Exploration of heavy Higgs bosons at a 100 TeV hadron collider withinthe semi-constrained next-to-minimal supersymmetric standard model

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Kun Wang, Pengfu Tian and Jingya Zhu. Exploring Heavy Higgs Bosons at a 100 TeV Hadron Collider within the Semi-Constrained NMSSM[J]. Chinese Physics C. doi: 10.1088/1674-1137/ad5663
Kun Wang, Pengfu Tian and Jingya Zhu. Exploring Heavy Higgs Bosons at a 100 TeV Hadron Collider within the Semi-Constrained NMSSM[J]. Chinese Physics C.  doi: 10.1088/1674-1137/ad5663 shu
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Exploration of heavy Higgs bosons at a 100 TeV hadron collider withinthe semi-constrained next-to-minimal supersymmetric standard model

    Corresponding author: Jingya Zhu, zhujy@henu.edu.cn
  • 1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
  • 2. School of Physics and Technology, Wuhan University, Wuhan 430072, China
  • 3. School of Physics and Electronics, Henan University, Kaifeng 475004, China

Abstract: In this study, we explore the detectability of heavy Higgs bosons in the ppbˉbH/Abˉbtˉt channel at a 100 TeV hadron collider within the semi-constrained next-to-minimal supersymmetric standard model. We calculate their production cross sections and decay branching ratios and compare them with simulation results from literature. We focus on the heavy doublet-dominated CP-even Higgs H and CP-odd Higgs A, with mass limits set below 10 TeV to ensure detectability. At a collider with an integrated luminosity of 3 ab1, the potential for detecting heavy Higgs bosons varies significantly with their mass and tanβ. Heavy Higgs bosons with masses below 2 TeV are within the testable range, while those heavier than 7 TeV are below the exclusion and discovery thresholds, rendering them undetectable. For masses between 2 and 7 TeV, heavy Higgs bosons with tanβ smaller than 20 can be detected, whereas those with tanβ larger than 20 are beyond the current discovery or exclusion capabilities.

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    I.   INTRODUCTION
    • It has been widely regarded, for an extended period, that the standard model (SM) of particle physics, despite its remarkable success in explaining a vast array of phenomena, fails to provide a complete description of the fundamental aspects of the universe. Consequently, the search for new physics beyond the SM (BSM) has become a crucial direction in modern physics research.

      The discovery of a Higgs boson with properties consistent with SM predictions at the large hadron collider (LHC) in 2012 significantly bolstered our understanding of the SM [14]. Nevertheless, this milestone also intensified the debate regarding the possible existence of additional Higgs bosons. These scalar particles are theoretically predicted by a large number of natural BSM models, which aim to address the limitations and unresolved questions on the SM, including the Minimal Supersymmetric Standard Model (MSSM) [516], Next-to-MSSM (NMSSM) [1732], Minimal Dilaton Model (MDM) [3337], and Little Higgs Models (LHMs) [38, 39]. The experimental search for heavy neutral Higgs bosons has focused on decay channels such as τ+τ [40, 41], tˉt, bˉb, μ+μ, ZZ, WW, hh, and hV, which are reviewed in [42, 43]. Recently, evidence for a new scalar around 151 GeV was accumulated with significances of 4.3σ locally and 3.9σ globally [44], subsequently revised to 4.1σ locally and 3.5σ globally [45].

      The exploration of new physics phenomena, particularly the detection of heavy Higgs bosons, requires colliders with higher energies. Future high-energy colliders, designed to exceed the capabilities of current facilities, will be able to examine these heavy particles. Notably, the Future Hadron-Hadron Circular Collider (FCC-hh) at CERN [46] and Super-pp-Collider (SppC) [47, 48] in China are among the most ambitious projects in this direction. Both initiatives aim to construct a 50−100 TeV pp collider [49], promising a significant leap in the energy frontier and potentially uncovering phenomena beyond the SM. Moreover, the concept of a multi-TeV muon collider provides an innovative approach to high-energy physics experiments [50, 51]. Extensive research has been conducted on the detection of heavy Higgs bosons at future colliders. In particular, the studies described in Ref. [52] examined the ppbˉbH/Abˉbττ and ppbˉbH/Abˉbtˉt channels at a 100 TeV pp collider and proposed pushing the exclusion limits for heavy Higgs searches up to MH10TeV, with exceptions in regions of low tanβ. Furthermore, the analysis in Ref. [13] explored the ppH/A˜χ01˜χ2 process, revealing the 4+E signal at a 100 TeV hadron collider, demonstrating its ability to probe new supersymmetric model sectors. In addition, the study in Ref. [53] explored the potential of a multi-TeV muon collider to discover heavy Higgs bosons within Two Higgs Doublet Models (2HDMs) and assess the discriminative power among different 2HDM types.

