Complementarity in direct searches for additional Higgs bosons at the LHC and the International Linear Collider
aa r X i v : . [ h e p - ph ] J u l UT-HET-087
Complementarity in direct searches for additional Higgs bosonsat the LHC and the International Linear Collider
Shinya Kanemura ∗ and Hiroshi Yokoya † Department of Physics, University of Toyama, Toyama 930-8555, Japan
Ya-Juan Zheng ‡ CTS, CASTS and Department of Physics,National Taiwan University, Taipei 10617, Taiwan (Dated: September 27, 2018)
Abstract
We discuss complementarity of discovery reaches of heavier neutral Higgs bosons and chargedHiggs bosons at the LHC and the International Linear Collider (ILC) in two Higgs doublet models(2HDMs). We perform a comprehensive analysis on their production and decay processes for alltypes of Yukawa interaction under the softly-broken discrete symmetry which is introduced to avoidflavour changing neutral currents, and we investigate parameter spaces of discovering additionalHiggs bosons at the ILC beyond the LHC reach. We find that the 500 GeV run of the ILC with theintegrated luminosity of 500 fb − shows an advantage for discovering the additional Higgs bosonsin the region where the LHC cannot discover them with the integrated luminosity of 300 fb − . Forthe 1 TeV run of the ILC with the integrated luminosity of 1 ab − , production processes of anadditional Higgs boson associated with the top quark can be useful as discovery channels in someparameter spaces where the LHC with the integrated luminosity of 3000 fb − cannot reach. It isemphasized that the complementary study at the LHC and the ILC is useful not only to surveyadditional Higgs bosons at the TeV scale, but also to discriminate types of Yukawa interaction inthe 2HDM. PACS numbers: 12.60.Fr, 13.66.Hk, 14.80.Ec, 14.80.Fd ∗ Electronic address: [email protected] † Electronic address: [email protected] ‡ Electronic address: [email protected] . INTRODUCTION In July 2012, both the ATLAS and CMS Collaborations announced the observation of along-sought new particle with a mass approximately at 126 GeV [1, 2]. Further measure-ments of the properties of this new particle manifest consistency with the Higgs boson inthe standard model (SM) within the errors which are not small up to now [3–6]. It makesthe SM much closer to its triumph in explaining electroweak symmetry breaking. However,this does not necessarily mean that the SM is fundamentally correct. There is no theoreticalprinciple to justify the minimal Higgs sector with only one Higgs doublet in the SM, andmany new physics models beyond the SM predict non-minimal Higgs sectors. Therefore, itis very important to determine the Higgs sector in order to understand the structure of thenew physics model by future experiments at the LHC and the International Linear Collider(ILC) [7, 8].The two Higgs doublet model (2HDM) is one of the simplest extensions of the SM Higgssector, which is useful in both exploring the phenomenology of extended Higgs sectors andinterpreting experimental results from searches for additional Higgs bosons. Some of thenew physics models contain two Higgs doublets, such as the minimal supersymmetric exten-sion of the SM (MSSM) [9–11], models for extra CP phases, models for electroweak baryo-genesis [12–14], and models for radiative neutrino mass generation mechanism [15–17]. Ingeneral, the extension with additional doublet fields causes flavour changing neutral currents(FCNCs), which are strongly bounded by experimental data. In order to avoid such danger-ous FCNCs, different quantum number should be assigned to each doublet field [18]. Thiscan be attained by introducing a softly-broken discrete symmetry under which Φ → +Φ and Φ → − Φ , where Φ and Φ are the two doublet fields . In this case, there can befour types of Yukawa interaction, depending on the assignment of charges of the discretesymmetry [22, 23]. In the 2HDMs, there are two CP-even neutral scalars h and H , oneCP-odd neutral scalar A , and a pair of charged scalars H ± . We assume that the lighterCP-even neutral scalar h is the discovered SM-like Higgs boson with the mass of about126 GeV. Additional neutral and charged Higgs bosons have rich phenomenology and serveas a cornerstone for physics beyond the SM.
2n the literature, there have been many discussions on various types of 2HDMs andtheir signatures at the LHC [24–27]. For a recent systematic study on the theory andphenomenology of 2HDMs, we refer to Ref. [28] and references therein. In light of the recentdata collected at the LHC 7-8 TeV run, many possibilities for explanation of the current dataof several decay channels for the observed Higgs boson are explored in the framework of the2HDMs [29–46]. Furthermore, the parameter regions in the 2HDMs have been constrainedby direct searches for additional Higgs bosons at the LHC [47, 48]. For the future run ofthe LHC with the collision energy of 14 TeV, additional Higgs bosons are expected to bedetected as long as their masses are smaller than 350 GeV to 800 GeV, depending on thescenario of the 2HDMs for the integrated luminosity of 300 fb − [49].The ILC is a future electron-positron linear collider with the collision energies to be from250 GeV to 1 TeV [7, 8]. The ILC can be used for precision measurements of the massesand couplings of the SM particles. We can expect that the first run of the ILC with thecollision energy at 250 GeV is capable of measuring the properties of the discovered SM-like Higgs boson with a considerable level. By the combination of the results with highercollision energies up to 1 TeV, all the coupling constants with the discovered Higgs bosoncan be measured with excellent accuracies. For instance, the Higgs couplings with weakgauge bosons can be measured by better than 1%, the Yukawa coupling constants can bemeasured by percent levels, and the triple Higgs boson coupling can be measured by a tenpercent level [49, 50]. Such precision measurements of coupling constants of the discoveredHiggs boson can make it possible to perform fingerprinting of extended Higgs sectors whendeviations from the SM predictions are detected, because each extended Higgs sector predictsa different pattern in deviations of coupling constants [49–53]. However, the deviations inthe coupling constants of the SM-like Higgs boson from the SM predictions can be smallerthan those detectable at the ILC, even when additional Higgs bosons are not too heavy.At the ILC, the direct searches can also be well performed for new particles in the modelsbeyond the SM as long as kinematically accessible. Additional Higgs bosons can be producedmainly in pair if the sum of the masses is less than the collision energy, via e + e − → hA [54], e + e − → HA [55] and e + e − → H + H − [55]. For the collision energy below the threshold ofthe pair production, single production processes of new additional Higgs bosons can be usedtoo, although the production cross sections are not large. The single charged Higgs bosonproduction has been studied in the framework of the MSSM [56, 57]. Preliminary detection3ossibilities were studied at linear colliders, and their analysis shows that in the parameterspace beyond the kinematic limit for pair production, single production of H ± associatedwith the top quark turns out to be a useful channel in studying the charged Higgs bosonphenomenology [57]. QCD corrections to the process e + e − → ¯ tbH + and its charge conjugatecounterpart have been studied in the MSSM in Ref. [58]. The single production processes ofadditional neutral Higgs bosons have been studied in Ref. [59], and QCD corrections to the e + e − → Q ¯ QH and e + e − → Q ¯ QA processes are calculated in Refs. [60, 61] where Q = t and b . The discovery potential for additional Higgs bosons through single and pair productionprocesses at linear collider are evaluated in the MSSM [62], which is useful in distinguishingthe MSSM from the other models.In this paper, we perform a comprehensive analysis on the production and decay processesof additional Higgs bosons for all types of Yukawa interaction under the discrete symmetry.The parameter space of discovering additional Higgs bosons at the LHC is shown for all typesof Yukawa interaction in the 2HDM according to the analysis given in Ref. [49]. We thenexamine detailed signatures of additional Higgs bosons for all types of Yukawa interactionat the ILC. We find that the complementary study at the LHC and the ILC is useful notonly to survey additional Higgs bosons at the TeV scale, but also to discriminate types ofYukawa interaction in the 2HDM.The paper is organized as follows. In Sec. II, we introduce the 2HDMs and the differenttypes of Yukawa interaction. In Sec. III, we present a brief summary of theoretical andexperimental (flavour and collider) constraints on the additional neutral and charged Higgsbosons. Our study on the future prospects of the LHC searches are also presented in thissection. Sec. IV is devoted to our systematic analysis on the ILC search for the additionalHiggs bosons. Based on several benchmark scenarios, further discussions on the prospectsof the direct searches of additional Higgs bosons at future collider experiments are given inSec. V. Finally, we draw a conclusion in Sec. VI.4 Φ u R d R ℓ R Q L L L Type-I + − − − − + +Type-II + − − + + + +Type-X + − − − + + +Type-Y + − − + − + +TABLE I: Four possible Z charge assignments of scalar and fermion fields to forbid tree-levelHiggs-mediated FCNCs [27]. II. TWO HIGGS DOUBLET MODELA. Basics of the model
