Non-standard Higgs couplings in single Higgs boson production at the LHC and future linear collider
aa r X i v : . [ h e p - ph ] O c t Non-standard Higgs couplings in single Higgs boson productionat the LHC and future linear collider
G. Akkaya Sel¸cin
1, 2, ∗ and ˙I. S¸ahin † Department of Physics, Faculty of Sciences,Ankara University, 06100 Tandogan, Ankara, Turkey Department of Physics, Faculty of Arts and Sciences,Bitlis Eren University, 13000 Bitlis, Turkey
Abstract
We investigate the potential of single Higgs boson photoproduction at the LHC and at eγ modeof future linear e − e + collider to probe non-standard HZγ and
Hγγ couplings. We consider thesemi-elastic production process pp → pγp → pHqX at the LHC where q represents the quarks and X represents the remnants of one of the initial protons. We also study the single Higgs productionthrough γe → He in the eγ collision at the future linear collider. We perform a model-independentanalysis and obtain the sensitivity bounds on the non-standard Higgs couplings for both colliders.We compare the capability of single Higgs photoproduction process at these two colliders to probenon-standard Higgs couplings. ∗ [email protected] † [email protected] . INTRODUCTION The Higgs boson predicted by Standard Model (SM) of particle physics was discovered byATLAS and CMS Collaborations at Large Hadron Collider (LHC) [1, 2]. After its discovery,intense experimental studies have been carried out to reveal its properties and couplings toother SM particles [3–5]. Precise determination of the Higgs couplings will either confirmthe gauge structure of SM, or provide signal of new physics beyond SM. In this paper weinvestigate the non-standard couplings of the Higgs to gauge bosons Z and γ through semi-elastic production of the Higgs boson at the LHC and single production at eγ mode of futurelinear e − e + collider. These production processes are electroweak in nature and provide cleanchannels with respect to deep inelastic proton-proton collision at the LHC. Therefore, theycan be used to perform precision measurements of the Higgs couplings.Non-standard Higgs couplings to gauge bosons have been constrained through severalHiggs decay processes at the LHC [3, 5–9]. There are also experimental constraints obtainedfrom electroweak precision measurements at LEP and Tevatron [6–8, 10, 11]. One way toexamine non-standard Higgs couplings is to employ the effective lagrangian method. Inthis method any contribution coming from new physics beyond SM is described by higherdimensional operators. These higher dimensional operators are added to the SM lagrangianand inversely proportional to some powers of Λ which is called the scale of new physics. Inthis paper we analyze non-standard HZγ and
Hγγ couplings in a model independent wayby means of the effective lagrangian formalism of Refs.[6–8, 12–16]. There are five C and P even dimension-6 operators which modify the Higgs boson couplings to Z and γ bosons[6–8, 12–16]: O W W = Φ † ˆ W µν ˆ W µν Φ O BB = Φ † ˆ B µν ˆ B µν Φ O BW = Φ † ˆ B µν ˆ W µν Φ (1) O W = ( D µ Φ) † ˆ W µν ( D ν Φ) O B = ( D µ Φ) † ˆ B µν ( D ν Φ)where Φ is the scalar doublet, D µ is the covariant derivative, ˆ W µν = i g ( ~σ · ~W µν ) and ˆ B µν = i g ′ B µν . Here g and g ′ are the SU (2) L and U (1) Y gauge couplings. The field strength tensors W iµν and B µν belong to SU (2) L and U (1) Y gauge groups respectively. The SM lagrangian2s then modified by the following dimension-6 effective lagrangian: L eff = X n f n Λ O n (2)where f n denote the non-standard couplings and Λ is the scale of new physics. After sym-metry breaking, the effective lagrangian in Eq.(2) give rise to the following HZγ and
Hγγ interactions [6]: L eff = g Hγγ HA µν A µν + g (1) HZγ A µν Z µ ∂ υ H + g (2) HZγ HA µν Z µν . (3)where V µν = ∂ µ V ν − ∂ ν V µ with V = A and Z field. The non-standard couplings g Hγγ , g (1) HZγ and g (2) HZγ are related to the couplings f n appearing in the effective lagrangian (2) beforesymmetry breaking as g Hγγ = − (cid:18) gM W Λ (cid:19) s ( f BB + f W W − f BW )2 (4) g (1) HZγ = (cid:18) gM W Λ (cid:19) s ( f W − f B )2 c (5) g (2) HZγ = (cid:18) gM W Λ (cid:19) s [2 s f BB − c f W W + ( c − s ) f BW ]2 c (6)where s = sin θ W , c = cos θ W , θ W is the Weinberg angle and M W is the mass of the W boson. In the calculations presented in this paper the energy scale of new physics is takento be Λ = 1TeV. The effective operators in (1) contribute also HZZ and
