Observability of 2HDM neutral Higgs bosons with different masses at future e+e− linear colliders

Available online at www.sciencedirect.com

ScienceDirect Nuclear Physics B 951 (2020) 114903 www.elsevier.com/locate/nuclphysb

Observability of 2HDM neutral Higgs bosons with different masses at future e+ e− linear colliders Majid Hashemi a,∗ , Gholamhossein Haghighat b a Physics Department, College of Sciences, Shiraz University, Shiraz, 71946-84795, Iran b School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531,

Tehran, Iran Received 13 February 2019; received in revised form 25 November 2019; accepted 14 December 2019 Available online 19 December 2019 Editor: Tommy Ohlsson

Abstract Assuming two-Higgs-doublet model (2HDM) at SM-like scenario as the theoretical framework, this study addresses the question of possibility of observation of neutral CP-even and CP-odd Higgs bosons H and A at a linear collider operating at center-of-mass energies of 500 and 1000 GeV. The signal production channel is e− e+ → AH → ZH H with subsequent leptonic decay of the Z boson and Higgs bosons decays into b quark pairs. To be specific, Type-I 2HDM is used to allow dominant Higgs boson decay to b-quark pairs below the top quark pair production threshold. The ISR+beamstrahlung effects are taken into account and the detector simulation is carried out based on the SiD detector at ILC. Several benchmark scenarios are defined and studied. Results indicate that in all scenarios, both Higgs bosons are observable with signals exceeding 5σ and with possibility of mass measurement. These results are beyond the current reach of LHC at 30 fb−1 and extend the exclusion contour of LHC in (mH , mA ) plane. © 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3 .

* Corresponding author.

E-mail addresses: [email protected] (M. Hashemi), [email protected] (G. Haghighat). https://doi.org/10.1016/j.nuclphysb.2019.114903 0550-3213/© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3 .

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0. Introduction The Standard Model of elementary particles has been verified by many experiments and played an important role in understanding a wide range of phenomena. Existence of the Higgs boson [1–6] as one of the most important predictions of the Standard Model was verified experimentally [7,8] and triggered an increasing interest in studying SM extensions. Extensions of the SM are also motivated by supersymmetry [9], axion models [10], the SM inability to explain the universe baryon asymmetry [11], etc. The simplest possible scalar structure with one SU (2) Higgs doublet is used in the SM. Such an assumption leads to the prediction of a single Higgs boson. However, employing two SU (2) Higgs doublets leads to a kind of model which has emerged as an important candidate for SM extension. As one of the simplest extensions of the Standard Model, two-Higgs-doublet model (2HDM) [12–19] predicts five Higgs bosons, four of which are assumed to be, yet undiscovered, Higgs bosons and the fifth one (the lightest one) is assumed to be the same as the observed SM Higgs boson. Two out of the four undiscovered Higgs bosons are neutral scalar and pseudoscalar Higgs bosons H and A, and the others are charged Higgs bosons H ± . This paper focuses on the neutral Higgs bosons H and A in the context of the Type-I 2HDM at SM-like scenario and addresses the question of observability of these Higgs bosons at a linear collider operating at the center-of-mass energies of 500 and 1000 GeV. Type-I 2HDM is one of the four types of the 2HDM which naturally conserve flavor and result from imposing the discrete Z2 symmetry. Although the center-of-mass energy required for producing heavy Higgs bosons can be provided by the LHC, a linear collider is chosen in this study to benefit from a cleaner environment with less background processes. ¯ bb ¯ b, ¯ where ¯ is an electron or a In this study, the process e− e+ → AH → ZH H → b muon pair, is assumed as the signal process. The decay mode H → bb¯ is analyzed as it is the dominant fermionic decay channel in 2HDM type I as long as the Higgs boson mass is below the on-shell production of the top quark pair production. Despite having a small branching ratio (≈ 0.066), the decay mode Z → e− e+ or μ− μ+ is chosen for signal to benefit from the clear signature electrons and muons provide at linear colliders. To assess the observability of the heavy neutral CP-even and CP-odd Higgs bosons H and A, several benchmark points with different mass hypotheses are assumed for the analysis at √ s = 500 and 1000 GeV separately, and the signal and background events are generated for each scenario. Both beams are assumed to be unpolarized in this study. The beamstrahlung effects [20] are taken into account and the simulation of the detector response is based on the SiD detector at the International Linear Collider (ILC) [21]. Comparing signal with background events, the Higgs boson candidates are identified resulting in mass distributions. It will be shown that in all of the considered benchmark scenarios, both Higgs bosons H and A are observable with signals exceeding 5σ and with possibility of mass measurement. In what follows, we provide a brief introduction to the 2HDM, and then the analysis and results will be discussed.