In the 2HDM, two isospin doublet scalar fields, Φ and Φ are introduced with a hyper-charge Y = 1. The Higgs potential in the general 2HDM is given as [10] V = m | Φ | + m | Φ | − ( m Φ † Φ + h . c . ) + λ | Φ | + λ | Φ | + λ | Φ | | Φ | + λ | Φ † Φ | + (cid:20) λ † Φ ) + n λ (Φ † Φ ) + λ (Φ † Φ ) o Φ † Φ + h . c . (cid:21) , (1)where m , m , λ − are real parameters while m , λ − are complex in general.For the most general 2HDM, the presence of Yukawa interactions leads to the FCNCs viatree-level Higgs-mediated diagrams which is not phenomenologically acceptable. To avoidsuch FCNCs, we consider 2HDMs with discrete Z symmetry, under which the two doubletsare transformed as Φ → +Φ and Φ → − Φ [18, 63–65]. For the SM fermions, four setsof parity assignment under the Z transformation are possible [22], which is summarized inTable I. Because of these types of Yukawa interaction, the 2HDM with Z parity contains avariety of phenomenology with quarks and leptons.To preserve the discrete symmetry, we hereafter restrict ourselves with the Higgs potentialin Eq. (1) with vanishing λ and λ which induce the explicit breaking of the symmetry.On the other hand, the presence of the m term induces the soft breaking of the symmetrycharacterized by the soft-breaking scale M = m / (sin β cos β ) [66]. Therefore, we allowthe m term and the soft breaking of the Z symmetry. Furthermore, we consider theCP-conserving scenario for simplicity by taking m and λ to be real.After the electroweak symmetry breaking and after the three Nambu-Goldstone bosons5re absorbed by the Higgs mechanism, five physical states are left; two CP-even neutralHiggs bosons, h and H ; one CP-odd neutral Higgs boson, A ; and charged Higgs bosons, H ± . Masses of these scalars are obtained by solving the stability conditions of the potentialin Eq. (1) [10]. In addition to the four kinds of masses m h , m H , m A and m H ± as well as thesoft-breaking parameter M , the remaining two parameters are chosen as follows. One istan β = v /v , the ratio of the vacuum expectation values (VEVs) of the two doublet fields,where v ≡ p v + v ≃
246 GeV is fixed by the Fermi constant G F = 1 / ( √ v ). The otheris α , a mixing angle for diagonalizing the mass matrix for the neutral CP-even component.The limit of sin( β − α ) = 1 is called the SM-like limit where the light CP-even scalar h behaves as the SM Higgs boson [67]. We take h as the observed SM-like Higgs boson with m h = 126 GeV.The input parameters of the model are v , m h , m H , m A , m H ± , M , α and β . In terms ofthese parameters, the quartic coupling constants are expressed as [66] λ = 1 v cos β ( − M sin β + m h sin α + m H cos α ) , (2a) λ = 1 v sin β ( − M cos β + m h cos α + m H sin α ) , (2b) λ = 1 v (cid:20) − M − sin 2 α sin 2 β ( m h − m H ) + 2 m H ± (cid:21) , (2c) λ = 1 v ( M + m A − m H ± ) , (2d) λ = 1 v ( M − m A ) . (2e)The interactions of the Higgs bosons to weak gauge bosons are common among thetypes of Yukawa interaction. Feynman rules for these interactions are read out from theLagrangian [10, 11]; hZ µ Z ν : 2 i m Z v sin( β − α ) g µν , HZ µ Z ν : 2 i m Z v cos( β − α ) g µν ,hW + µ W − ν : 2 i m W v sin( β − α ) g µν , HW + µ W − ν : 2 i m W v cos( β − α ) g µν (3)6nd hAZ µ : g Z β − α )( p + p ′ ) µ , HAZ µ : − g Z β − α )( p + p ′ ) µ ,H + H − Z µ : − g Z θ W ( p + p ′ ) µ , H + H − γ µ : − ie ( p + p ′ ) µ ,H ± hW ∓ µ : ∓ i g W β − α )( p + p ′ ) µ , H ± HW ∓ µ : ± i g W β − α )( p + p ′ ) µ ,H ± AW ∓ µ : g W p + p ′ ) µ , (4)where p µ and p ′ µ are outgoing four-momenta of the first and the second scalars, respectively,and g Z = g W / cos θ W . B. Type of Yukawa interaction
The Yukawa interactions of the 2HDM Higgs bosons to the SM fermions are written as L = − ¯ Q L Y u ˜Φ u u R − ¯ Q L Y d Φ d d R − ¯ L L Y ℓ Φ ℓ ℓ R + h . c ., (5)where R and L represent the right-handed and left-handed chirality of fermions, respectively.Φ f = u,d,ℓ is chosen from Φ or Φ to make the interaction term Z invariant, according to theTable I. The Type-I 2HDM is the case that all the quarks and charged leptons obtain themasses from v , and the Type-II 2HDM is that up-type quark masses are generated by v but the masses of down-type quarks and charged leptons are generated by v . In the Type-X2HDM, both up- and down- type quarks couple to Φ while charged leptons couple to Φ .The last case is the Type-Y 2HDM where up-type quarks and charged leptons couple to Φ while up-type quarks couple to Φ . We note that the Type-II 2HDM is predicted in thecontext of the MSSM [9, 10] and that the Type-X 2HDM is used in some of radiative seesawmodels [16, 17].In terms of the mass eigenstates, Eq. (5) is rewritten as L = − X f = u,d,ℓ h m f v ξ fh ¯ f f h + m f v ξ fH ¯ f f H − i m f v ξ fA γ ¯ f f A i − ( √ V ud v ¯ u (cid:2) m u ξ uA P L + m d ξ dA P R (cid:3) dH + + √ m ℓ v ξ ℓA ¯ v L ℓ R H + + h . c . ) , (6)where P R,L are the chiral projection operators. The coefficients ξ fφ are summarized in Ta-ble II. 7 uh ξ dh ξ ℓh ξ uH ξ dH ξ ℓH ξ uA ξ dA ξ ℓA Type-I c α /s β c α /s β c α /s β s α /s β s α /s β s α /s β cot β − cot β − cot β Type-II c α /s β − s α /c β − s α /c β s α /s β c α /c β c α /c β cot β tan β tan β Type-X c α /s β c α /s β − s α /c β s α /s β s α /s β c α /c β cot β − cot β tan β Type-Y c α /s β − s α /c β c α /s β s α /s β c α /c β s α /s β cot β tan β − cot β TABLE II: The coefficients for different type of Yukawa interactions [27]. c θ = cos θ, and s θ = sin θ for θ = α, β . In the SM-like limit, all the φV V vertices in Eq. (3) and φhV in Eq. (4) in which oneadditional Higgs boson is involved disappear, where φ represents H , A or H ± . On theother hand, the Yukawa interactions of additional Higgs boson remain even in this limit.Therefore, Yukawa interactions of the additional Higgs bosons are very important for thedecay and production processes of additional Higgs bosons in this limit. C. Decay widths and decay branching ratios
For each type of Yukawa interaction, the decay widths and branching ratios of additionalHiggs bosons can be calculated for given values of tan β , sin( β − α ) and the masses. Thetotal decay widths of additional Higgs bosons are necessary for the consistent treatmentof the production and decays of additional Higgs bosons. We refer to Ref. [27] where thetotal decay widths are discussed in details for sin( β − α ) ≃
1. Explicit formulae for allthe partial decay widths can be found, e.g., in Ref. [27]. Here, we review the characteristicbehaviors of the decays of additional Higgs bosons in each type of Yukawa interaction bypresenting numerical results of the branching ratios. For simplicity, we set sin( β − α ) = 1,the SM-like limit. In this limit, the decay modes of H → W + W − , ZZ , hh as well as A → Zh are absent. Decay branching ratios of the SM-like Higgs boson become completelythe same as those in the SM at the leading order, so that we cannot distinguish models bythe precision measurement of the couplings of the SM-like Higgs boson . As we discuss later,the branching ratios can drastically change if sin( β − α ) is slightly deviated from unity. The decay branching ratios can be different from the SM prediction at the next-to-leading order [52, 66, 68–70]. -3 -2 -1 B R ( H X ) Type-I Type-II Type-X Type-Y -3 -2 -1 B R ( A X ) tan β -3 -2 -1 B R ( H + X ) tan β tan β tan β τ + τ - ggbb τ + τ - µ + µ - cc τ + ν cb µ + ν cc cc ccgg gg gg gggg ggggcc cc cc ccbbbb τ + τ - τ + ν cb bb bb bbbbbb µ + µ - τ + τ - τ + τ - τ + τ - γγ τ + τ - τ + τ - τ + ν cs cs cb cs cs cb τ + ν µ + νµ + ν µ + ν γγ γγ γγγγ FIG. 1: Branching ratios of H , A , H ± as a function of tan β for m H = m A = m H ± = M = 125 GeVin the Type-I, II, X and Y 2HDM with sin( β − α ) = 1. For numerical evaluation, MS masses of fermions at their own mass scales are taken tobe m b = 4 . m c = 1 . m s = 0 .
12 GeV, and the leading order QCD runningof them to the mass of the Higgs boson is taken into account. In addition, we include theoff-diagonal CKM matrix elements in our analysis, | V cb | = | V ts | = 0 .