HW W couplings.Since the processes that we consider in this paper do not contain these couplings, we do notpresent the contributions coming from effective lagrangian (2) to
HZZ and
HW W . Theeffective operator O BW modifies also the W − B mixing. It is stringently restricted bythe electroweak precision measurements [14, 15, 17]. Therefore, during the analysis we set f BW = 0 and consider the contributions from four couplings f W W , f BB , f W and f B . For thepurpose of simplicity, we will consider the following six different new physics scenarios: Scenario I : f B = f W = 0 , f BB = f W W
Scenario II : f B = − f W , f BB = f W W = 0
Scenario III : f B = f W = 0 , f BB = − f W W
Scenario IV : f B = f W = 0 , f W W = tan θ W f BB Scenario V : f W = f W W = 0
Scenario V I : f B = f BB = 03n scenarios I − IV we impose three constraints and therefore we have one free parameter.On the other hand, in scenarios V and VI two constraints are imposed and two parametersremain free. Here we should note the following important point: In this paper, we employthe set of bosonic operators in the Hagiwara-Ishihara-Szalapski-Zeppenfeld (HISZ) basis[15]. The operators O W and O B do not appear in the Warsaw basis [18]. They could betranslated into other operators, including O W W , O BW , O BB and other dimension-6 operators.Therefore all five operators given in Eq.(1) are not independent. In scenarios I, III and IV weignore the contributions from O W and O B operators which are absent in the Warsaw basis.In scenarios II, V and VI we consider the contributions from these operators. However, weconsider at most two of the couplings as independent parameters. Therefore, our scenariosdo not overwhelm the degrees of freedom in the effective lagrangian. HZγ and
Hγγ interactions do not appear in the SM at the tree-level. However, theyreceive contributions at one-loop level. One-loop contributions to these interactions can beapproximated to the following effective lagrangian [19, 20]: L eff = g ( SM ) Hγγ HA µν A µν + g ( SM ) HZγ HA µν Z µν (7)where, g ( SM ) Hγγ = α πν and g ( SM ) HZγ = α πν sin θ W (5 . − . i ). Here, α is the fine structureconstant and ν is the electroweak vacuum expectation value.The semi-elastic single Higgs boson production at the LHC has been studied in Refs.[21,22]. However, in these studies only non-standard HZγ coupling has been taken into account.In our analysis of semi-elastic Higgs production we consider both non-standard
HZγ and
Hγγ couplings. We do not assume that
HZγ and
Hγγ couplings are independent from eachother. We obtain bounds on f n couplings of the operators (1) before symmetry breakingwhich contribute to both HZγ and
Hγγ . The non-standard Higgs couplings to gaugebosons have also been investigated at future linear e − e + collider and its eγ and γγ modes[23–41]. The non-standard HZγ and
Hγγ interactions were investigated through singleproduction process γe → He in Refs.[24, 26]. In Ref.[26] the authors analyzed CP -oddinteractions which are different from C and P even effective interactions that we consider.In Ref.[24] the authors considered a similar (but not equivalent) effective lagrangian for thenon-standard Higgs interactions. The difference is that the effective interaction proportionalto g (1) HZγ (see Eq. (3)) was omitted in Ref.[24]. Another difference between our work and thatof [24] is that Ref.[24] was published long before the discovery of Higgs boson. Therefore,4he authors couldn’t perform a detailed statistical analysis considering the exact value of theHiggs mass. In our analysis of single Higgs production γe → He , we perform a χ test andestimate sensitivity of the linear collider based eγ collider to non-standard Higgs couplingsfor various integrated luminosity values. II. SINGLE HIGGS PRODUCTION THROUGH PHOTON-PROTON COLLI-SION AT THE LHC
