes ggH, V BF, V H, and ttH. ǫ i j denotes the assumed signal composition of the partonic process j, which are given in tables I-V of [64]. The χ 2 for an uncorrelated observable is where µ exp i and σ i denote the experimental central value and uncertainty for the i channel. The uncertainty asymmetry is retained in our calculations. For the two correlated observables, we use where ρ is the correlation coefficient. We sum over the χ 2 for the 29 channels, and pay particular attention to the surviving samples with χ 2 −χ 2 min ≤ 6.18, where χ 2 min denotes the minimum of χ 2 . These samples correspond to the 95.4% confidence level regions in any two dimensional plane of the model parameters when explaining the Higgs data (corresponding to be within 2σ range).
We employ 2HDMC-1.6.4 [65,66] to implement the theoretical constraints from the vacuum stability, unitarity and coupling-constant perturbativity, and calculate the oblique parameters (S, T , U ) and δρ, whose experimental data are from ref. [67]. δρ has been precisely measured to be very close to 1 via Z-pole precision observables, which gives a strong constraint on the mass difference between various Higgses in the 2HDMs. SuperIso-3.3 [68] is used to implement the constraints from flavor observables, including B → X s γ [69], B s → µ + µ − [70], B u → τ ν [71] and D s → τ ν [69]. HiggsBounds-4.1.3 [72,73] is employed to implement the exclusion constraints from the neutral and charged Higgses searches at LEP, Tevatron and LHC at 95% confidence level. The constrains from ∆m B d and ∆m Bs 1 are considered, which are calculated using the formulas in [74]. In addition, R b is calculated by and 3000 fb −1 sensitivities are taken from ref. [80] for ATLAS and ref. [81] for CMS. The assumed signal composition is taken from ref. [79].
We take the SM value R SM b = 0.21550 ± 0.00003 [75] and the experimental data R exp b = 0.21629 ± 0.00066 [76]. Following the calculations of ref. [77], we can obtain the contributions of the charged and neutral Higgses to the tree-level couplingsḡ L b andḡ R b , and the QCD corrections is included, whose expressions are given in ref. [78].
The measurement uncertainties of Higgs signal rates will be sizably reduced at the LHC-300 fb −1 and LHC-3000 fb −1 . The projected 1σ sensitivities for channels are shown in table 2. The sensitivities of ATLAS include the current theory systematic uncertainties, the statistical and experimental systematic uncertainties. The sensitivities of ATLAS taken in ref. [79] does not include the theory uncertainty. Therefore, the sensitivities of ATLAS in table 2 differ considerably from those in ref. [79]. The sensitivities of CMS correspond to Scenario 2, which extrapolates the analyses of 7 and 8 TeV data to 14 TeV assuming the theory uncertainties will be reduced by a factor of 2 while other uncertainties are reduced JHEP11(2014)085 by a factor of 1/ √ L. The assumed signal composition is taken from ref. [79], which obtains the signal composition for ATLAS from refs. [80,82], and assumes typical values of the signal composition for CMS guided by present LHC measurements since CMS does not provide the signal composition.
Using the projected 1σ sensitivities for channels, we define with j denoting the partonic processes ggH, V BF, W H, ZH and ttH. ǫ i j and σ i denote the assumed signal composition of the partonic process j and 1σ uncertainty for the signal i, respectively. Thus, χ 2 is used to determine how well 2HDMs can be distinguished from the SM by the future measurement of the 125 GeV Higgs at the LHC. In another words, we assume the future Higgs signal data have no deviation from the SM expectation, and estimate the limits on the 2HDMs using the projected 1σ uncertainties for channels at the LHC-300 fb −1 and LHC-3000 fb −1 .