04 [71].In the following, we show the branching ratios of additional Higgs bosons in each typeof Yukawa interaction, for the masses of 125 GeV, 250 GeV and 500 GeV. In Fig. 1, decaybranching ratios of additional Higgs bosons, H , A , and H ± for m H = m A = m H ± = M =125 GeV are plotted as a function of tan β in each type of Yukawa interaction. Here, for thepurpose of completeness, we do not take seriously the direct and indirect exclusion limits,which are discussed later. Decay modes of H, A → t ¯ t and H ± → tb are yet to open. ForType-I, since all the Yukawa couplings are modified by the same factor, the tan β dependenceon the branching ratios is small. For large tan β , all the Yukawa couplings are suppressed,9 -3 -2 -1 B R ( H X ) Type-I Type-II Type-X Type-Y -3 -2 -1 B R ( A X ) tan β -3 -2 -1 B R ( H + X ) tan β tan β tan β τ + τ - ggbb τ + τ - µ + µ - cc τ + ν tb µ + ν cc cc cc ts gg gggggg ggggcc cc cc ccbbbb τ + τ - τ + ν tb bb bb bbbbbb µ + µ - τ + τ - τ + τ - τ + τ - γγγγ τ + τ - τ + τ - tb ts cb gg ts tb cbts µ + ν γγ γγ γγγγ γγ γγ FIG. 2: The same as Fig. 1, but for m H = m A = m H ± = M = 250 GeV. which leads to very narrow widths of additional Higgs bosons. The dominant decay modesare b ¯ b for the decays of H and A , and τ ν and cs for that of H ± . For Type-II, the Yukawainteraction of down-type quarks and charged leptons are scaled by tan β , while up-typequarks are by cot β . The decays of H and A are dominated by the b ¯ b mode ( ∼ τ + τ − mode ( ∼ β , except in the small tan β regions where gg and c ¯ c decays become major modes. The decay of H ± is dominated by the τ ν mode fortan β &
1. For tan β .
1, the dominant decay mode becomes cs . For Type-X, since leptonicdecay modes are enhanced by tan β , τ + τ − would be the dominant decay mode of H and A for tan β &
2, while τ ν is dominant in the H ± decay for tan β &
1. For the smaller tan β values, the dominant decay modes are b ¯ b for H and A , and cs for H ± . For Type-Y, only theYukawa couplings of down-type quarks are enhanced by tan β , b ¯ b would be the dominantdecay mode of H and A for tan β &
1. The dominant decay mode of H ± is cb for large tan β values, and τ ν and cs for smaller tan β ones.10 -3 -2 -1 B R ( H X ) Type-I Type-II Type-X Type-Y -3 -2 -1 B R ( A X ) tan β -3 -2 -1 B R ( H + X ) tan β tan β tan β tt gg bb τ + τ - µ + µ - tb τ + ν cb µ + ν tt tt tt gg gg gggggg gggg tttttttt tb tb tb τ + ν cb bb bb bbbbbb µ + µ - τ + τ - τ + τ - τ + τ - ts ts ts ts FIG. 3: The same as Fig. 1, but for m H = m A = m H ± = M = 500 GeV. In Fig. 2, the same branching ratios are evaluated for m H = m A = m H ± = M = 250 GeV.The decay branching ratios of H and A are almost unchanged from the results for 125 GeV,but those of H ± are changed due to the new decay mode tb . This decay mode dominatesfor all the tan β regions for the Type-I, Type-II and Type-Y, and for tan β .
10 for Type-X.The τ ν mode can be dominant and sub-dominant ( ∼ .
3) for tan β &
10 for Type-X andType-II, respectively.In Fig. 3, the same branching ratios are evaluated for m H = m A = m H ± = M = 500 GeV.In this case, the t ¯ t mode opens in the decays of H and A . The t ¯ t decay dominates in all thetan β regions for Type-I, tan β . H ± are similar to those in the 250 GeV cases.11 II. CONSTRAINTS ON 2HDM PARAMETERS
In this section, we briefly review the theoretical and experimental constraints on theparameters in the 2HDMs.
A. Constraints on the Higgs potential from perturbative unitarity and vacuumstability
First, we introduce the constraints on the parameters by theoretical arguments, namelyperturbative unitarity and vacuum stability. The tree-level unitarity requires the scatteringamplitudes to be perturbative [72], i.e. | a i | < / a i are the eigenvalues of the S -wave amplitudes of two-to-two elastic scatterings of the longitudinal component of weakgauge bosons and the Higgs boson. In the 2HDM with the softly-broken Z symmetry, thiscondition gives constraints on the quartic couplings in the Higgs potential [73–75]. Theeigenvalues for 14 ×
14 scattering matrix for neutral states are given as [73], a ± = 116 π "
32 ( λ + λ ) ± r
94 ( λ − λ ) + (2 λ + λ ) , (7a) a ± = 116 π "
12 ( λ + λ ) ± r
14 ( λ − λ ) + λ , (7b) a ± = 116 π "
12 ( λ + λ ) ± r
14 ( λ − λ ) + λ , (7c) a = 116 π ( λ + 2 λ − λ ) , (7d) a = 116 π ( λ − λ ) , (7e) a = 116 π ( λ + 2 λ + 3 λ ) , (7f) a = 116 π ( λ + λ ) , (7g) a = 116 π ( λ + λ ) , (7h)and for singly charged states, one additional eigenvalue is added [74], a = 116 π ( λ − λ ) . (8)12econd, the requirement of vacuum stability that the Higgs potential must be bounded frombelow gives [76–78] λ > , λ > , p λ λ + λ + Min(0 , λ − | λ | ) > . (9)The parameter space of the model is constrained by these conditions on the coupling con-stants in the Higgs potential. B. Constraints on the Higgs potential from electroweak precision observables
Further constraints on the Higgs potential of the 2HDM are from the electroweak precisionmeasurements. The S , T and U parameters are defined to disentangle new physics effects inthe radiative corrections to the gauge bosons two-point functions [79]. Those are sensitiveto the effects of Higgs bosons through the loop corrections [80, 81]. The T parametercorresponds to the ρ parameter, which is severely constrained by experimental observationsas ρ = 1 . +0 . − . where U = 0 is assumed [71]. Because of this constraint, the masssplitting among the additional Higgs bosons are constrained in the 2HDM with the lightSM-like Higgs boson [82, 83]. C. Flavour constraints on m H ± and tan β Flavour experiments constrain the 2HDM through the H ± contribution to the flavourmixing observables by tree-level or loop diagrams [27, 84, 85]. Since the amplitudes ofthese processes contain the Yukawa interaction, constraints from the flavour physics stronglydepends on the type of Yukawa interaction. In Ref. [86], the limits on the general couplingsby flavour physics are translated to the limits in the ( m H ± , tan β ) plane in each type ofYukawa interaction in the 2HDM. See also recent studies in Refs. [87–89].The strong exclusion limit is provided from the measurements of the branching ratioof B → X s γ processes [90]. For Type-II and Type-Y, a tan β -independent lower limit of m H ± &
380 GeV is obtained [91] by combining with the NNLO calculation [92]. On theother hand, for Type-I and Type-X, tan β . m H ± .
800 GeV, but no lowerbound on m H ± can be obtained.For all types of Yukawa interaction, lower tan β regions (tan β ≤
1) are also excluded13or m H ± .
500 GeV by the measurement of B d - ¯ B d mixing [90], because of the universalcouplings of H ± to the up-type quarks.Constraints for larger tan β regions are obtained only in the Type-II 2HDM by usingthe leptonic meson decay processes [90], B → τ ν [93] and D s → τ ν [94]. This is becausethe relevant couplings behave ξ dA ξ ℓA = tan β in Type-II, but ξ dA ξ ℓA = − β ) for Type-X and Type-Y (Type-I). For Type-II, upper bounds of tan β are given at around 30 for m H ± ≃
350 GeV and around 60 for m H ± ≃
700 GeV [86].
D. Collider constraints on Higgs boson masses and tan β Here, we briefly summarize constraints on the additional neutral and charged Higgsbosons in the 2HDM from previous collider data at LEP, Tevatron and LHC experiments.Most of the searches before have been performed in the context of the MSSM, namely, theType-II 2HDM. Some of the results can be used to analyze the constraints on the othertypes of 2HDMs. There have also been other studies which directly investigate some typesof Yukawa interaction such as Type-I, Type-X and Type-Y.From the LEP experiment, lower mass bounds on H and A have been obtained as m H > . m A > . H ± give the mass bound of m H ± >
80 GeV assuming B ( H + → τ + ν ) + B ( H + → c ¯ s ) = 1 [97–99].CDF and D0 Collaborations at the Fermilab Tevatron have searched for the processesof p ¯ p → b ¯ bH/A , followed by H/A → b ¯ b or H/A → τ + τ − [100–102]. By utilizing the τ + τ − ( b ¯ b ) decay mode, which can be sensitive to the cases of Type-II (Type-II and Type-Y),upper bounds of tan β have been obtained from around 25 to 80 (40 to 90) for m A from100 GeV to 300 GeV, respectively. For the H ± search at the Tevatron, the decay modes of H ± → τ ν and H ± → cs have been investigated using the production from the top quarkdecay of t → bH ± [103–105]. Upper bounds on the decay branching ratio B ( t → bH ± ) havebeen obtained, which can be translated into the bound on tan β in various scenarios. Inthe Type-I 2HDM, for H ± heavier than the top quark, upper bounds on tan β have beenobtained to be from around 20 to 70 for m H ± from 180 GeV to 190 GeV, respectively [104].At the LHC, direct searches for the additional Higgs bosons have been performed byusing the recorded events at a center-of-mass energy of 7 TeV with 4.9 fb − and 8 TeV14ith 19.7 fb − in 2011 and 2012, respectively. The CMS experiment has searched H and A decaying to the τ + τ − final state, and upper limits on tan β have been obtained for theMSSM scenario or the Type-II 2HDM from 4 to 60 for m A from 140 GeV to 900 GeV,respectively [106]. Similar searches have been also performed by ATLAS [107]. In Type-IIand Type-Y 2HDMs, the CMS experiment has also searched the bottom-quark associatedproduction of H or A which decays into the b ¯ b final state [108], and has obtained the upperbounds on tan β ; i.e., tan β &
16 (28) is excluded at m A = 100 GeV (350 GeV). ATLAShas reported the H ± searches via the τ +jets final state [109, 110]. In the Type-II 2HDM,for m H ± . m t , wide parameter regions have been excluded for 100 GeV . m H ± .