The LHC is designed as a high-energy proton-proton collider and the majority of thestudies at the LHC focused on deep inelastic scattering (DIS) processes where both of thecolliding protons dissociate into partons. On the other hand, it was firstly shown experi-mentally at the Fermilab Tevatron that complementary to hadron-hadron collisions, hadroncolliders can also be studied as a photon-photon and photon-hadron collider [42–44]. Recentexperimental studies by CMS and ATLAS Collaborations have verified the existence of suchphoton-induced reactions at the LHC [45–49]. It was also shown that these photon-inducedprocesses at the LHC have a significant potential to probe new physics beyond the SM[47–49]. The photon-photon collisions take place when both of the incoming protons emitquasireal photons. These emitted quasireal photons can interact mutually and the photon-photon collision occurs as a subprocess of the proton-proton collision. Similarly when oneof the incoming proton emits a quasireal photon then a photon-proton collision can occur.These photon-proton collision processes are sometimes called semi-elastic processes due totheir hybrid nature. Here, the essential point is the distinguishability of such photon-photonand photon-proton processes from those in which initial photons are described by propaga-tors. According to equivalent photon approximation (EPA) [50–52], emitted photons havea very low virtuality and up to a high degree of approximation they are accepted to bereal. Furthermore, since the virtuality of the quasireal photons is very low, photon emittingprotons do not generally dissociate into partons but they remain intact [53, 54]. After elasticphoton emission protons generally deviate slightly from the direction of beam pipe and es-cape from the central detectors without interacting. This causes a missing energy signatureknown as the forward large-rapidity gap, in the corresponding forward region of the centraldetector [53–55]. Moreover, the LHC is planned to be equipped with very forward detectorswhich can detect intact protons escaping from the central detectors [56–58]. The installa-5ion of very forward detectors should allow to separate more easily the photon-photon andphoton-proton processes, where one or both of the incident protons remain intact [59–62].The range of the forward detectors are characterized by the ξ parameter which representsthe momentum fraction loss of the proton. If ~p represents the initial proton’s momentumand ~p ′ represents forward proton’s momentum after scattering then, ξ parameter is given bythe formula ξ ≡ ( | ~p | − | ~p ′ | ) / | ~p | . In this paper, we will consider a forward detector acceptancerange of 0 . < ξ < .
15 [56–58].There is an increasing interest in probing new physics through photon-photon and photon-proton collision at the LHC. Phenomenological studies on this subject have been growingrapidly in recent years and cover a wide spectrum of new physics scenarios. It is impossibleto cite all of the references here, but some representative ones might be Refs. [21, 22, 63–89] The semi-elastic single Higgs boson production can be studied through the process pp → pγp → pHqX at the LHC. This process consists of the subprocesses γq → Hq where q represents the quarks. We ignore the top quark distribution and consider 10 independentsubprocess for q = u, d, s, c, b, ¯ u, ¯ d, ¯ s, ¯ c, ¯ b . In the presence of non-standard HZγ and
Hγγ interactions the subprocess γq → Hq is described by the Feynman diagrams given in Fig.1.The semi-elastic process pp → pγp → pHqX consists of two different types of protonscattering; elastic photon emission takes place from one of the initial protons, whereas otherinitial proton interact strongly with the emitted photon and undergoes an inelastic scattering(Fig.2). Therefore, the cross section for the semi-elastic process pp → pγp → pHqX isobtained by integrating the cross sections for the subprocesses over the photon and quarkdistributions: σ ( pp → pγp → pHqX ) = X q Z x max x min dx Z dx (cid:18) dN γ dx (cid:19) (cid:18) dN q dx (cid:19) ˆ σ γq → Hq (ˆ s ) . (8)Here, dN γ dx and dN q dx are the equivalent photon and quark distribution functions, respectively.The quark distribution functions can be evaluated numerically by using the code MSTW2008[90]. In Eq.