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Table 1 Higgs coupling to up-type quarks, down-type quarks and leptons in different types. The superscript i is a generation index. Type I Type II Type X Type Y

uiR

i dR

iR

2 2 2 2

2 1 2 1

2 1 1 2

1. Two-Higgs-doublet model A general 2HDM assumes the Higgs potential to be   V = m211 †1 1 + m222 †2 2 − m212 †1 2 + h.c. 2 1  2    1  + λ1 †1 1 + λ2 †2 2 + λ3 †1 1 †2 2 2 2    1  2    † † + λ4 1 2 2 1 + λ5 †1 2 + λ6 †1 1    2  † † + λ7 2 2 1 2 + h.c. ,

(1)

where 1 and 2 are SU (2) Higgs doublets. Employing the extended scalar structure with two Higgs doublets leads to the prediction of three neutral Higgs bosons h, H and A, and two charged Higgs bosons H ± . h and H are scalar CP-even bosons and A is a pseudoscalar CP-odd boson. Working in the “physical basis”, physical Higgs masses, tan β, CP-even Higgs mixing angle α, m212 , λ6 and λ7 are free parameters of the model and must be determined [12]. m211 and m222 in the Higgs potential (1) are determined by the minimization conditions for a minimum of the vacuum once tan β is determined. Imposing discrete Z2 symmetry [14–16] to avoid tree level flavor-changing neutral currents (FCNC) implies that the values of the parameters λ6 , λ7 and m212 must be zero. However, setting λ6 , λ7 to zero and allowing a non-zero value for m212 , Z2 symmetry is softly broken in 2HDM. Imposing Z2 symmetry restricts Higgs coupling to fermions and implies that there are four types of the 2HDM which naturally conserve flavor. Table 1 shows how Higgs doublets couple to fermions in different types. The types “X” and “Y” are also called “lepton-specific” and “flipped” respectively. Following the coupling prescription of Table 1, Higgs-fermion interaction part of the Lagrangian becomes [12]   mf  f f f LY ukawa = − ξh f¯f h + ξH f¯f H − iξA f¯γ5 f A v f =u,d, √  2V

ud (2) − u¯ mu ξAu PL + md ξAd PR dH + v √  2m ξA + νL R H + + H.c. . v Table 2 provides ξYX factors corresponding to different types. In order to respect experimental observations, it is assumed that the lightest Higgs boson h predicted by the 2HDM is the same

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Table 2 ξYX factors corresponding to different types (cx ≡ cos x and sx ≡ sin x). I

II

X

Y

ξhu

cα /sβ

cα /sβ

cα /sβ

cα /sβ

ξhd

cα /sβ

−sα /cβ

cα /sβ

−sα /cβ

ξh u ξH d ξH  ξH u ξA d ξA  ξA

cα /sβ

−sα /cβ

−sα /cβ

cα /sβ

sα /sβ

sα /sβ

sα /sβ

sα /sβ

sα /sβ

cα /cβ

sα /sβ

cα /cβ

sα /sβ

cα /cβ

cα /cβ

sα /sβ

cot β

cot β

cot β

cot β

− cot β

tan β

− cot β

tan β

− cot β

tan β

tan β

− cot β

Table 3 ρ X factors of the neutral Higgs part of the Yukawa Lagrangian corresponding to different types. I

II

X

Y

ρd ρu

cot β cot β

− tan β cot β

cot β cot β

− tan β cot β

ρ

cot β

− tan β

− tan β

cot β

as the discovered SM Higgs boson and thus the SM-like scenario is chosen by assuming sin(β − α) = 1 [12]. From experimental point of view, the allowed range of cos(β − α) is a region around zero and becomes narrower by taking more data from experiment to experiment [22]. With the above assumption, the h-fermion couplings of the Yukawa Lagrangian of the 2HDM reduce to the corresponding couplings in the Standard Model. As a result, the neutral Higgs part of the Yukawa Lagrangian takes the form [23]   ¯ h ¯ + mu uu LY ukawa = −v −1 md dd ¯ + m    ¯ H ¯ + ρ u mu uu + v −1 ρ d md dd ¯ + ρ  m    ¯ 5  A, ¯ 5 d + ρ u mu uγ + iv −1 − ρ d md dγ ¯ 5 u − ρ  m γ

(3)

where ρ X factors are given in Table 3. Different types of the 2HDM show different characteristics [18] due to the difference among their coupling factors. As Table 3 shows, leptonic decays of the neutral Higgs boson H /A are enhanced at large tan β values in the type-X which has been studied in [24]. In Type-I, neutral Higgs couplings to fermions are all proportional to cot β as shown in Table 3. Due to sin(β − α) = 1 requirement, the neutral Higgs boson coupling with gauge bosons is forbidden. Therefore below the top quark pair production threshold, H /A → bb¯ is the dominant tan β-independent decay channel for the neutral Higgs bosons. In this paper, we focus on this decay channel.