On the other hand, the design center of mass energy at the International Linear Collider (ILC) are 250 GeV and 500 GeV with a possibility to upgrade to 1 TeV. For the Higgs measurements, the beam polarizations are tuned to be (e − , e + ) = (−0.8, +0.3) at 250 GeV and 500 GeV as well as (e − , e + ) = (−0.8, +0.2) at 1 TeV. At √ s = 250 GeV, an absolute measurement of the production cross section can be performed from the Z Higgsstrahlung near threshold. The weak boson fusion process dominates over the Z Higgsstrahlung process at 500 GeV and 1000 GeV. The projected 1σ sensitivities of channels at the ILC are shown in table 3. Using the projected 1σ sensitivities for channels at the ILC, we define where R i and σ i represent the signal strength prediction from the 2HDMs and the 1σ uncertainty for the signal i, respectively. In our calculations, the input parameters are taken as m 2 12 , tan β, sin(β − α) and the physical Higgs masses (m h , m H , m A , m H ± ). We fix m H as 125 GeV, and scan randomly the parameters in the following ranges:

Results and discussions
In addition to that the theoretical constraints are satisfied, we require the 2HDMs to explain the experimental data of flavor observables and the electroweak precision data within 2σ range, and fit the current Higgs signal data, the future LHC and ILC data at the 2σ level.
In figure 1, we project the surviving samples on the plane of sin(β − α) versus tan β. tan β is required to be larger than 1.6 for the Type-I and Lepton-specific models, and 1.1 for the Type-II and Flipped models. The main constraints are from ∆m B d and ∆m Bs which are sensitive to cot β. The Type-I model is less constrained than the other three models by the current data. sin(β − α) is allowed to vary in the range of -0.55 and 0.5. In the Type-I model, the neutral CP-even Higgs couplings to fermions have a universal varying factor. In addition, the charged Higgs Yukawa couplings approach to zero in the large tan β limit, which is less constrained by B → X s γ and R b . For sin α sin β , sin α sin β = cos(β − α) − sin(β − α) cot β. In the wrong-sign Yukawa coupling region where both | ε | and sin 2 (β −α) are much smaller than 1,

JHEP11(2014)085
From eqs. (4.1) and (4.2), we obtain This implies the wrong-sign hff coupling with a normalized factor sin α sin β can only be achieved for tan β is much smaller than 1, which is excluded by the current experimental data as the above discussions.
In the SM-like region, From eqs. (4.4) and (4.9), we obtain Therefore, the wrong-sign Yukawa coupling can be achieved for the hdd and hll couplings in the Type-II model, hll in the Lepton-specific model, and hdd in the Flipped model. The above analyses are confirmed by what are shown in the figure 1. In the wrong-sign Yukawa coupling regions, the current data require tan β > 2.5 for the Type-II model, tan β > 4 for the Lepton-specific model and tan β > 3 for the Flipped model. sin(β −α) is allowed to be as low as -0.62 for the Type-II model, -0.4 for the Lepton-specific model and -0.5 for the Flipped model. In the SM-like regions, the current data require −0.18 < sin(β − α) < 0.16 for the Lepton-specific model, and −0.1 < sin(β − α) < 0.1 for the Type-II model and the Flipped model.
In figure 2 and figure 3, we project the surviving samples on the planes of the 125 GeV Higgs couplings. From figure 2, for the Type-I model, we find that the allowed ranges of R HV V and R Hff are 0.86 ∼ 1.0 and 0.   For the Lepton-specific model, in the wrong-sign Hll coupling region, the current data require 0.915 < R HV V < 0.995, −1.3 < R Hll < −0.675 and 0.992 < R Huū (R Hdd ) < 1.01. The LHC-300 fb −1 , LHC-3000 fb −1 and ILC-250 GeV can gradually constrain the absolute values of Higgs couplings to ff and V V to be close to SM values in the wrong-sign Hll JHEP11(2014)085 coupling region, and the ILC-1000 GeV can exclude the whole wrong-sign Hll coupling region at the 2σ level. In the SM-like region, the current data require 0.986 < R HV V < 1.0, 0.675 < R Hll < 1.288 and 0.9 < R Huū (R Hdd ) < 1.085. The future LHC-300 fb −1 will require R HV V to be in the range of 0.998 and 1.0. The other future LHC and ILC experiments will require R HV V to be very close to 1. The allowed ranges of R Huū (R Hdd ) and R Hll are 0.97 ∼ 1.03 and 0.901 ∼ 1.091 for the LHC-300 fb −1 , 0.982 ∼ 1.018 and 0.94 ∼ 1.058 for the LHC-3000 fb −1 , 0.988 ∼ 1.013 and 0.946 ∼ 1.051 for the ILC-250 GeV, 0.991 ∼ 1.01 and 0.945 ∼ 1.053 for the ILC-500 GeV as well as 0.993 ∼ 1.007 and 0.963 ∼ 1.037 for the ILC-1000 GeV.