(8) the integral variable x is the energy fraction that represents the ratio betweenthe emitted equivalent photon and initial proton energy. The other variable x representsthe momentum fraction of the proton’s momentum carried by the quark. The equivalentphoton distribution dN γ dx is given by an analytical expression. We do not give its explicit form.Its explicit form can be found in the literature (for example see [50] or [66]). At the LHCenergies where the energy of the incoming proton is much greater than its mass ( E >> m p ),6he ξ parameter is approximated as ξ ≈ E − E ′ E = E γ E = x . Here, E and E ′ are the energyof the initial and final (scattered) proton and E γ is the energy of the equivalent photon.Therefore, the upper and lower limits of the dx integration are determined by the limits ofthe forward detector acceptance and we take x min = ξ min = 0 . x max = ξ max = 0 . pp → pγp → pHqX as a functionof non-standard Higgs couplings for scenarios I-IV. In addition to new physics contributionswe have also considered the effective lagrangian (7) that contains SM one-loop contributions.For a concrete result we have obtained 95% confidence level (C.L.) bounds on non-standardcouplings using the simple χ criterion. The χ function is given by χ = (cid:18) N NS − N SM N SM δ (cid:19) (9)where, N NS is the number of events containing both new physics and SM contributions, N SM is the number of events expected in the SM and δ = √ N SM is the statistical error. Thenumber of events has been calculated considering the H → b ¯ b decay of the Higgs boson asthe signal. Hence, we assume that N NS ( SM ) = E × S × L int × σ NS ( SM ) × BR where, E isthe b-tagging efficiency, S is the survival probability factor, L int is the integrated luminosityand BR is the branching ratio for H → b ¯ b . σ SM represents the SM cross section and σ NS represents the cross section containing both new physics and SM contributions. We havetaken into account a b-tagging efficiency of E = 0 .
6, survival probability factor of S = 0 . BR = 0 .
6. The survival probability factor of 0 . .
6. According to experimental works aconstant average value of 0.6 for b-tagging efficiency is reasonable [93]. We have also placeda pseudorapidity cut of | η | < . pp → pγp → pb ¯ bqX . There are totally 18 background subprocessof the type γq → k, b, ¯ b where, q = u, d, s, c, b, ¯ u, ¯ d, ¯ s, ¯ c, ¯ b and k = u, d, s, c, b, t, ¯ u, ¯ d, ¯ s, ¯ c, ¯ b, ¯ t quarks. The background contributions have been calculated by using CalcHEP 3.6.20 [94].The determination of an on-shell Higgs boson with mass approximately 125 GeV requiresan invariant mass measurement of the final-state b ¯ b pairs. If we impose a cut and demand7hat the invariant mass of the b ¯ b pairs is in the interval 120 GeV < M b ¯ b <
130 GeV then thebackground cross section is reduced considerably and gives σ background = 0 .
05 pb. Since thebackground contribution cannot be discerned from Higgs production cross section, duringstatistical analysis we add the background contribution to the SM cross section and assumethat σ NS ( SM ) = σ ( pp → pγp → pHqX ) NS ( SM ) + BR × σ background . Here, the factor BR isused to cancel out the branching ratio in N NS ( SM ) .In Table I we present 95% C.L. bounds on non-standard f ww , f w and f bb couplings forscenarios I-IV. The bounds are obtained via one-parameter χ analysis and we considerthe integrated luminosity values of L int = 10 , , , , f b − . For scenarios V and VIwe have two free coupling parameters and therefore the bounds are obtained using two-parameter χ analysis. In Fig.7 and Fig.8, we plot 95% C.L. bounds on two dimensionalparameter spaces f B − f BB and f W − f W W for scenarios V and VI respectively.The CMS collaboration at the LHC has determined direct experimental bounds on non-standard Higgs-gauge boson couplings by studying Higgs boson decay to ZZ , Zγ , γγ and W W [5]. The following 95% C.L. bounds have been given on the ratio of
HZγ and
Hγγ couplings to
HZZ : − . < a Zγ a < .
044 and − . < a γγ a < .