140 GeVwith tan β &
1. In addition, for m H ± &
180 GeV, the parameter regions of tan β &
50 at m H ± = 200 GeV and tan β &
65 at m H ± = 300 GeV have been excluded, respectively. Thesearches for H ± in the cs final-state have been performed by ATLAS [111], and the upperlimit on the branching ratio of t → bH ± decay is obtained assuming the 100% branchingratio of H ± → cs . For sin( β − α ) <
1, searches for H → W + W − , hh and A → Zh signalsgive constraints on the 2HDMs with Type-I and Type-II Yukawa interactions [47, 48]. E. Prospect for the searches at the LHC
In the previous subsections, we have seen the current bounds on the additional Higgsbosons via the flavour and collider experiments. However, until the time when ILC experi-ments start, the LHC will be further operated with higher energies and luminosity. There-fore, it is important to summarize future prospects for additional Higgs boson searches inthe 2HDMs at the LHC with the highest energy of 14 TeV.According to Refs. [49, 51], we evaluate the expected discovery potential of additionalHiggs bosons at the LHC with the integrated luminosity of L = 300 fb − and 3000 fb − by using the signal and background analysis for various channels [112], which are combinedwith the production cross sections and the decay branching ratios for each type of Yukawainteraction. Processes available for the searches are • H/A (+ b ¯ b ) inclusive and associated production followed by the H/A → τ + τ − de-cay [113]. • H/A + b ¯ b associated production followed by the H/A → b ¯ b decay [113–115].15 gb → tH ± production followed by the H ± → tb decay [116, 117]. • q ¯ q → HA → τ process [118, 119].For the production cross sections, we utilize the Born-level cross sections convoluted withthe CTEQ6L parton distribution functions [120]. The scales of the strong coupling constantand parton distribution functions are chosen to the values used in Ref. [11, 121]. For the lastprocess, we follow the analysis in Ref. [118] by re-evaluating the signal events for the differentmass, and combine the statistical significance of all channels for the decay patterns of 4 τ .The similar analysis on the HH ± and AH ± production processes resulting the signatureof 3 τ plus large missing transverse momentum gives comparable exclusion curves to the 4 τ analysis [118].In Fig. 4, we show the contour plots of the expected exclusion regions [2 σ confidencelevel (CL)] in the ( m φ , tan β ) plane, where m φ represents common masses of additionalHiggs bosons, at the LHC √ s = 14 TeV with the integrated luminosity of 300 fb − (thicksolid lines) and 3000 fb − (thin dashed lines). The value of M is also taken to the sameas m φ . From the top-left panel to the bottom-right panel, the results for Type-I, Type-II, Type-X and Type-Y are shown separately. According to the analysis in Ref. [112], wechange the reference values of the expected numbers of signal and background events atcertain values of the mass of additional Higgs bosons [51]. This makes sharp artificial edgesof the curves in Fig. 4.For Type-I, H/A production followed by their τ + τ − decay can be probed for the param-eter regions of tan β . m H,A ≤
350 GeV, where the inclusive production cross sectionis enhanced by the relatively large top Yukawa coupling and also the τ + τ − branching ratiois sizable. The tH ± production followed by the H ± → tb decay can be used to search H ± in relatively smaller tan β regions. The mass reach for the discovery of H ± can be up to800 GeV for tan β . − (3000 fb − ).For Type-II, the inclusive and the bottom-quark-associated production processes of H/A followed by the τ + τ − decay or the bb decay can be used to search H and A in relatively largetan β regions. They can also be used in relatively small tan β regions with m H,A .
350 GeV.Because of the difficulty of separating the signal from the SM background, the lighter massregions (200 ∼
300 GeV) may not be excluded with the 300 fb − data as loopholes areseen in the figure. H ± can be probed by the tH ± production followed by the H ± → tb [GeV] φ m100 200 300 400 500 600 700 800 β t a n Type-I ττ → H / A t b → ± , H ± t H → gb - L = f b - L = f b [GeV] φ m100 200 300 400 500 600 700 800 β t a n Type-II ττ → H / A t b → ± , H ± t H → gb b b → H / A - L = f b - L = f b [GeV] φ m100 200 300 400 500 600 700 800 β t a n Type-X ττ→
H/A τ → HA t b → ± , H ± t H → gb - L = f b - L = f b [GeV] φ m100 200 300 400 500 600 700 800 β t a n Type-Y ττ → H / A t b → ± , H ± t H → gb b b → H / A - L = f b - L = f b FIG. 4: Expected exclusion regions (2 σ CL) in the plane of tan β and the mass scale m φ of theadditional Higgs bosons at the LHC. Curves are evaluated by using the signal and backgroundanalysis given in Ref. [112] for each process, where the signal events are rescaled to the predictionin each case [49, 51], except the 4 τ process for which we follow the analysis in Ref. [118]. Thicksolid lines are the expected exclusion contours by L = 300 fb − data, and thin dashed lines arefor L = 3000 fb − data. For Type-II, the regions indicated by circles may not be excluded by H/A → τ + τ − search by using the 300 fb − data due to the large SM background. decay for m H ± &
180 GeV with relatively small and large tan β regions. The regions of m H ± &
350 GeV (500 GeV) can be excluded with the 300 fb − (3000 fb − ) data.For Type-X, H and A can be searched via the inclusive production and HA pair pro-duction processes by using their dominant decays into τ + τ − . The inclusive productioncan exclude the regions of tan β .
10 with m H,A .
350 GeV, and the regions of up to17
H,A ≃
500 GeV (700 GeV) with tan β &
10 can be excluded by using the pair productionwith the 300 fb − (3000 fb − ) data. The search for H ± is the similar to that for Type-I.For Type-Y, the inclusive production of H and A followed by their τ + τ − decays can besearched for the regions of tan β . m H,A ≤
350 GeV, where the inclusive produc-tion cross section is enhanced due to a large top Yukawa coupling constant and the τ + τ − branching ratio is sizable. The bottom-quark associated production of H and A followedby H/A → b ¯ b decays can be searched for the regions of tan β &
30 up to m H,A ≃
800 GeV.This process is also relevant for Type-II, but the constraint is weaker than
H/A → τ + τ − mode. The search of H ± is similar to that for Type-II.If all the curves are combined by assuming that all the masses of additional Higgs bosonsare the same, the mass below 400 GeV (350 GeV) can be excluded by the 300 fb − data, andthe mass below 550 GeV (400 GeV) can be excluded by the 3000 fb − data for any value oftan β for Type-II and Type-Y (Type-X). Only for Type-I, a universal mass bound cannot begiven, namely the regions with tan β & − (3000 fb − )data. However, in the general 2HDM, the mass spectrum of additional Higgs boson is lessconstrained, and has more degrees of freedom. Therefore, we can still find allowed parameterregions where we keep m H to be relatively light but taking m A ( ≃ m H ± ) rather heavy for therho parameter constraint [83]. Thus, the overlaying of these exclusion curves for differentadditional Higgs bosons may be applied to only the case with m H = m A = m H ± .At the LHC, the discovery reach of H ± is extensive in all types of Yukawa interaction,because of the large cross section of the gb → tH ± process followed by the H ± → tb decay. If H ± is discovered at the LHC, the determination of its mass would follow immedi-ately [112, 122]. Hence, the next progress would be the determination of the type of Yukawainteraction. At the LHC, although some methods have been proposed by using the observ-ables related to the top-quark spin [122, 123], we could not completely distinguish the typesof Yukawa interaction, because the Type-I and Type-X, or Type-II and Type-Y posses thesame coupling structure for the tbH ± interaction. Therefore, we have to look at the otherprocess like the neutral Higgs boson production processes. However, as we have seen inFig. 4, there can be no complementary process for the neutral Higgs boson searches in someparameter regions; e.g., m H,A &
350 GeV with relatively small tan β depending on the typeof the Yukawa interaction. On the other hand, at the ILC, as long as m H,A .
500 GeV, theneutral Higgs bosons can be produced and investigated almost independent of tan β . There-18ore, it would be an important task of the ILC to search for the additional Higgs bosonswith the mass of 350-500 GeV, and to determine the models and parameters, even after theLHC.We also note that the above results are obtained in the SM-like limit, sin( β − α ) = 1.However, in the general 2HDM, sin( β − α ) is also a free parameter. It is known that adeviation from the SM-like limit induces decay modes of H → W + W − , ZZ , hh as wellas A → Zh [10, 124–127]. Especially, for Type-I with a large value of tan β , branchingratios of these decay modes can be dominant even with a small deviation from the SM-like limit [27, 125]. For example, if sin ( β − α ) = 0 .
96, the decay mode of H → W + W − is dominant in tan β & ∼ . β for the other types [27]. Therefore, searches for additionalHiggs bosons in these decay modes can give significant constraints on the deviation of sin( β − α ) from the SM-like limit [47, 48], which is independent of coupling constants of hV V . IV. PROSPECT FOR THE SEARCHES FOR THE ADDITIONAL HIGGSBOSONS AT THE ILC
In this section, we perform the detailed studies on the production cross section of ad-ditional Higgs bosons at the ILC and their collider signatures via the subsequent decaysof them. We compare the results among the four types of the Yukawa interaction in thegeneral 2HDM, and see how the type of Yukawa interaction can be discriminated and howthe parameters can be determined from the collider signatures or kinematical distributionsin the observed processes.