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2. Signal process The signal production process is assumed to be e− e+ → AH in the context of the Type-I 2HDM. This is the best choice among other possibilities like e+ e− → Zh, e+ e− → ZH or e+ e− → Ah. The first process involves SM-like Higgs boson (h) and is not relevant for a search for beyond SM Higgs bosons. The second and third processes involve H.Z.Z and h.Z.A vertices which are both proportional to cos(β − α) and vanish under the SM-like requirement sin(β − α) = 1. The Higgs bosons are selected with different masses to provide possibility of A → ZH decay. Scenarios with equal masses were studied earlier leading to promising results under the same collider conditions [25]. The two scalar Higgs bosons then decay like H → bb¯ which is dominated in Type-I 2HDM and the Z boson undergoes Z → ¯ decay where ¯ is an electron or a muon pair and b is the bottom quark. The center-of-mass energies of 500 and 1000 GeV are assumed for the initial collision at a linear collider. Several benchmark points with different mass hypotheses are assumed as shown in Table 4. The physical mass of the H Higgs boson is assumed to range from 150 to 250 GeV, and the mass splitting between H and A Higgs bosons is set to 50 or 90 GeV. A mass splitting of 50-90 GeV provides possibility of A → ZH decay which is essential to our analysis. Since the signal is assumed to be simulated at the center-of-mass energies of 500 and 1000 GeV, only H Higgs masses up to 250 GeV can be considered since the cross section of the signal production process decreases substantially for higher Higgs masses and scenarios with higher masses can not be observed. The value of tan β is also set to 20 for all of the benchmark points. The chosen Higgs boson masses are checked to be consistent with results of 86 analyses with the use of HiggsBounds 4.3.1 [26] and HiggsSignals 1.3.0 [27]. These analysis results included in these versions of HiggsBounds and HiggsSignals do not include the recent LHC 13 TeV data results. Therefore, recent experimental results from LHC 13 TeV run are checked manually due to missing software interfaces. For each benchmark scenario there is a range of m212 parameter (quoted in Table 4) which satisfies theoretical requirements of potential stability [28], perturbativity and unitarity [29–32] which are all checked using 2HDMC 1.7.0 [33,34]. There are several possible scenarios with mA > mH or mA < mH as discussed in detail in [35]. Here the first assumption is made and the masses of the Higgs bosons A and H ± are assumed to be equal in all of the scenarios to make sure that the experimental constraint [36,37] is satisfied. This constraint results from the measurement performed at LEP [38] and puts a limit on the deviation of the parameter ρ = m2W (mZ cos θW )−2 from its Standard Model value. Since it is demonstrated that the deviation of this parameter is negligible if any of the conditions [39,40] mA = mH ± , mH = mH ± ,

(4)

is satisfied, the assumed benchmark points are guaranteed to be consistent with the mentioned experimental constraint. As indicated by the direct search [41] at the LHC, the CP-odd Higgs mass ranges mA = 310 − 410, 335 − 400, 350 − 400 GeV have been excluded for mH = 150, 200, 250 GeV masses respectively at tan β = 10 in the Type-I. In this search, m212 is a fixed parameter, while in the present study, we have not limited m212 to a fixed value, and it can take any value in the ranges provided in Table 4. However, the constraints obtained in [41] are totally respected by the benchmark points considered in this study. Moreover, the LHC experiment [42] has excluded the mass range mH = 170 − 360 GeV for tan β < 1.5 in the Type-I 2HDM. The constraint mA > 350

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Table 4 Assumed benchmark points for the center-of-mass energies a) 500 and b) 1000 GeV. mh , mH , mA , mH ± are physical masses of the Higgs bosons. The m212 range satisfies theoretical requirements. The branching fractions H → bb¯ and A → ZH are provided in percent. All mass values are given in GeV. √ s = 500 GeV BP1

BP2 125

mh mH mA mH ±

150 200 200

m212

1093-1124

tan β sin(β − α) H → bb¯

150 240 240 1093-1124 20 1

63 89 16.5

A → ZH σtotal [fb]

67 99 9.7 a

√ s = 1000 GeV BP1 mh mH mA mH ± m212 tan β sin(β − α) H → bb¯ A → ZH σtotal [fb]

BP2

BP3

BP4

BP5

150 200 200

150 240 240

125 200 250 250

200 290 290

250 300 300

1093-1124

1093-1124

1966-1996 20 1

1966-1996

3088-3119

63 89 12.2

67 99 11.0

62 83 9.5

62 99 8.4

51 72 6.9

b

is also obtained for tan β < 5 in this type as shown in [43,44]. A comparison shows that the assumed benchmark scenarios are obviously consistent with the mentioned constraints. Flavor physics data puts the constraints mH ± ≥ 570 and 700 GeV for tan β > 2 and tan β < 2 respectively on the charged Higgs mass in the context of Type-II [45,46]. However, as indicated in [46], the Type-I is not constrained by any restriction for tan β > 2. The Tevatron, LEP and LHC searches also result in no exclusion around sin(β − α) = 1 in this type for mH /A/H ± = 500 GeV [47]. Thus, it is concluded that the assumed benchmark points in this study are completely consistent with the current experimental and theoretical constraints. According to the full Lagrangian of the Type-I 2HDM, the Z-H -A vertex depends on sin(β − α) which is assumed to be unity in the SM-like scenario. This vertex appears both in the production process, i.e., e+ e− → Z ∗ → H A and the subsequent decay A → ZH . Therefore, the production process followed by A → ZH decay is independent of tan β as long as sin(β − α) = 1.