054 [5]. Here, a couplingsare defined by a = 2 g HZZ /m Z , a Zγ = g (2) HZγ and a γγ = 2 g Hγγ , where g Hγγ and g (2) HZγ are the couplings in the effective lagrangian in Eq.(3) and g HZZ is the coupling of theHiggs to two Z boson, i.e., g HZZ HZ µ Z µ . If we assume that g HZZ coupling is equal to itsSM value ( g HZZ = m Z /ν ; ν = 246 GeV) then we can extract the experimental boundson the couplings g (2) HZγ and g Hγγ . The scenario III and scenario IV isolate the couplings g (2) HZγ and g Hγγ respectively. Therefore, these scenarios give us the opportunity to compareour bounds with the experimental bounds of Ref.[5]. In scenario III, the experimentalbound on a Zγ a can be converted to the bounds on f couplings as − < f BB < . − . < f W W <
13. Similarly, in scenario IV the experimental bound on a γγ a can beconverted as − . < f BB < .
83 and − . < f W W < .
35. When we compare these boundswith the corresponding bounds given in Table I, we see that our bounds for the integratedluminosity of 200 f b − are approximately a factor of 3 better than the experimental boundsin the case of scenario III and approximately a factor of 2.5 better in the case of scenarioIV. 8 II. SINGLE HIGGS PRODUCTION THROUGH PHOTON-ELECTRON COLLI-SION AT THE FUTURE LINEAR COLLIDER
The non-standard
Hγγ and
HZγ couplings can be investigated with a high precision atfuture linear e − e + collider and its eγ and γγ modes. We consider the single Higgs productionin the eγ collision via the subprocess γe → He . The tree-level Feynman diagrams for γe → He is very similar to that of Fig.1, but we should replace quarks with electrons (orpositrons), q → e . The initial photon beam can be obtained through equivalent photonemission from incoming electron or positron beam, similar to equivalent photon emissionfrom protons at the LHC. However in the case of future linear collider, we have a moreappealing option. A real photon beam can be obtained through Compton backscattering oflaser light off the linear electron beam. Contrary to EPA, Compton backscattering providesan increasing photon spectrum as a function of the energy fraction y = E γ /E e , where E γ and E e represent the energy of the backscattered photon and initial electron beam, respectively[95, 96]. The backscattered photon spectrum is given by [95, 96] f γ/e ( y ) = 1 g ( ζ ) [1 − y + 11 − y − yζ (1 − y ) + 4 y ζ (1 − y ) ] (10)where, g ( ζ ) = (1 − ζ − ζ ) ln ( ζ + 1) + 12 + 8 ζ − ζ + 1) . (11)Here, ζ = 4 E e E /M e and E is the energy of initial laser photon before Compton backscat-tering. The ζ parameter can be taken to be ζ = 4 . y max = 0 .
83. The process γe → He takes part as a subprocess in themain e − e + collision. Therefore, the total cross section observed in the e − e + collision canbe obtained by integrating the cross section for γe → He over the backscattered photonspectrum: σ e − e + = Z . y min f γ/e ( y ) σ γe → He dy (12)where, y min = m H s and s is the Mandelstam parameter of the e − e + collision. The behavior ofthe total cross section as a function of non-standard Higgs couplings is shown in Figs.9-12 forscenarios I-IV. In these figures, the center of mass energy of the main e − e + collider is taken9o be √ s = 0 . γe → He can be safely neglected. Therefore the SM contributions to γe → He are coming from the loop-level. We consider SM one-loop contributions described by theeffective lagrangian (7).Using the simple χ criterion we estimate sensitivity of the linear collider-based eγ collider to non-standard Higgs couplings for the integrated luminosity values of L int =10 , , , , f b − and √ s = 0 . H → b ¯ b decay channel of the Higgsboson and assume that b ¯ b final state with invariant mass in the interval 120 GeV < M b ¯ b <
130 GeV is identified as the signal. In the χ function the number of events is given by N NS ( SM ) = E × L int × σ NS ( SM ) × BR . We take into account a b-tagging efficiency of E = 0 . BR = 0 .