      This study extend the investigation initiated in our previous study on heavy Higgs bosons within the framework of the semi-constrained NMSSM (scNMSSM) [54]. The NMSSM incorporates an additional singlet superfield to the MSSM, thereby enriching the Higgs and neutralino sectors. Our analysis focuses on the computational evaluation of production cross sections and decay branching ratios for these heavy Higgs bosons. Through these calculations, we aim to provide a comprehensive understanding of the behavior and detectability of heavy Higgs bosons within the scNMSSM. Furthermore, we delve into the exploration of the discovery potential of these heavy Higgs bosons through the ppbˉbH/Abˉbtˉt channel at a future 100 TeV collider. The selection of a 100 TeV collider is driven by its exceptional ability to achieve the high energy levels required for producing such massive particles, which provides new avenues for their discovery.

      The remainder of this manuscript is organized as follows. In Sec. II, we provide a brief overview of the scNMSSM, outlining its fundamental aspects and theoretical significance. In Sec. III, we present a detailed description of our computational methodology, followed by a comprehensive discussion on the results obtained from our analysis. In Sec. IV, we conclude the paper by summarizing the main results and their implications for future research in this area.

    II.   SEMI-CONSTRAINED NMSSM
    • The NMSSM extends the MSSM by introducing an additional singlet superfield, denoted as ˆS, where the superpotential of the Z3-symmetric NMSSM is defined as

      WNMSSM=WMSSM|μ=0+λˆSˆHuˆHd+κˆS33,

      (1)

      where WMSSM|μ=0 is the superpotential of the MSSM without the μ-term, λ and κ are coupling constants, ˆHu and ˆHd are the doublet Higgs superfields, and ˆS is the added singlet superfield. After electroweak symmetry breaking, the singlet scalar's vacuum expectation value (VEV), denoted as vs, dynamically generates the massive μ-term [55, 56]

      μλvs.

      (2)

      Concurrently, the scalar components Hu and Hd also attain VEVs, labeled as vu and vd, respectively. This leads to the introduction of a new parameter tanβ, defined as

      tanβvu/vd,

      (3)

      where the sum of their squares is v2u+v2d=v2= (174GeV)2.

      The NMSSM introduces specific soft supersymmetry (SUSY) breaking terms, distinct from those in the MSSM, expressed by

      LsoftNMSSM=LsoftMSSM|μ=0+m2S|S|2+λAλSHuHd+13κAκS3+h.c.,

      (4)

      where LsoftMSSM|μ=0 denotes the MSSM's soft SUSY breaking terms with the μ parameter set to zero. The symbols Hu and Hd refer to the scalar components of the Higgs doublets, Aλ and Aκ represent the trilinear coupling constants with mass dimension, and mS is the mass of the singlet scalar field.

      In the scNMSSM, the Higgs sector is allowed to deviate from universality at the Grand Unified Theory (GUT) scale, a characteristic also known as NMSSM with non-universal Higgs masses. Specifically, the soft masses for the Higgs fields, m2Hu, m2Hd, and m2S, can differ from M20+μ2. Furthermore, the trilinear coupling constants Aλ and Aκ may vary independently from A0. Consequently, the parameter space of the scNMSSM is defined by nine parameters:

      λ, κ, tanβ, μ, Aλ, Aκ, A0, M1/2, M0.

      (5)

      Here, the last five parameters are set at the GUT scale. M1/2 and M0 represent the universal sfermion mass and universal gaugino mass, respectively, while A0 denotes the universal trilinear coupling constant in the sfermion sector. This set of nine parameters at the GUT scale effectively constrains the NMSSM. Through the renormalization group equations (RGEs) to the SUSY scale, these parameters determine mass spectra at lower energy scales.

      The Higgs sector within the NMSSM is predictedto contain three CP-even Higgs bosons, two CP-odd Higgs bosons, and a pair of charged Higgs bosons. For convenience, the scalar components of the superfields Hu, Hd, and S are often rotated so that they can be represented as

      H1=cosβHu+εsinβHd=(H+S1+iP12),

      (6)

      H2=sinβHuεcosβHd=(G+v+S2+iG02),

      (7)

      H3=S=vs+S3+iP22,

      (8)

      where ε=(0110), and S1, S2, and S3 create the CP-even basis, while P1 and P2 establish the CP-odd basis. H2 is identified as the SM-like Higgs, H1 represents a new Higgs doublet field, and H3 introduces a new singlet field.

      The CP-even Higgs mass matrix M2S in the basis (S1,S2,S3) is expressed by [21, 57]

      M2S,11=M2A+(m2Zλ2v2)sin22β,

      (9)

      M2S,12=12(m2Zλ2v2)sin4β,

      (10)

      M2S,13=(M2A2μ/sin2β+κvs)λvcos2β,

      (11)

      M2S,22=m2Zc o s22β+λ2v2sin22β,

      (12)

      M2S,23=2λμv[1(MA2μ/sin2β)2κ2λsin2β],

      (13)

      M2S,33=14λ2v2(MAμ/sin2β)2+κvsAκ+4(κvs)212λκv2sin2β,

      (14)

      where M2A is defined as

      M2A=2μ(ASUSYλ+κvs)sin2β.