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Using 2HDMC 1.7.0, the branching fractions, BR(A → ZH ), are obtained for each benchmark point as shown in Table 4, which shows dominance of this decay mode at the tested scenarios. The A decay into a fermion pair f f¯ at large tan β is suppressed because A-f -f¯ vertex is proportional to cot β as seen in Eq. (3) and Table 3. Therefore, A → ZH decay is preferred even if it occurs in off-shell mode. ¯ are also shown on Table 4 as calculated by 2HDMC The branching fractions, BR(H → bb), 1.7.0. At the SM-like limit (sin(β − α) = 1), the H Higgs boson is gauge-phobic since the H -V -V vertex, where V is a gauge boson, depends on cos(β − α) (= 0), and therefore, the decay of the H Higgs boson into a pair of gauge bosons is impossible. Moreover, the H coupling to different fermion pairs f f¯ (f = u, d, ...) depends on the fermion mass mf and the common factor cot β (see Eq. (3) and Table 3), leading to the dominance of the H → bb¯ below the threshold of top quark pair production. Observation of any deviation of the Higgs-gauge coupling from the SM-like scenario with precision data can fingerprint extended Higgs sectors. The expected precision of the Higgs-gauge √ coupling has been obtained to be ∼ 0.5% at ILC operating at s = 500 GeV [48]. Therefore if the coupling measurement is compatible with SM (sin(β − α) = 1) with 0.5% uncertainty, the allowed range of sin(β − α) at 2σ is 0.99 < sin(β − α) < 1. For example, for tan β = 20, this would leave an allowed region of −0.05 < α < 0.09. On the other hand, any improvement on Higgs pair production cross section measurement would certainly improve our knowledge of Higgs-gauge coupling and can be propagated to a better constraint on alpha parameter. Processes involving Higgs-fermion couplings like t t¯H would also serve as channels useful for verification of the 2HDM type as the Higgs-fermion couplings depend on the type of 2HDM we assume, while Higgs-gauge couplings are independent of the 2HDM type. According to the signal process, the produced Z boson annihilates into a lepton pair (μ− μ+ or e− e+ ). Although the branching ratio of this decay mode (≈ 0.066) is so small compared with the hadronic decay mode, the leptonic decay is chosen since leptons provide a simple and clear signature at linear colliders and this feature can partially compensate for the smallness of the branching ratio. b quark pairs produced by the H Higgs bosons decays annihilate into hadronic jets which are used to reconstruct the H Higgs boson. Reconstruction of the A Higgs boson is then performed with the use of reconstructed H and Z bosons. Because of the possible enhancements and also the opportunity of observing both of the heavy neutral Higgs bosons at once, the assumed signal process is expected to serve as a tool for searches for heavy neutral Higgs bosons posited in the Type-I 2HDM. The cross section of the signal production process e− e+ → AH is computed at the assumed benchmark points using CompHEP 4.5.2 [49]. Table 4 provides the obtained values. As seen, the signal cross section is smaller for benchmark points with heavier Higgs masses. Therefore, observing heavier Higgs bosons is expected to be more difficult. The cross section of the sig¯ bb ¯ b¯ is obtained by multiplying the total cross nal process chain e− e+ → AH → ZH H → b sections of Table 4 by branching fractions of the relevant decay modes A → ZH , H → bb¯ and ¯ Z → l l. Background processes contributing to this analysis include top quark pair production, W ± pair production, Z pair production and Z/γ production. Corresponding background cross sections at √ s = 500 and 1000 GeV are also obtained by CompHEP 4.5.2 and are provided in Table 5.

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Table 5 Background cross sections computed by CompHEP 4.5.2. √ σ [fb] ( s = 500 GeV) √ σ [fb] ( s = 1000 GeV)

t t¯

W +W −

ZZ

Z/γ

562 226

7887 3410

450 190

16846 4335

Table 6 √ Beam parameters corresponding to s = 500 and 1000 GeV taken from Tab. 8.2 of ILC technical design report v3.II [50]. RMS horizontal beam size (nm) RMS vertical beam size (nm) RMS bunch length (mm) No. of particles / bunch (×1010 )

500 GeV

1000 GeV

474 5.9 0.3 2

335 2.7 0.225 1.74

3. Event generation and selection Both beams are assumed to be unpolarized in this study. Parton-level events are produced by CompHEP 4.5.2. In order to simulate the beamstrahlung effects, the beam parameters provided in Table 6 are given to CompHEP. Basic parameters of the model are also generated in SLHA (SUSY Les Houches Accord) format by 2HDMC 1.7.0. The generated parton-level events and SLHA files are passed to PYTHIA 8.2.15 [51] for further processing including multi-particle interactions, parton showers and hadronization. PYTHIA output events are then internally used by DELPHES 3.4 [52] for simulating detector response with the DSiD detector card which is based on the full simulation performance of the SiD detector at the ILC. The jet reconstruction is performed using FASTJET 3.1.0 [53,54] based on anti-kt algorithm [55] with  the cone size R = ( η)2 + ( φ)2 = 0.4. Here, η = −ln tan(θ/2) and φ (θ ) is the azimuthal (polar) angle with respect to the beam axis. The DELPHES outputs reconstructed jets, electrons, muons and b-tagging flags stored as ROOT files [56]. In what follows, event selection method is provided in two separate parts for the center-of-mass energies of 500 and 1000 GeV. 3.1.