For the Flipped model, in the wrong-sign Hdd coupling region, the current data require 0.865 < R HV V < 0.993, −1.35 < R Hdd < −0.81 and 0.991 < R Huū (R Hll ) < 1.015. The LHC-300 fb −1 can exclude some samples with R Hdd < −1 and R Huū very close to 1. The LHC-3000 fb −1 can exclude the whole wrong-sign Hdd coupling region at the 2σ level. In the SM-like region, the current data require 0.996 < R HV V < 1.0, 0.825 < R Hdd < 1.195 and 0.932 < R Huū (R Hll ) < 1.064. The future LHC and ILC experiments will require R HV V to be very close to 1. The allowed ranges of R Hdd and R Huū (R Hll ) are 0.946 ∼ 1.056 and 0.981 ∼ 1.018 for the LHC-300 fb −1 , 0.965 ∼ 1.034 and 0.988 ∼ 1.015 for the LHC-3000 fb −1 , 0.97 ∼ 1.032 and 0.986 ∼ 1.013 for the ILC-250 GeV, 0.983 ∼ 1.018 and 0.992 ∼ 1.008 for the ILC-500 GeV as well as 0.987 ∼ 1.013 and 0.994 ∼ 1.005 for the ILC-1000 GeV. Now we examine the allowed mass ranges of the light CP-even Higgs, pseudoscalar and charged Higgs with the heavy CP-even Higgs being the 125 GeV Higgs. Since the focus of this paper is studying the limits on the heavy CP-even Higgs with mass 125 GeV at the current and future collider, the projected limits on m h , m A and m H ± from the future collider are beyond the scope of this paper. Therefore, we only show the mass ranges of m h , m A and m H ± allowed by the current limits in figure 4 and figure 5. Since the decay H → hh is open for m h < 62.5 GeV, the BR(H → hh) has to be small enough that H can fit the LHC Higgs signal data at an adequate level. As a result, we only obtain a few scattering of points for m h < 62.5 GeV in the Type-I, Type-II, Lepton-specific, and Flipped models, respectively, as shown in figure 4. If a very "fine-tuned" scan is employed, the more low-m h points may be obtained. Figure 5 shows that m H ± is required to be larger than 250 GeV in the Type-II and Flipped models due to the constraints from the low energy flavor observables. There is small mass difference between m A and m H ± mainly due to the constraints of ∆ρ. Since there is small mass difference between m h and m H , m A and m H ± should have the small mass difference to cancel the contributions of m h and m H to ∆ρ. In the Type-I and Lepton-specific models, since the charged Higgs Yukawa couplings are suppressed by 1 tan β , m H ± is allowed to be smaller than 100 GeV. Further, for m H ± is around m H , the contributions to ∆ρ from (m h , m H ± ) and (m A , m H ± ) loops can be canceled by the (m h , m H ) and (m A , m H ) loops. Thus m A is allowed to have large mass difference from m H ± for m H ± is around 100 GeV.