6. We assume that the central detectors have a pseudorapid-ity coverage of | η | < .
5. Therefore, we place a cut of | η | < . γe → b ¯ be . It is described by 8 tree-level Feynmandiagrams and gives a total cross section of σ background = 4 . × − pb after imposing thecuts 120 GeV < M b ¯ b <
130 GeV and | η | < .
5. Similar to the statistical analysis performedin the previous section, we assume that the background contribution cannot be discernedfrom Higgs production. Therefore, during statistical analysis we add the background contri-bution to the SM cross section and assume that σ NS ( SM ) = ( σ e − e + ) NS ( SM ) + BR × σ background where ( σ e − e + ) NS ( SM ) is the integrated cross section defined in (12). The subscript N S rep-resents the cross section containing both new physics and SM contributions and subscript SM represents the SM cross section alone. The 95% C.L. bounds on non-standard f ww , f w and f bb couplings are given in Table II for scenarios I-IV. We observe from Tables I and IIthat the bounds of Table II are more restrictive with respect to the corresponding bounds ofTable I. The average improvement factors are approximately 6 for scenario I, 3 for scenariosII and III and 8 . f B − f BB and f W − f W W . The 95% C.L. restricted regionsin these parameter spaces are given in Fig.13 and Fig.14. When we compare the bounds ofFigs.13 and 14 with the similar LHC bounds given in Figs.7 and 8, we see that the boundsof the linear collider are approximately a factor of 5 better than the corresponding boundsof the LHC.We can also compare the bounds of future linear collider with the current experimentalbounds. The CMS bounds on f BB and f W W couplings have been given in the last paragraph10f the previous section. When we compare these experimental bounds with the correspondingbounds given in Table II, we see that our bounds for the integrated luminosity of 200 f b − are approximately a factor of 8 better than the experimental bounds in the case of scenarioIII and approximately a factor of 20 better in the case of scenario IV. IV. CONCLUSIONS
One of the prominent motivations of the future e − e + collider is that it provides cleanexperimental environment which allows to make high precision measurements [97, 98]. Indeep inelastic hadron-hadron collisions, initial hadron beams dissociate into partons andcreate myriad of jets which cause uncertainties and make it difficult to discern the signalsthat we want to observe. Moreover, in hadron colliders there are systematic uncertaintiesarising from the proton structure functions, from unknown higherorder perturbative QCDcorrections, and from nonperturbative QCD effects [98]. Lepton colliders do not suffer fromthese kind of uncertainties, and the level of precision is expected to be enhanced consider-ably compared to hadron colliders. On the other hand, ultraperipheral collisions in a hadroncollider provides a unique opportunity to search for the physics beyond the SM in a ratherclean environment with respect to deep inelastic hadron-hadron collisions. Exclusive andsemielastic processes are examples of the reactions in an ultraperipheral collision. In semi-elastic Higgs production pp → pγp → pHqX only one of the incoming proton dissociatesinto partons but the other proton remains intact. The absence of the remnants of one of theproton beam, allows to discern the signal more easily. Furthermore, tagging the intact scat-tered protons in the forward detectors allows us to reconstruct quasireal photons’ momenta.The knowledge obtained in this way is very useful in reconstructing the kinematics of thereaction. The semi-elastic Higgs production is electroweak in nature and free from back-grounds containing strong interaction. Due to above reasons, the uncertainties associatedwith the Higgs detection for pp → pγp → pHqX are expected to be reduced considerablycompared to deep inelastic processes at the LHC. Therefore, the comparison of the resultsobtained in semi-elastic production at the LHC and future e − e + collider is important andcontributes to the physics program of the future e − e + collider.In the paper, we consider similar subprocesses γq → Hq and γe → He at the LHCand at future e − e + collider. We investigate the potential of these two colliders to probe11on-standard Higgs couplings. We show that eγ mode of the linear collider with center ofmass energy of √ s = 0 . HZγ and