√ s = 500 GeV

Reconstructed jets, electrons and muons are required to satisfy the kinematic thresholds pT j et ≥ 10 GeV, |ηj et | ≤ 3, pT e,μ ≥ 5 GeV, |ηe,μ | ≤ 2.5,

(5)

where pT is the transverse momentum. Based on the obtained jet multiplicity distribution of Fig. 1(a), the condition N jet ≥ 3,

(6)

where Njet is the number of jets, is applied to events. Identifying b-jets with the help of b-tagging flags and imposing the kinematic threshold pT b-jet ≥ 20 GeV on the identified b-jets, b-jet multiplicity distribution of Fig. 1(b) is obtained and the condition N b-jet ≥ 3,

(7)

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Fig. 1. a) Jet, b) b-jet and c) di-lepton multiplicity distributions obtained for different signal and background processes at √ s = 500 GeV. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)

where Nb-jet is the number of b-jets, is applied. Counting the number of di-leptons (di-electrons and di-muons), di-lepton multiplicity distribution of Fig. 1(c) is obtained and the selection cut

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N ¯ ≥ 1,

(8)

where N¯ is the number of di-leptons, is applied to rule out events in which the Z boson cannot be reconstructed. Events are then subject to the conditions R ¯ ≥ 0.25, M ¯ ≤ 90 GeV, where R ¯ is the distance between the two leptons obtained by the definition

R = ( η)2 + ( φ)2 ,

(9)

(10)

and M ¯ is the invariant mass of the di-lepton. According to the selection cut (7), selected events contain at least three b-jets with which the b-jet pairs originating from the H Higgs bosons are identified. In events with three b-jets, R bb , where R follows the definition of Eq. (10), is computed for all possible b-jet pairs, and the pair with minimum R bb value is considered as the true pair if the condition R bb ≥ 0.8 is satisfied. If the Higgs boson mass is known, the b-jet pair with closest invariant mass to the nominal mass can easily be identified. However, since there are no assumptions about the Higgs boson mass in the analysis, this approach is aborted. Using the distance R between b-jets as a measure to discriminate between true and false b-jet pairs is motivated by the fact that, in signal events, b-quarks originating from the same parent H Higgs boson are likely to have close flight directions. The choice of the lower limit of 0.8 on R bb is motivated by a comparison between R bb distributions of signal and background events. Such limits throughout this analysis provide the optimum signal efficiency versus background rejection, leading to the best achievable signal significance. In events with at least four b-jets, the difference between the invariant masses of the two b-jet pairs |M b1b2 − M b3 b4 | in all possible combinations of two b-jet pairs is computed and the combination with minimum invariant mass difference is considered as the true combination. Identifying true b-jet pairs, events satisfying the condition N bb¯ ≥ 1,

(11)

where Nbb¯ is the number of identified true b-jet pairs, are selected and the H Higgs bosons are reconstructed using the identified b-jet pairs. Reconstructing the Z boson using the existing dilepton, the A Higgs boson is reconstructed by combining the reconstructed H and Z bosons. Each event contains one reconstructed Z boson and one or two reconstructed H Higgs bosons. In events with one reconstructed H Higgs boson, the A Higgs boson is reconstructed by combining the reconstructed H and Z bosons. In events with two reconstructed H Higgs bosons,

R ZH , where R follows the definition of Eq. (10), is computed for the two possible ZH combinations and the combination with smaller R ZH value is selected as the true combination which originates from the A Higgs boson decay. Imposing all the selection cuts on the signal and background events at the center-of-mass energy of 500 GeV results in the selection efficiencies provided in Table 7. 3.2.

√ s = 1000 GeV

The required kinematic thresholds for reconstructed objects and the constraint on the number of jets are the same as the conditions (5) and (6). Jet multiplicity distribution is shown in Fig. 2(a).

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Table 7 Event selection efficiencies corresponding to the a) signal and b) background √ processes assuming different benchmark scenarios at s = 500 GeV. √ s = 500 GeV BP1

BP2

Nj et ≥ 3

0.941

0.943

Nb-jet ≥ 3 N¯ ≥ 1

R ¯ ≥ 0.25, M ¯ ≤ 90 Nbb¯ ≥ 1 Total eff.