A. Cross Sections
The main production mechanisms of additional Higgs bosons are e + e − → HA and e + e − → H + H − , where a pair of additional Higgs bosons is produced via gauge interactions.These processes open when the collision energy is above the sum of the masses of the twoscalars. For energies below the threshold, the single production processes, e + e − → H ( A ) f ¯ f and e + e − → H ± f ¯ f ′ are the leading contributions [56]. The single production processes areenhanced when the relevant Yukawa coupling constants of φf ¯ f ( ′ ) are large. The cross sec-19ions of these processes have been studied extensively [8, 56, 57, 62], mainly for the MSSMor for the Type-II 2HDM.Here, we give numerical results in the general 2HDMs but with softly-broken discretesymmetry with all types of Yukawa interaction. We consider the processes of e + e − → τ + τ − H, (10a) e + e − → b ¯ bH, (10b) e + e − → t ¯ tH, (10c) e + e − → τ − νH + , (10d) e + e − → ¯ tbH + . (10e)The cross sections of the processes where H is replaced by A in Eqs. (10a-10c), and those ofthe charge conjugated processes of the processes in Eqs. (10d, 10e) are not explicitly shown.For energies above the threshold of the pair production, √ s > m H + m A , the contributionfrom e + e − → HA can be significant in the processes in Eqs. (10a-10c). Similarly for √ s > m H ± , the contribution from e + e − → H + H − can be significant in the processes in Eqs. (10d,10e). Below the threshold, the processes including diagrams of e + e − → f ¯ f ∗ and e + e − → f ∗ ¯ f dominate.In Fig. 5, the cross sections of e + e − → τ + τ − H are shown as a function of m H for varioussituations. The cross sections for √ s = 250 GeV, 500 GeV and 1 TeV are shown in thefigures of the first, second and third rows, while figures in the first to the fourth columnsshow the results in Type-I to Type-Y, respectively. In the first row, curves are the crosssections of e + e − → τ + τ − H for tan β = 1, 3, 10, 30 and 100 at the ILC √ s = 250 GeV. Thecross sections rapidly fall down at the mass threshold √ s = m H + m A . As stated above,for energies above the threshold of the HA production, √ s > m H + m A , the cross sectionscome mainly from the pair production e + e − → HA followed by the A → τ + τ − decay. Sincethe HA production cross section does not depend on the type of Yukawa interaction northe value of tan β , the tan β dependence in the process of e + e − → HA with H/A → τ + τ − only comes from the decay branching ratios of H and A , which are shown in Fig. 1. Belowthe threshold, √ s < m H + m A , only the single production processes contribute which aresensitive to tan β , depending on the type of Yukawa interaction. For Type-II and Type-Xwith large tan β , the cross sections of e + e − → τ + τ − H via the single production mechanismare enhanced by the Yukawa couplings of Hτ τ /Aτ τ , while for Type-I and Type-Y the cross20 m H [GeV] -3 -2 -1 σ ττ H [f b ] tan β =1tan β =3tan β =10tan β =30tan β =100
80 100 120 140 160 180 200m H [GeV]10 -3 -2 -1 Type-I Type-II/s = 250 GeV /s = 250 GeV
80 100 120 140 160 180 200m H [GeV]10 -3 -2 -1 σ ττ H [f b ]
80 100 120 140 160 180 200m H [GeV]10 -3 -2 -1 Type-X Type-Y/s = 250 GeV /s = 250 GeV
150 200 250 300 350m H [GeV]10 -3 -2 -1 σ ττ H [f b ] tan β =1tan β =3tan β =10tan β =30tan β =100
150 200 250 300 350m H [GeV]10 -3 -2 -1 Type-I Type-II/s = 500 GeV /s = 500 GeV
150 200 250 300 350m H [GeV]10 -3 -2 -1 σ ττ H [f b ]
150 200 250 300 350m H [GeV]10 -3 -2 -1 Type-X Type-Y/s = 500 GeV /s = 500 GeV
300 400 500 600 m H [GeV] -4 -3 -2 -1 σ ττ H [f b ] tan β =1tan β =3tan β =10tan β =30tan β =100
300 400 500 600m H [GeV]10 -4 -3 -2 -1 Type-I Type-II/s = 1 TeV /s = 1 TeV
300 400 500 600m H [GeV]10 -4 -3 -2 -1 σ ττ H [f b ]
300 400 500 600m H [GeV]10 -4 -3 -2 -1 Type-X Type-Y/s = 1 TeV /s = 1 TeV
FIG. 5: Cross sections of e + e − → τ + τ − H process as a function of m H = m A at the ILC √ s =250 GeV, 500 GeV and 1 TeV. Several values of tan β are examined with fixing sin( β − α ) = 1. sections are negligible. Figures in the second and third rows show the similar results but for √ s = 500 GeV and 1 TeV, respectively. For the latter case, the decay of H/A → t ¯ t opensfor m H &
350 GeV, and then the decay into τ + τ − is suppressed to a large extent.In Fig. 6, the cross sections of e + e − → b ¯ bH are shown as a function of m H for varioussituations in the same manner as Fig. 5. In the first row, cross sections of e + e − → b ¯ bH are plotted for tan β = 1, 3, 10, 30 and 100 at the ILC √ s = 250 GeV. For this process,Type-II and Type-Y have enhanced single production cross section for large tan β , dueto the enhanced Yukawa couplings of H and A to b quarks. Figures in the second andthird rows show the similar results but for √ s = 500 GeV and 1 TeV, respectively. For21 H [GeV]10 -3 -2 -1 σ bb H [f b ] tan β =1tan β =3tan β =10tan β =30tan β =100
80 100 120 140 160 180 200m H [GeV]10 -3 -2 -1 Type-I Type-II/s = 250 GeV /s = 250 GeV
80 100 120 140 160 180 200 m H [GeV] -3 -2 -1 σ bb H [f b ]
80 100 120 140 160 180 200 m H [GeV] -3 -2 -1 Type-X Type-Y/s = 250 GeV /s = 250 GeV
150 200 250 300 350 m H [GeV] -3 -2 -1 σ bb H [f b ] tan β =1tan β =3tan β =10tan β =30tan β =100
150 200 250 300 350m H [GeV]10 -3 -2 -1 Type-I Type-II/s = 500 GeV /s = 500 GeV
150 200 250 300 350M H [GeV]10 -3 -2 -1 σ bb H [f b ]
150 200 250 300 350m H [GeV]10 -3 -2 -1 Type-X Type-Y/s = 500 GeV /s = 500 GeV
300 400 500 600m H [GeV]10 -4 -3 -2 -1 σ bb H [f b ] tan β =1tan β =3tan β =10tan β =30tan β =100
300 400 500 600m H [GeV]10 -4 -3 -2 -1 Type-I Type-II/s = 1 TeV /s = 1 TeV
300 400 500 600m H [GeV]10 -4 -3 -2 -1 σ bb H [f b ]
300 400 500 600m H [GeV]10 -4 -3 -2 -1 Type-X Type-Y/s = 1 TeV /s = 1 TeV
FIG. 6: Cross sections of e + e − → b ¯ bH process at the ILC √ s = 250 GeV, 500 GeV and 1 TeV,evaluated as the same manner as Fig. 5. m H,A &
350 GeV, the cross sections decrease because the decay of
H/A → t ¯ t becomesdominant.In Fig. 7, cross sections of e + e − → τ − νH + are shown as a function of m H ± for varioussituations in the same manner as Fig. 5. In the first row, cross sections of e + e − → τ − νH + are plotted for tan β = 1, 3, 10, 30 and 100 at the ILC √ s = 250 GeV. For energies below thethreshold, √ s < m H ± , the single production process can be sizable for Type-II and Type-X, due to the enhanced τ νH ± couplings by tan β . In the second row, for √ s = 500 GeV,there is a sharp edge at around m H ± = 180 GeV for Type-I, Type-Y and also for Type-IIand Type-X with small tan β , because the decay of H ± → tb opens. In the third row, for22 m H + [GeV] -3 -2 -1 σ τ − ν H + [f b ] tan β =1tan β =3tan β =10tan β =30tan β =100
80 100 120 140 160 180 200 m H + [GeV] -3 -2 -1 Type-I Type-II/s = 250 GeV /s = 250 GeV
80 100 120 140 160 180 200 m H + [GeV] -3 -2 -1 σ τ − ν H + [f b ]
80 100 120 140 160 180 200m H + [GeV]10 -3 -2 -1 Type-X Type-Y/s = 250 GeV /s = 250 GeV
150 200 250 300 m H + [GeV] -3 -2 -1 σ τ − ν H + [f b ] tan β =1tan β =3tan β =10tan β =30tan β=100
150 200 250 300 m H + [GeV] -3 -2 -1 Type-I Type-II/s = 500 GeV /s = 500 GeV
150 200 250 300 m H + [GeV] -3 -2 -1 σ τ − ν H + [f b ]
150 200 250 300m H + [GeV]10 -3 -2 -1 Type-X Type-Y/s = 500 GeV /s = 500 GeV
300 400 500 600 m H + [GeV] -4 -3 -2 -1 σ τ − ν H + [f b ] tan β =1tan β =3tan β =10tan β =30tan β =100
300 400 500 600 m H + [GeV] -4 -3 -2 -1 Type-I Type-II/s = 1 TeV /s = 1 TeV
300 400 500 600 m H + [GeV] -4 -3 -2 -1 σ τ − ν H + [f b ]
300 400 500 600m H + [GeV]10 -4 -3 -2 -1 Type-X Type-Y/s = 1 TeV /s = 1 TeV
FIG. 7: Cross sections of e + e − → τ − νH + process as a function of m H ± at the ILC √ s = 250 GeV,500 GeV and 1 TeV. Several values of tan β are examined with fixing sin( β − α ) = 1. √ s = 1 TeV, only for Type-II and Type-X the cross sections increase with tan β .In Fig. 8, cross sections of e + e − → t ¯ tH are shown as a function of m H for varioussituations for √ s = 1 TeV. Figures from left to right show the results in Type-I to Type-Y,respectively. The cross sections rise sharply at the top quark pair threshold, m H ≃