Ref. [84] shows that the second light Higgs boson explanation of 125 GeV in the MSSM is ruled out by the present experiments. Compared to Type-II model, the five Higgs masses in the MSSM are not independent. Taking the mass of the second light Higgs boson as 125 GeV, the mass of charged Higgs should be smaller than 200 GeV, which is excluded by at the ILC for R Hbb < 0 is sizably smaller than those for R Hbb > 0. According to the projected sensitivities of diphoton signal shown in the table 3, the diphoton Higgs rates are within 2σ range of ILC-250 GeV -1.3 < R Hbb < 1.2, and ILC-500 GeV for R Hbb > 0, and the ILC-1000 GeV can probe the wrong-sign Yukawa coupling of b-quark in the Type-II and Flipped models by measuring the diphoton Higgs signal via W W fusion at 2σ level. By measuring the inclusive diphoton Higgs signal at the LHC-300 fb −1 , CMS can detect the wrong-sign Yukawa coupling of Type-II model and Flipped model at 2σ level.
Assuming the light CP-even Higgs is the discovered 125 GeV Higgs, ref. [39] shows tan β and cos(β − α) within 2σ ranges of the current Higgs data and the projected limits from the future collider. Similar to the heavy CP-even Higgs, the wrong-sign Yukawa coupling is absent in the Type-I model, and can appear in the Type-II, Lepton-specific and Flipped models for tan β > 3. For the Type-II, Lepton-specific and Flipped models, cos(β − α) is strongly constrained in the SM-like region, and cos(β − α) in the wrong-sign Yukawa coupling region is allowed to be much larger than that in the SM-like region. The current Higgs data allow cos(β − α) to be as large as 0.55 for the Type-I, Type-II and Flipped models, and 0.5 for the Lepton-specific model. The ILC-1000 GeV can give the strongest constraints on cos(β − α), | cos(β − α) |< 0.4% for the Type-II, Lepton-specific and Flipped models as well as | cos(β − α) |< 8% for the Type-I model. For the heavy CP-even Higgs as the 125 GeV Higgs, this paper shows that the ILC-1000 GeV gives the similar constraints on sin(β − α), | sin(β − α) |< 10% for the Type-I model, | sin(β − α) |< 0.8% for the Type-II model and Flipped models, and | sin(β − α) |< 1.4% for the Lepton-specific model. This leads to that R HV V is very close to 1 due to R HV V = cos(β − α) ≃ 1 − 1 2 sin(β − α) 2 .

Conclusion
In this paper, we assume the 125 GeV Higgs discovered at the LHC is the heavy CPeven Higgs of the Type-I, Type-II, Lepton-specific and Flipped 2HDMs, and examine the parameter space allowed by the latest Higgs signal data, the non-observation of additional Higgs at the collider, and the theoretical constraints from vacuum stability, unitarity and perturbativity as well as the experimental constraints from the electroweak precision data and flavor observables. We obtain the following observations: (i) The current theoretical and experimental constraints favor a small tan β, but give a lower limit of tan β, tan β > 1.6 for the Type-I model, tan β > 1.1 (2.5) for the SM-like JHEP11(2014)085 region (wrong-sign Yukawa coupling region) of the Type-II model, tan β > 1.6 (4.0) for the SM-like region (wrong-sign Yukawa coupling region) of the Lepton-specific model, and tan β > 1.1 (3.0) for the SM-like region (wrong-sign Yukawa coupling region) of the Flipped model.
(ii) For the Type-I model, the current experimental data require 0.86 < R HV V < 1.0 and 0.8 < R Hff (u, d, l) < 1.17.
Further, we give the projected limits on tan β, sin(β − α), Hff and HV V couplings from the future measurements of the 125 GeV Higgs at the LHC and ILC, including the LHC-300 fb −1 , LHC-3000 fb −1 , ILC-250 GeV, ILC-500 GeV and ILC-1000 GeV. Assuming that the future Higgs signal data have no deviation from the SM expectation, the LHC-300 fb −1 , LHC-3000 fb −1 and ILC-1000 GeV can exclude the wrong-sign Yukawa coupling regions of the Type-II, Flipped and Lepton-specific models at the 2σ level, respectively. The future experiments at the LHC and ILC will constrain the Higgs couplings to be very close to SM values, especially for the HV V coupling.