0.454 0.638 0.947

0.459 0.708 0.980

0.807 0.208

0.759 0.228

a √ s = 500 GeV t t¯

WW

ZZ

Z/γ

Nj et ≥ 3

0.944

0.717

0.568

0.164

Nb-jet ≥ 3 N¯ ≥ 1

R ¯ ≥ 0.25, M ¯ ≤ 90 Nbb¯ ≥ 1 Total eff.

0.029 0.020 0.612

1e-05 0 0

0.015 0.023 0.171

0.046 0.004 0.206

0.113 4e-05

0 0

0.398 1e-05

0.167 1e-06

b

Multiplicity distribution of b-jets satisfying the threshold condition pT b-jet ≥ 20 GeV is also provided in Fig. 2(b) based of which the selection cut N b-jet ≥ 2,

(12)

is applied. Di-lepton multiplicity distribution is provided in Fig. 2(c) and suggests imposing the same condition as the condition (8) on the number of di-leptons to rule out events with no reconstructable Z boson. Conditions R ¯ ≥ 0.15, M ¯ ≤ 90 GeV,

(13)

where R follows the same definition as the definition of Eq. (10), are then applied. Events surviving the mentioned cuts contain at least two b-jets which are analyzed to identify the b-jet pairs originating from the H Higgs bosons decays. In events with two b-jets, the b-jet pair is identified as the true pair if the condition 0.6 ≤ R bb ≤ 2.2 is satisfied. In events with three b-jets, among all possible b-jet pairs, the pair with minimum R bb value is identified as the true pair if the condition R bb ≥ 0.6 is satisfied. In events with at least four b-jets, all possible combinations of two b-jet pairs are considered and computing the difference between the invariant masses of the two b-jet pairs in all of the combinations, the combination with minimum invariant mass difference is considered as the true combination if the condition R bb ≥ 0.6 is met. Events are now subject to the condition N bb¯ ≥ 1,

(14)

where Nbb¯ is the number of identified true b-jet pairs, to select events with at least one reconstructable H Higgs boson. The A Higgs boson is then reconstructed by identifying the true

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Fig. 2. a) Jet, b) b-jet and c) di-lept on multiplicity distributions obtained for different signal and background processes √ at s = 1000 GeV.

ZH combination which originates from the A Higgs boson decay. In events with one reconstructed H Higgs boson, the ZH combination is considered as a true combination if the condition

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Table 8 Event selection efficiencies corresponding to the a) signal and b) background processes as√ suming different benchmark scenarios at s = 1000 GeV. Parentheses enclosed efficiencies correspond to the selection cut specialized for the benchmark point BP5. √ s = 1000 GeV BP1

BP2

BP3

BP4

BP5

Nj et ≥ 3 Nb-jet ≥ 2 N¯ ≥ 1

R ¯ ≥ 0.15, M ¯ ≤ 90 Nbb¯ ≥ 1 Total eff.

0.903 0.801 0.659 0.921

0.911 0.807 0.712 0.940

0.943 0.819 0.663 0.918

0.945 0.826 0.719 0.942

0.959 0.831 0.663 0.918

0.679 0.298

0.707 0.348

0.735 0.345

0.753 0.399

0.757 0.367

NZH = 1 Total eff.

0.558 0.166

0.568 0.198

0.577 0.199

0.584 0.233

0.547 0.201

a √ s = 1000 GeV t t¯

WW

ZZ

Z/γ

Nj et ≥ 3

0.947

0.611

0.537

0.155

Nb-jet ≥ 2 N¯ ≥ 1

R ¯ ≥ 0.15, M ¯ ≤ 90 Nbb¯ ≥ 1 Total eff.

0.389 0.031 0.471

5e-4 0.004 0.160

0.079 0.018 0.182

0.410 0.007 0.152

0.177 0.001

0 0

0.412 6e-05

0.227 2e-05

NZH = 1

0.158 (0.084) 2e-4

0

0.153 (0.138) 9e-06

0.270 (0.209) 4e-06

(8e-06)

(3e-06)

Total eff.

0

(8e-05) b

R ZH ≤ 2 (≤ 1.5 for the benchmark point BP5) is met. In events with two reconstructed H Higgs bosons, between the two possible ZH combinations, the combination with smaller R ZH value is selected. Identifying true combinations, the condition N ZH = 1,

(15)

where NZH is the number of true ZH combinations, is imposed and the A Higgs boson is reconstructed using the reconstructed Z and H bosons. Event selection efficiencies corresponding to the applied selection cuts are provided in Table 8. Since H and A Higgs bosons are reconstructed after five and six cuts respectively, total efficiencies corresponding to the first five cuts and all the six cuts are also provided. 4. Higgs boson reconstruction ¯ b, ¯ candidate mass distributions of the H and Using the identified combinations bb¯ and b A Higgs bosons are obtained. Figs. 3 and 4 provide the obtained candidate mass distributions

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Fig. 3. Candidate mass distributions of the H and A Higgs bosons with corresponding fitting results in different bench√ mark points at s = 500 GeV. Errors are also shown.