350 GeV.Below the top pair threshold, m A < m t , e + e − → HA → Ht ¯ t process is kinematicallysuppressed, but only the single production mechanism through the Yukawa interaction tothe top quark can contribute. For 350 GeV ≤ m H ≤
500 GeV, as long as the decay branchingratio of A → t ¯ t is sizable, the cross section is enhanced via the HA production process. For23
00 300 400 500 600 m H [GeV] -2 -1 σ tt H [f b ] tan β =1tan β =3tan β =10tan β =30tan β =100
200 300 400 500 600m H [GeV]10 -2 -1 Type-I Type-II/s=1 TeV /s=1 TeV
200 300 400 500 600 m H [GeV] -2 -1 σ tt H [f b ]
200 300 400 500 600m H [GeV]10 -2 -1 Type-X Type-Y/s = 1 TeV /s = 1 TeV
FIG. 8: Cross sections of e + e − → t ¯ tH process at the ILC √ s = 1 TeV. m H ≥
500 GeV, HA pair production is kinematically forbidden, and the single productionbecomes the leading mechanism. In all types, the Yukawa couplings of H and A to the topquark are suppressed for large tan β .In Fig. 9, cross sections of e + e − → ¯ tbH + are plotted as a function of m H ± . In the firstrow, the results for √ s = 500 GeV are shown. For m t + m b ≤ m H ± ≤
250 GeV, the pairproduction e + e − → H + H − followed by the decay of H − → ¯ tb gives the largest contribution.The cross section of e + e − → H + H − does not depend on tan β , but only the branching ratioof the decay H ± → tb does. For m H ± ≤ m t − m b and √ s ≥ m t , there is a productionmechanism of ¯ tbH + from e + e − → t ¯ t followed by the decay of t → bH + . The partial decaywidth of t → bH ± can be found e.g. in Ref. [27]. For m H ± ≥
250 GeV, only the singleproduction mechanism contributes for Type-II and Type-Y, which is enhanced by cot β viathe top quark Yukawa coupling or by tan β via the bottom quark Yukawa coupling. In thesecond row, the same results but for √ s = 1 TeV are shown. B. Contour Plot
Now we discuss the collider signatures of additional Higgs boson production at the ILC.Both the pair and single production processes of additional Higgs bosons tend to resultin four-particle final-states (including neutrinos) when the decays of the additional Higgsbosons are taken into account. To evaluate the net production rates of them, the productioncross sections and the decay branching ratios of additional Higgs bosons have to be takeninto account consistently. We calculate the cross sections of various four-particle final-states24
50 200 250 300m H + [GeV]10 -3 -2 -1 σ t b H + [f b ] tan β =1tan β =3tan β =10tan β =30tan β =100
150 200 250 300m H + [GeV]10 -3 -2 -1 Type-I Type-II/s = 500 GeV /s = 500 GeV
150 200 250 300m H + [GeV]10 -3 -2 -1 σ t b H + [f b ]
150 200 250 300m H + [GeV]10 -3 -2 -1 Type-X Type-Y/s = 500 GeV /s = 500 GeV
200 300 400 500 600m H + [GeV]10 -2 -1 σ t b H + [f b ] tan β =1tan β =3tan β =10tan β =30tan β =100
200 300 400 500 600m H + [GeV]10 -2 -1 Type-I Type-II/s = 1 TeV /s = 1 TeV
200 300 400 500 600m H + [GeV]10 -2 -1 σ t b H + [f b ]
200 300 400 500 600m H + [GeV]10 -2 -1 Type-X Type-Y/s = 1 TeV /s = 1 TeV
FIG. 9: Cross sections of e + e − → t ¯ bH − process at the ILC √ s = 500 GeV and 1 TeV. for given masses of additional Higgs bosons and tan β with setting sin( β − α ) = 1, and drawcontour curves where the cross sections are 0 . Madgraph [128], by taking into account both the pair and single production ofadditional Higgs bosons followed by their subsequent decays. We note that in Ref. [62], thecross sections without including the decay of additional Higgs bosons have been studied inthe MSSM, while in our paper we study the cross sections of the four-particle final-states byincluding the decays of additional Higgs bosons in the 2HDMs with four types of Yukawa25nteraction.In Fig. 10, contour plots of the cross sections of four-particle production processes through H and/or A are shown in the ( m H/A , tan β ) plane. The results for √ s = 250 GeV, 500 GeVand 1 TeV are shown in the figures in the first, second and third columns, while figuresin the first to the fourth rows show the results in Type-I to Type-Y, respectively. Werestrict ourselves to consider the degenerated mass case, m H = m A . Discussions on thenon-degenerated mass cases as well as the case where sin( β − α ) is slightly less than unityare given later.The figures in the first row are for Type-I. The signatures come dominantly from HA pairproduction followed by their subsequent decays. For m H/A .
350 GeV, the t ¯ t decay modedoes not open, and then the decays are mostly into b ¯ b , τ + τ − and gg as shown in Fig. 1 andFig. 2. Thus, 4 b , 2 b τ and 4 τ signatures as well as the signatures with gluons 2 b g , 2 τ g and 4 g are expected to be observed. For m H/A &
350 GeV where the t ¯ t decay mode opens,only the 4 t signature is expected to be significant. Because the HA pair production crosssection sharply fall down at the threshold, the signatures are not expected above the massthreshold for each collider energy. Only in the small tan β regions (tan β < t signature is extended to above the mass threshold, because of the large top Yukawacoupling enhancing the single production cross section associated with top-quark pair, t ¯ tH and t ¯ tA .The figures in the second row are for Type-II. Since the bottom and tau Yukawa in-teraction are enhanced by tan β , 4 b , 2 b τ and 4 τ signatures are expected to be seen evenbelow the mass threshold through the single production processes. For m H/A .
350 GeV,in small tan β regions, gg decay mode can be dominant, therefore 4 g and 2 b g signatureswhich tend to be four-jet events would be significant. Although the SM backgrounds obscuresuch signatures, the invariant-mass distributions of dijets may help to distinguish them. For m H/A &
350 GeV, 4 t and 2 t b signatures are expected for tan β .
10 because of the largetop Yukawa coupling constants.The figures in the third row are for Type-X. The 4 τ signature can be expected for largetan β regions even below the pair production mass threshold. The detailed studies for the4 τ signature can be found in Ref. [129]. For relatively small tan β regions, 4 b or 4 t signatureis expected depending on the masses of H and A . In between, 2 b τ or 2 t τ signature canhave sizable rates. 26 [GeV] H,A m100 110 120 130 140 150 β t an -1 Type-I=250 GeVs =0.1 fb σ Contour plot of g τ b , b g ,4g τ τ [GeV] H,A m150 200 250 300 350 β t an -1 Type-I=500 GeVs =0.1 fb σ Contour plot of g , g τ b , b g τ τ [GeV] H,A m350 400 450 500 550 600 β t an -1 Type-I=1 TeVs =0.1 fb σ Contour plot of [GeV] H,A m100 110 120 130 140 150 β t an -1 Type-II=250 GeVs =0.1 fb σ Contour plot of τ τ [GeV] H,A m150 200 250 300 350 β t an -1 Type-II=500 GeVs =0.1 fb σ Contour plot of τ τ [GeV] H,A m350 400 450 500 550 600 β t an -1 Type-II=1 TeVs =0.1 fb σ Contour plot of τ τ [GeV] H,A m100 110 120 130 140 150 β t an -1 Type-X=250 GeVs =0.1 fb σ Contour plot of τ τ [GeV] H,A m150 200 250 300 350 β t an -1 Type-X=500 GeVs =0.1 fb σ Contour plot of τ τ [GeV] H,A m350 400 450 500 550 600 β t an -1 Type-X=1 TeVs =0.1 fb σ Contour plot of τ τ [GeV] H,A m100 110 120 130 140 150 β t an -1 Type-Y=250 GeVs =0.1 fb σ Contour plot of τ τ τ [GeV] H,A m150 200 250 300 350 β t an -1 Type-Y=500 GeVs =0.1 fb σ Contour plot of τ τ τ [GeV] H,A m350 400 450 500 550 600 β t an -1 Type-Y=1 TeVs =0.1 fb σ Contour plot of
FIG. 10: Contour plots of the four-particle production cross sections through the H and/or A production processes at the ILC with √ s = 250 GeV, 500 GeV and 1 TeV in the ( m H,A , tan β )plane. Contour of σ = 0 . b signature is dominant for largetan β regions, while for the small tan β regions with m H/A .
350 GeV, various signaturesincluding τ + τ − , gg and c ¯ c can be expected because all these decay branching ratios arecomparably sizable. To avoid too much overlapping, we ignore the curves for the signaturesincluding c ¯ c , which are however comparable with those of the 4 g , 2 g τ and 4 τ signatures.For m H/A &
350 GeV, the 4 t and 2 t b signatures are expected to appear for tan β . H ± areshown in the ( m H ± , tan β ) plane in the same manner as Fig. 10.The figures in the first row are for Type-I. For m H ± .
180 GeV below the H ± → tb threshold, H ± → τ ν and cs are the dominant decay modes, as illustrated in Fig. 1.Therefore, the τ ντ ν , τ νcs and cscs signatures are expected to appear as long as √ s ≥ m H ± .For m H ± .