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IG. 1: Tree-level Feynman diagrams for the subprocess γq → Hq γ FIG. 2: The illustration of the process pp → pγp → pHqX .TABLE I: 95% C.L. bounds on f ww , f w and f bb for various integrated LHC luminosities and scenar-ios. Bounds are given in units of TeV − . The center of mass energy of the proton-proton systemis taken to be √ s = 14TeV.Luminosity ( Scenario -I) f ww ( Scenario -II) f w ( Scenario -III) f bb ( Scenario -IV) f bb f b − (-6.3,7.9) (-19.8,15.4) (-9.9,7.7) (-13.2,15.6)30 f b − (-4.6,6.2) (-15.6,11.3) (-7.8,5.6) (-9.8,12.2)50 f b − (-3.9,5.6) (-14.1,9.7) (-7.0,4.9) (-8.5,10.8)100 f b − (-3.2,4.8) (-12.2,7.9) (-6.1,3.9) (-7.0,9.3)200 f b − (-2.6,4.2) (-10.7,6.4) (-5.3,3.2) (-5.7,8.1) σ ( pb ) f WW =f BB (TeV -2 )Scenario If W =f B ,f WW =f BB FIG. 3: The total cross section of the process pp → pγp → pHqX as a function of non-standardHiggs coupling for scenario I. The center of mass energy of the proton-proton system is taken tobe √ s = 14TeV. σ ( pb ) f W (TeV -2 )Scenario IIf B =-f W ,f WW =f BB =0 FIG. 4: The same as Fig.3 but for scenario II. σ ( pb ) f BB (TeV -2 )Scenario IIIf B =f W ,f WW =-f BB FIG. 5: The same as Fig.3 but for scenario III. σ ( pb ) f BB (TeV -2 )Scenario IVf B =f W ,f WW =tan ( θ W )f BB FIG. 6: The same as Fig.3 but for scenario IV. f BB ( T e V - ) f B (TeV -2 )10fb -1 -1 -1 -1 -1 FIG. 7: The areas restricted by the lines show 95% C.L. sensitivity bounds on the parameter space f B − f BB for various integrated LHC luminosities stated on the figure. The scenario V is taken intoconsideration. The center of mass energy of the proton-proton system is taken to be √ s = 14TeV.TABLE II: 95% C.L. bounds on f ww , f w and f bb for various integrated linear collider luminositiesand scenarios. Bounds are given in units of T eV − . The main e − e + collider energy is taken to be √ s = 0 . Scenario -I) f ww ( Scenario -II) f w ( Scenario -III) f bb ( Scenario -IV) f bb f b − (-0.8,1.3) (-7.6,3.4) (-3.8,1.7) (-1.3,2.0)30 f b − (-0.5,1.1) (-6.5,2.3) (-3.2,1.2) (-1.0,1.6)50 f b − (-0.5,1.0) (-6.1,1.9) (-3.0,1.0) (-0.8,1.5)100 f b − (-0.4,0.9) (-5.6,1.5) (-2.8,0.7) (-0.6,1.3)200 f b − (-0.3,0.9) (-5.3,1.1) (-2.6,0.6) (-0.5,1.2) f WW ( T e V - ) f W (TeV -2 )10fb -1 -1 -1 -1 -1 FIG. 8: The areas restricted by the lines show 95% C.L. sensitivity bounds on the parameterspace f W − f W W for various integrated LHC luminosities stated on the figure. The scenario VI istaken into consideration. The center of mass energy of the proton-proton system is taken to be √ s = 14TeV. σ ( pb ) f WW =f BB (TeV -2 )Scenario If W =f B ,f WW =f BB E cm =0.5TeV FIG. 9: The total cross section observed in the e − e + collision as a function of non-standard Higgscoupling for scenario I. The main e − e + collider energy is taken to be √ s = 0 . σ ( pb ) f W (TeV -2 )Scenario IIf B =-f W ,f WW =f BB =0E cm =0.5 TeV FIG. 10: The same as Fig.9 but for scenario II. σ ( pb ) f BB (TeV -2 )Scenario IIIf B =f W ,f WW =-f BB E cm =0.5 TeV FIG. 11: The same as Fig.9 but for scenario III. σ ( pb ) f BB (TeV -2 )Scenario IVf B =f W ,f WW =tan ( θ W )f BB E cm =0.5 TeV FIG. 12: The same as Fig.9 but for scenario IV. f BB ( T e V - ) f B (TeV -2 )10fb -1 -1 -1 -1 -1 FIG. 13: The areas restricted by the lines show 95% C.L. sensitivity bounds on the parameterspace f B − f BB for various integrated linear collider luminosities stated on the figure. The scenarioV is taken into consideration. The main e − e + collider energy is taken to be √ s = 0 . f WW ( T e V - ) f W (TeV -2 )10fb -1 -1 -1 -1 -1 FIG. 14: The areas restricted by the lines show 95% C.L. sensitivity bounds on the parameter space f W − f W W for various integrated linear collider luminosities stated on the figure. The scenario VIis taken into consideration. The main e − e + collider energy is taken to be √ s = 0 .5TeV.