√ corresponding to s = 500 and 1000 GeV respectively. Contributions of the signal and different background processes are shown separately and the signal contribution can be seen as a significant excess of data on top of the SM background. The W W process has no contribution due to its perfect suppression as seen in Tables 7 and 8. Among the background processes, the most contribution belongs to the t t¯ process which is, however, well under control. Normalization of the distributions is based on σ × L × , where σ is the cross section of either background processes (Table 5) or the signal process (Table 4), L is the integrated luminosity and  is the total efficiency. The integrated luminosity of 500 fb−1 is assumed for all distributions except for the distribution of Fig. 4(j) which uses the integrated luminosity of 2000 fb−1 . Total efficiencies used for normalizing A mass distributions are taken from the last rows of Tables 7 and 8. However, total efficiencies corresponding to the first five selection cuts of Tables 7 and 8 cannot be used to normalize H mass distributions since the number of reconstructed H Higgs bosons in events is different from event to event. Therefore, based on the number of reconstructed H Higgs bosons, appropriate total efficiencies are computed and used for normalizing H mass distributions. As seen in Figs. 3 and 4, fitting results of the signal plus background (S+B) distributions show significant peaks near the generated Higgs masses. Fitting is performed by ROOT 5.34 [57] and the fit function used for the S+B distribution is a combination of the polynomial and Gaussian functions. A polynomial function is first used as the fit function for the total background distribution and is then used as input for the total S+B fit. Reconstructed masses of the

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Fig. 4. Candidate mass distributions of the H and A bosons with corresponding fitting results in different benchmark √ points at s = 1000 GeV. Errors are also shown.

Higgs bosons H and A can be read from the “Mean” parameter of the Gaussian function assumed as the signal distribution function. The obtained reconstructed masses are provided in Table 9. The difference between the generated and reconstructed masses of Table 9 can be due to the uncertainty arising from fitting method and choice of the fit function, jet reconstruction algorithm and jet mis-identification, b-tagging algorithm and jets mis-tag rate, errors in energy and momentum of the particles, etc. Optimization of the b-tagging algorithm, fitting method and also optimization of the jet reconstruction algorithm can reduce the errors. In addition to the

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Fig. 4. (continued)

mentioned error sources, electronic noise, pile up, underlying-events, etc., can give rise to more errors in real experiments, and thus a careful correction must be applied. In this work, a simple off-set correction is applied as follows. According to Table 9a, on average, reconstructed masses of the H and A Higgs bosons are 17.5 and 28.4 GeV smaller than the corresponding generated masses respectively. The corresponding values for Table 9b are 16.0 and 23.8 GeV. To apply the off-set correction, reconstructed masses of the H and A Higgs bosons are increased by the same values respectively. The obtained results are provided in Table 9 as corrected reconstructed masses. As seen, the corrected masses are in reasonable agreement with the generated masses.

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Table 9 Generated mass (m Gen. ), reconstructed mass (m Rec. ) and corrected reconstructed mass (m Corr. rec. ) of the H and A Higgs bosons with associated uncertainties at the center-of-mass energies of a) 500 and b) 1000 GeV. The mass values are in GeV unit. √ s = 500 GeV m Gen.

m Rec.

m Corr. rec.

H

BP1 BP2

150 150

132.8 ± 6.6 132.2±8.8

150.3±14.3 149.7±16.5

A

BP1 BP2

200 240

172.0±12.0 211.2±18.4

200.4±27.2 239.6±33.6

a √

s = 1000 GeV m Gen.

m Rec.

m Corr. rec.

H

BP1 BP2 BP3 BP4 BP5

150 150 200 200 250

134.1±4.7 133.6±4.4 187.4±2.4 186.7±2.6 228.3±6.2

150.1±8.8 149.6±8.5 203.4±6.5 202.7±6.7 244.3±10.3

A

BP1 BP2 BP3 BP4 BP5

200 240 250 290 300

178.1±8.9 217.0±7.9 228.8±16.5 263.9±13.6 273.2±20.0

201.9±22.3 240.8±21.3 252.6±29.9 287.7±27.0 297.0±33.4

b

5. Signal significance Using the Higgs candidate mass distributions of Figs. 3 and 4, signal significance is obtained to assess the observability of the Higgs bosons. A mass window cut is applied to distributions and the signal significance is computed by counting signal and background events which pass the mass window. The integrated luminosity at which computation is performed is set to 500 fb−1 for all of the distributions except for the distribution of Fig. 4(j) for which the integrated luminosity of 2000 fb−1 is assumed. Table 10 provides computation results, namely mass window and the corresponding efficiency, signal selection total efficiency, number of signal (S) and background (B) Higgs√candidates which pass the mass window, signal to background ratio and signal significance at s = 500 and 1000 GeV. Results indicate that in all benchmark scenarios, both Higgs bosons H and A are observable with signals exceeding 5σ and mass measurement is also possible. To be specific, both of the Higgs bosons are observable in the region of parameter space √ with mH = 150 GeV and 200 ≤ mA ≤ 240 GeV at the integrated luminosity of 500 fb−1 at s = 500 GeV. Also, at the center-of-mass energy of 1000 GeV, the H Higgs boson is observable in the region with mH = 150-250 GeV and mA = 200-300 GeV with a mass splitting of 50-90 GeV −1 between the H and A Higgs √ bosons at the integrated luminosity of 500 fb . The A Higgs boson is also observable at s = 1000 GeV in the same region at an integrated luminosity up to 2000 fb−1 . The above results are based on tan β = 20. The ATLAS collaboration has recently announced results of their search for A → ZH signal with interpretation of the results in all 2HDM types in [58]. In order to compare our results with those of LHC, the ATLAS exclusion contour at tan β = 10 is used as the reference and our results are scaled to tan β = 10. Event kinematics