180 GeV and √ s ≥
350 GeV, H ± can be produced through the decay of topquarks in the top quark pair production process. In the middle column at √ s = 500 GeV,the signature of tbτ ν comes from this contribution followed by the decay of H ± → τ ν . For m H ± &
180 GeV, the dominant decay mode quickly switches into tb . Therefore the tbtb signature becomes the largest.The figures in the second row are for Type-II. For the mass below the tb threshold, H + H − pair production tends to be the τ ντ ν signature in the large tan β regions, and the τ νcs , cscs signatures in the medium to small tan β regions. In addition, because of the large Yukawacoupling of top quarks, single tbH ± production followed by H ± → τ ν and cs decays givessizable tbτ ν and tbcs signatures, respectively. On the other hand, for the mass above the tb threshold, the tbtb signature is the dominant signature for any values of tan β because of theenhanced tbH ± Yukawa interaction. The tbτ ν and τ ντ ν signatures are still visible in largetan β regions, because of the large H ± → τ ν branching ratio.The figures in the third row are for Type-X. As is the case for Type-II, for the massbelow the tb threshold, the τ ντ ν signature in the large tan β regions, and the τ νcs , cscs signatures in the medium to small tan β regions are expected. Through the tbH ± productionwhich is sizable only in the small and medium tan β regions, the tbτ ν and tbcs signatures areexpected to be seen. Above the tb threshold, the signatures are tbtb for small and mediumtan β and τ ντ ν for large tan β . In between, tbτ ν can also be large.The figures in the fourth row are for Type-Y. In this case, for the mass below the tb threshold the dominant decay mode of H ± is cb for large tan β . Therefore, cbcb signature28 [GeV] ± H m100 110 120 130 140 150 β t an -1 Type-I=250 GeVs =0.1 fb σ Contour plot of ντντ cs ντ cscs [GeV] ± H m150 200 250 300 350 β t an -1 =0.1 fb σ Contour plot of
Type-I=500 GeVstbtb ν τ t b ντντ cs ντ cscs [GeV] ± H m350 400 450 500 550 600 β t an -1 Type-I=1 TeVs =0.1 fb σ Contour plot of tbtb [GeV] ± H m100 110 120 130 140 150 β t an -1 Type-II=250 GeVs =0.1 fb σ Contour plot of cscscs ντ ντντ [GeV] ± H m150 200 250 300 350 β t an -1 =0.1 fb σ Contour plot of
Type-II=500 GeVstbtb ντ tb ντντ cs ντ cscs tbcs [GeV] ± H m350 400 450 500 550 600 β t an -1 Type-II=1 TeVs =0.1 fb σ Contour plot of tbtb ντ tb ντντ [GeV] ± H m100 110 120 130 140 150 β t an -1 Type-X=250 GeVs =0.1 fb σ Contour plot of cscscs ντ ντντ [GeV] ± H m150 200 250 300 350 β t an -1 =0.1 fb σ Contour plot of
Type-X=500 GeVstbtb ντ tb ντντ cs ντ cscs tbcs [GeV] ± H m350 400 450 500 550 600 β t an -1 Type-X=1 TeVs =0.1 fb σ Contour plot of tbtb ντ tb ντντ [GeV] ± H m100 110 120 130 140 150 β t an -1 Type-Y=250 GeVs =0.1 fb σ Contour plot of cbcbcb ντ ντντ [GeV] ± H m150 200 250 300 350 β t an -1 =0.1 fb σ Contour plot of
Type-Y=500 GeVstbtb ντ tb ντντ cb ντ cbcbtbcb [GeV] ± H m350 400 450 500 550 600 β t an -1 Type-Y=1 TeVs =0.1 fb σ Contour plot of tbtb
FIG. 11: Contour plots of the four-particle production cross sections through the H ± productionprocess at the ILC √ s = 250 GeV, 500 GeV and 1 TeV in the ( m H ± , tan β ) plane. Contour of σ = 0 .
29s expected for large tan β regions. In small tan β regions, τ ν and cs would be the domi-nant. Therefore, τ ντ ν , τ νcs and cscs signatures are expected to be significant. To avoidoverlapped plotting, we ignore to plot the contours which include the cs mode. Above the tb threshold, since the tb decay mode is dominant for any values of tan β , the tbtb signaturewould be the only visible mode. C. SM background processes
Here, we discuss the SM background processes and their cross sections. In Table III,total cross sections without kinematical cuts are calculated by
Madgraph [128]. The cross-section for the signatures including gluons is neglected, because the partonic calculation ismeaningless unless an infrared safe observable is defined, such as the cross-section for jetsproduction. In general, for the four-particle production processes, the SM background crosssections are larger for √ s = 250 GeV, but decrease with the collision energy. The typicalorders of cross sections are of the order of 1 fb to 10 fb for the Z/γ mediated processes,and of the order of 10 to 100 fb for the processes which are also mediated by W ± . Forthe four-quark production processes, gluon exchange diagrams also contribute. Some of thebackground cross sections are larger than the expected signal cross sections. In order toreduce the background events, efficient kinematical cuts are required. Since the additionalHiggs bosons are expected to have narrow decay widths and since there are many backgroundcontributions from the decays of Z bosons, a cut on the invariant mass of the decay particlesis useful.The cross section of the 4 t production is very small in the SM, see Table III. Therefore,a clean signature can be expected to be detected in this mode. However, because of thedecays of top quarks, more complicated background processes can be involved, and theevent reconstruction is not straightforward. Detailed studies on the signal and backgroundprocesses for tbtb production can be found in Ref. [57], and the signal-to-background analysisfor the 4 τ production can be found in Ref. [129] with the reconstruction method of the massesof additional Higgs bosons. 30 ignature √ s = 250 GeV √ s = 500 GeV √ s = 1 TeV4 b
18 7.2 2.94 τ τ b
28 10 3.52 τ ν
210 94.4 35 . tbτ ν . × − t b − t τ − t − − . × − TABLE III: Background cross sections in unit of fb for the four-particle processes at the ILC. Totalcross sections without kinematical cuts are calculated by
Madgraph [128].
V. DISCUSSIONS
In this section, we further discuss future prospects for the additional Higgs boson searchesand the parameter determinations at the LHC and the ILC, and their complementarity inthe general framework of the 2HDM with the softly-broken discrete symmetry. As we haveseen in Sec. III E, ability of the LHC for discovery or exclusion of additional Higgs bosonsis high. However, there are still wide regions in the parameter space where the LHC cannotdiscover all the additional Higgs bosons, or where the type of Yukawa interaction cannot bedetermined even if they are discovered. In the previous section, we have seen that at theILC, as long as the masses of these bosons are within a kinematical reach, various signaturesare expected to be used for the discrimination of the type of Yukawa interaction. Here, asan example, we give some concrete scenarios to show the complementarity of direct searchesfor the additional Higgs bosons in the 2HDMs at the LHC and the ILC.We take six sets of ( m φ , tan β ) as benchmark scenarios, where m φ represents the commonmass of H , A and H ± , namely m φ = 220 GeV and 400 GeV, and tan β = 2, 7 and 20, forall types of Yukawa interaction. We fix the value of sin( β − α ) to be unity. In Table IV,we summarize the expected signatures of H/A and H ± to be observed at the LHC with300 fb − , 3000 fb − and at the ILC with √ s = 500 GeV, according to our estimation in thelast sections for the benchmark scenarios with m φ = 220 GeV. In Table V, the expected31 m φ , tan β ) Type-I Type-II Type-X Type-Y H, A H ± H, A H ± H, A H ± H, A H ± LHC300 − − τ τ , bb tb τ − bb tb (220 GeV, 20) LHC3000 − − τ τ , bb tb τ − bb tb ILC500 4 b, b τ, g ,2 b g, τ g tbtb b, b τ ,4 τ tbtb, tbτ ν , τ ντ ν τ tbτ ν , τ ντ ν b tbtb, tbcb LHC300 − − τ τ tb τ − − tb (220 GeV, 7) LHC3000 − tb τ τ tb τ τ, τ − − tb ILC500 4 b, b τ, g ,2 b g, τ g tbtb b, b τ ,4 τ tbtb, tbτ ν , τ ντ ν b τ, τ tbtb, tbτ ν , τ ντ ν b tbtb, tbcb LHC300 − tb τ τ tb τ τ, τ tb − tb (220 GeV, 2) LHC3000 τ τ tb τ τ tb τ τ, τ tb − tb ILC500 4 b, b τ, g ,2 b g, τ g tbtb b, b τ ,4 τ, b g tbtb , tbτ ν b, b τ ,4 τ tbtb , tbτ ν b, b τ ,2 b g tbtb TABLE IV: Expected signatures to be observed at the LHC and ILC for the benchmark scenar-ios with m φ = 220 GeV. Observable final-states are listed as the signatures of additional Higgsbosons, H , A and H ± . LHC300, LHC3000, ILC500 represent the LHC run of 300 fb − , 3000 fb − luminosity, ILC run of 500 GeV, respectively. signatures of H/A and H ± are summarized at the LHC with 300 fb − , 3000 fb − and at theILC with √ s = 1 TeV for the benchmark scenarios with m φ = 400 GeV. We note again thatat the ILC signatures are assumed to be detected by a criterion whether the cross section isgreater than 0.1 fb. We present the results for each type of Yukawa interaction, Type-I toType-Y from the left column to right column, respectively.In Table IV, the expected signals are summarized for each benchmark scenario with a rela-tively light mass, m φ = 220 GeV. Let us look at the scenario of ( m φ , tan β ) = (220 GeV , − and 3000 fb − , no signature is predicted for Type-I, while differentsignatures are predicted for Type-II, Type-X and Type-Y. Therefore those three types canbe discriminated at the LHC. On the other hand, at the ILC with √ s = 500 GeV, all thefour types of the Yukawa interaction including Type-I predict signatures which are differentfrom each other. Therefore, at the ILC, complete discrimination of the type of Yukawainteraction can be performed. This benchmark scenario demonstrates necessity of the ILC32500 GeV) to completely separate the all four types of Yukawa interaction.Next, we turn to the second scenario, ( m φ , tan β ) = (220 GeV , − , Type-I cannot be observed, while Type-II, Type-X and Type-Y are expected to beobserved with different signatures. At the LHC with 3000 fb − , the signature of Type-I canalso be observed with the same final state as Type-Y. Type-I and Type-Y can be basicallyseparated, because for Type-Y the signals can be observed already with 300 fb − while forType-I that can be observed only with 3000 fb − . Therefore, at the LHC with 3000 fb − , thecomplete discrimination can be achieved. At the ILC, the four types of Yukawa interactioncan also be separated by a more variety of the signatures for both channels with the neutraland charged Higgs bosons.Finally, we discuss the scenario of ( m φ , tan β ) = (220 GeV , − ,signals for all the four types of Yukawa interaction can be observed. However, the signaturesof Type-I and Type-Y are identical, so that the two types cannot be discriminated. Withthe 3000 fb − data at the LHC, the difference between the Type-I and Type-Y emerges inthe H/A signature. Therefore the two types can be discriminated at this stage. Again, atthe ILC, the four types can also be separated with a more variety of the signatures for bothchannels with the neutral and charged Higgs bosons.In Table V, the expected signals are summarized for each benchmark scenario with arelatively heavy mass, m φ = 400 GeV. First, we discuss the scenario of ( m φ , tan β ) =(400 GeV , − , while for Type-I no signature can be observed, τ τ and tb signatures can be observed for Type-II, and a 4 τ ( tb ) signature can be observedfor Type-X (Type-Y). Thus, at least the three types (Type-II, Type-X and Type-Y) canbe discovered and discriminated by checking the pattern of the observed signatures at theLHC with 300 fb − . With the 3000 fb − data at the LHC, the situation is not improved,but for Type-X, one additional signature τ τ would be observed. Therefore, at the LHCwith 3000 fb − all types of Yukawa interaction except Type-I can be separated basically.At the ILC with √ s = 1 TeV, signatures in various modes can be observed for both theneutral and charged Higgs bosons depending on the type of Yukawa interaction. Signaturesfor Type-I are expected in 4 t and tbtb modes. Since the signatures are all different amongthe four types of Yukawa interaction, all the types can also be discriminated at the ILC.This benchmark scenario demonstrates necessity of the ILC (1 TeV) to completely separatethe all four types of Yukawa interaction. 33 m φ , tan β ) Type-I Type-II Type-X Type-Y H, A H ± H, A H ± H, A H ± H, A H ± LHC300 − − τ τ tb τ − − tb (400 GeV, 20) LHC3000 − − τ τ tb τ τ, τ − − tb ILC1TeV 4 t tbtb b, b τ ,2 t b tbtb, tbτ ν , τ ντ ν τ, t τ tbτ ν , τ ντ ν b, t b tbtb LHC300 − − − − − − − − (400 GeV, 7) LHC3000 − − τ τ tb τ τ, τ − − tb ILC1TeV 4 t tbtb b, b τ ,2 t b, t tbtb, tbτ ν t, t τ tbtb , tbτ ν b, t b, t tbtb LHC300 − tb − tb − tb − tb (400 GeV, 2) LHC3000 − tb − tb − tb − tb ILC1TeV 4 t tbtb t, t b tbtb t tbtb t, t b tbtb TABLE V: The similar table as Table IV, but for m φ = 400 GeV. ILC1TeV represents the ILCrun of 1 TeV. Next, we discuss the scenario of ( m φ , tan β ) = (400 GeV , − ,no signature is discovered for all types of Yukawa interaction at all. At the LHC 3000 fb − ,the signals of Type-II, Type-X and Type-Y can be discovered with different signatures,while Type-I cannot be seen. At the ILC, all types are observed with different signatures.Therefore, the complete discrimination or exclusion needs the ILC in this scenario too.Finally, we discuss the scenario of ( m φ , tan β ) = (400 GeV , − ,only the H ± → tb signature is predicted for all types of Yukawa interaction. The situationdoes not change even with 3000 fb − . Therefore, the signals for all types of Yukawa inter-action can be discovered, but the type cannot be discriminated at the LHC. At the ILC, tbtb signature is observed for the pair and single production of H ± for all types of Yukawainteraction. For the neutral Higgs bosons, for Type-I and Type-X only the 4 t signature isobserved, while 4 t and 2 t b signatures are observed for Type-II and Type-Y. Therefore, atthe ILC, we are able to discriminate the type of Yukawa interaction as either Type-I orType-X, or either Type-II or Type-Y. However, precision measurements of the number ofsignal events at the ILC could be used for further discrimination.To summarize, the additional Higgs bosons can be discovered for all the benchmark34cenarios by the combination of searches at the LHC and ILC. Furthermore, the type ofYukawa interaction can be separated by looking at the pattern of the observed signatures.For the scenarios with ( m φ , tan β ) = (220 GeV, 20), (400 GeV, 20) and (400 GeV, 7), theILC is necessary for the complete separation of the type of Yukawa interaction. For thescenario with ( m φ , tan β ) = (400 GeV, 2), the LHC cannot discriminate the type of Yukawainteraction, while at the ILC two groups of the type, Type-I or Type-X and Type-II or Type-Y can be separated by looking at the difference of signatures, and further discriminationmay be possible by precision measurements of the number of signal events. Therefore,the LHC and the ILC are complementary for additional Higgs boson searches and also fordiscrimination the type of Yukawa interaction in the 2HDM. Furthermore, the determinationof tan β can be performed through the observation of the branching ratio or the total decaywidths of additional Higgs bosons [130–133].We briefly give a comment for the cases with m φ <
200 GeV and m φ >
500 GeV. For m H,A <
200 GeV, the current LHC data already have excluded regions of tan β & H/A → τ + τ − search [106] and tan β &
15 for Type-Y in the
H/A → b ¯ b search [108]. Furthermore, wide parameter regions of tan β with m H ± <
140 GeV havebeen excluded for Type-II via the H ± → τ ν search in the decay of top quarks [110]. ForType-I and Type-X, the H ± → τ ν signals may be searched in the pair production process pp → H + H − . For Type-Y with large tan β , H ± → cb decays can be searched in the topquark decay t → bH ± . For m φ >
500 GeV, the LHC searches can be extended into relativelysmall and/or large tan β regions. On the other hand, the ILC with √ s ≤ β values.In our discussion above, the SM-like limit, sin( β − α ) = 1, has been commonly assumedin the benchmark scenarios in Tables IV and V. We here discuss the case in which theSM-like limit is slightly relaxed, i.e., sin ( β − α ) = 0 . ( β − α ) = 1 and Fig. 3 in Ref. [27] for sin ( β − α ) = 0 .
96. In particular, forsin ( β − α ) = 0 . H can decay into weak gauge bosons, whose decay branching ratios caneasily be substantially large. Consequently, our discussion above can be changed. We mayexpect that the discovery signal of H can be clearer in this case because of the decay intoweak gauge boson pairs. The analysis for such a case will be separately performed in the35uture. We also note that if sin ( β − α ) is slightly less than unity, the coupling constants ofthe SM-like Higgs boson with the SM particles differ from the SM predictions. The patternof the deviations depends on the type of Yukawa interactions. Therefore, by detecting thepattern by precision measurements of the coupling constants of the SM-like Higgs boson atthe ILC, we can fingerprint the specific type of Yukawa interaction in the 2HDM [49, 51].Notice that fingerprinting of the model by using the measurement of SM-like Higgs bosoncoupling constants is powerful as long as sin ( β − α ) is less than unity by more than 1%. Ifthe deviation is much smaller, we cannot fingerprint the 2HDM by looking at the SM-likeHiggs boson coupling constants. In such a case, namely the SM-like limit, only the directsearches for the additional Higgs bosons at the LHC and the ILC are useful.Finally, we mention the case where our assumption of the common mass for additionalHiggs bosons is relaxed. In general, masses of additional Higgs bosons are given by m φ = M + ˜ λ i v (cid:20) O (cid:18) v M (cid:19)(cid:21) , (11)where ˜ λ i represent specific combinations of λ coupling constants. Our assumption is basi-cally reasonable when additional Higgs bosons are heavy enough, because their masses arebasically given by the unique scale M , the scale of soft breaking of the discrete symmetry.When their masses are around the electroweak scale, they can be varied by the contributionof the term ˜ λ i v without contradicting the constraints from the rho parameter and also fromperturbative unitarity etc. In this case, the signals from neutral Higgs boson processes andthose from charged Higgs boson processes are independent. However, even in such a case,we can repeat the discussion of discrimination of the type of Yukawa interaction by usingTables IV and V, although the situation becomes more complicated. VI. CONCLUSIONS
In this paper, we have studied the direct searches of additional Higgs bosons in the general2HDM with the Z symmetry imposed to avoid FCNCs. We have considered the possiblefour types of Yukawa interaction which are determined by generic charge assignment of the Z parity to the SM fermions.We have discussed the prospect of direct searches for the additional Higgs bosons at theLHC, and stressed that the exclusion potential is extensive but not conclusive. It means that36y taking into account the wide parameter space of the general 2HDM, there are possibilitiesthat the LHC can discover only part of the additional Higgs bosons or that even the LHCcannot discover any additional Higgs boson but the ILC can discover.We have studied the collider signatures of additional Higgs boson production by evaluat-ing the production cross sections as well as the decay branching ratios of additional Higgsbosons at the ILC for the all types of Yukawa interaction. We find that various signaturescan be expected depending on the type of Yukawa interaction, the masses of additional Higgsbosons and tan β . Thus, as long as the additional Higgs bosons are kinematically accessi-ble, their production can be detected at the ILC, and further details around the additionalHiggs bosons, i.e. the type of Yukawa interaction and the model parameters can be studied.Therefore, the searches at the ILC would be a useful complementary survey even after theLHC results. Acknowledgments
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