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Table 10 Mass window (m W. ) and associated efficiency ( W. ), signal total efficiency ( T otal ), number of signal (S) and background (B) Higgs candidates after all cuts, signal to background ratio, signal significance and integrated luminosity in different scenarios at the center-of-mass energies of a) 500 and b) 1000 GeV. √ s = 500 GeV BP1 H

A

m W. [GeV]  W.  T otal S B S/B √ S/ B L I nt. [fb−1 ]

BP2 0-300 1

0.14 68.7 18.2 3.8 16.1

0.16 50.6 18.2 2.8 11.9 500

m W. [GeV]  W.  T otal S B S/B √ S/ B L I nt. [fb−1 ]

0-500 1 0.21 50.8 15.2 3.3 13.0

0.23 36.7 15.2 2.4 9.4 500

a √

s = 1000 GeV BP1

BP2

BP3

BP4

BP5

H

m W. [GeV]  W.  T otal S B S/B √ S/ B L I nt. [fb−1 ]

0-400 1 0.18 63.9 119.8 0.53 5.8

0-400 1 0.21 77.0 119.8 0.64 7.0

≥ 78 0.92 0.19 38.8 59.6 0.65 5.0 500

≥ 36 0.99 0.25 51.3 104.5 0.49 5.0

≥ 156 0.67 0.15 13.0 6.7 1.94 5.0

A

m W. [GeV]  W.  T otal S B S/B √ S/ B L I nt. [fb−1 ]

0-700 1 0.17 30.0 19.5 1.5 6.8

0-700 1 0.20 36.1 19.5 1.8 8.2

≥ 167 0.90 0.18 17.8 12.7 1.4 5.0

0-700 1 0.23 24.2 19.5 1.2 5.5

0-700 1 0.20 33.8 44.8 0.8 5.0 2000

500 b

and total cross sections are the same but branching ratio of Higgs boson decays depend on tan β. The resulting contour is shown in Fig. 5 where LHC result obtained from integrated luminosity of 30 fb−1 is compared with the ILC reach at 500 fb−1 with tan β = 10 and 20. As seen, for a given mH , the region of mA which leads to 5σ discovery is lower than the excluded area of LHC and is extended down to mass splitting below 90 GeV which is the limit at LHC.

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Fig. 5. The 5σ contour of ILC laid on the exclusion region of LHC at 30 fb−1 .

6. Conclusions ¯ bb ¯ b, ¯ where ¯ is a di-electron or a The signal process chain e− e+ → AH → ZH H → b di-muon, was investigated to assess the observability of the neutral CP-even (H ) and CP-odd (A) Higgs bosons in the framework of the Type-I 2HDM at SM-like scenario. The signal benefits from the large enhancements due to the decay modes A → ZH and H → bb¯ at a relatively low tan β value. The leptonic decay Z → ¯ is also assumed to benefit from the clear signature of leptons at lepton colliders. Several benchmark scenarios with different mass hypotheses were assumed at the center-of-mass energies of 500 and 1000 GeV at a linear collider and the simulation of the detector response was performed based on the SiD detector at the ILC and the beamstrahlung effects were also taken into account. Analyzing the simulated events, Higgs candidate mass distributions were obtained and reconstructed masses of the Higgs bosons were extracted by fitting a proper function to the mass distributions. Signal significance was also computed to assess observability of the Higgs bosons. In all of the benchmark scenarios under consideration, both of the Higgs bosons H and A are observable with signals exceeding 5σ and with possibility of mass √ measurement. The parameter space region with mH = 150 GeV and 200 ≤ mA ≤ 240 GeV at s = 500 GeV can be discovered or excluded at the integrated luminosity of 500 fb−1 . At the center-of-mass energy of 1000 GeV, the region with mH = 150-250 GeV and mA = 200-300 GeV with a mass splitting of 50-90 GeV between the H and A Higgs bosons can be discovered or excluded at the same integrated luminosity. Results obtained in this study show reasonable ILC potential for simultaneous reconstruction of both Higgs bosons in a wide region of the parameter space beyond the current reach of LHC. Acknowledgements We would like to thank the college of sciences at Shiraz university for providing computational facilities and maintaining the computing cluster during the research program. References [1] F. Englert, R. Brout, Phys. Rev. Lett. 13 (1964) 321.

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