      (15)

      Notably, ASUSYλ is the SUSY scale equivalent of Aλ, derived from the GUT scale parameters by running through RGEs.

      The CP-odd Higgs mass matrix M2P in the basis (P1,P2) is expressed by

      M2P,11=M2A,

      (16)

      M2P,12=λv(Aλ2κvs),

      (17)

      M2P,22=λ(Aλ+4κvs)vuvdvs3κvsAκ.

      (18)

      Three CP-even mass eigenstates h1, h2, and h3 (mh1<mh2<mh3) are derived from the mixture of (S1,S2,S3), and two CP-odd mass eigenstates a1 and a2 (ma1<ma2) are derived from (P1,P2). This can be represented as

      (h1h2h3)=Sij(S1S2S3),

      (19)

      (a1a2)=Pij(P1P2),

      (20)

      where Sij and Pij are the mixing matrices that diagonalize the mass matrices M2S and M2P, respectively. For corrections to Higgs boson masses, we consider adjustments using a combination of full one-loop top/bottom, leading-log two-loop top/bottom, and leading-log one-loop electroweak effects [55], which have been implemented in the NMSSMTools-6.0.2 package.

      Among the three CP-even Higgs bosons (hi, where i=1,2,3), the 125GeV SM-like Higgs could be either h1 or h2, both of which are predominantly doublet-dominated scalars. The remaining CP-even Higgs bosons include another doublet-dominated scalar and a singlet-dominated scalar. For the two CP-odd Higgs bosons (ai, where i=1,2), one is doublet-dominated, and the other is singlet-dominated. The singlet-dominated Higgs boson rarely couples to fermions because the singlet S interacts only with the Higgs sector. This property makes it difficult to detect at the LHC. In contrast, the doublet-dominated Higgs boson couples to fermions, which facilitates its detection. Our study focuses only on the heavy doublet-dominated CP-even Higgs H and CP-odd Higgs A because of their detectability. The couplings to up/down-type fermions of these heavy Higgs bosons, H and A, are defined as follows:

      CSUSYHuu=imuvcotβ

      (21)

      CSUSYHdd=imdvtanβ

      (22)

      CSUSYAuu=muvcotβγ5

      (23)

      CSUSYAdd=mdvtanβγ5

      (24)

      The reduced couplings of these heavy Higgs bosons, H and A, are defined as follows:

      CHuu=CSUSYHuu/CSMHuu=cotβ

      (25)

      CAuu=CSUSYAuu/CSMAuu=cotβ

      (26)

      CHdd=CSUSYHdd/CSMHdd=tanβ

      (27)

      CAdd=CSUSYAdd/CSMAdd=tanβ

      (28)

      Furthermore, when tanβ is significantly larger than 1 (tanβ1), M2S,11 closely approximates M2A. In addition, the Higgs bosons H and A become degenerate, which implies that they have the same mass and exhibit identical couplings to quarks.

    III.   RESULTS AND DISCUSSION
    • In this study, we explore the detectability of the heavy doublet-dominated CP-even Higgs (H) and CP-odd Higgs (A) in the scNMSSM, at a 100 TeV hadron collider. We set the upper mass limit for the Higgs at 10 TeV, represented as

      hi,aj<10TeVfor  i=1,2,3;j=1,2.

      (29)

      Therefore, we consider the relevant parameter space in the scNMSSM as follows:

      0.0<λ<0.7,|κ|<0.7,1<tanβ<60,0.0<μ,M0,M1/2<10TeV,|A0|,|Aλ|,|Aκ|<10TeV.

      λ is set to be positive to ensure that μ>0. κ is allowed to be either positive or negative, providing a more comprehensive exploration of the parameter space.

      We use the package NMSSMTools-6.0.2 [5861] to scan the parameter space and calculate relevant quantities, considering the following constraints: (i) theoretical constraints including vacuum stability and without Landau pole below the GUT scale [58, 59]; (ii) flavor constraints from rare B-meson decays and D-meson mass differences [6265]; (iii) 123−127 GeV Higgs boson with signal predictions that are globally consistent with LHC Higgs data [3, 4, 6669]; (iv) constraints from searches for additional Higgs bosons and exotic decays of the SM-like Higgs, using HiggsBounds-5.5.0, including a limit of 10.7% on invisible Higgs decay [6974]; (v) upper bounds on the dark matter relic density from WMAP/ Planck [75, 76]; (vi) direct dark matter search constraints from XENON1T [77, 78], PICO-60 [79], PandaX-4T [80, 81], and LUX-ZEPLIN [82]; and (vii) constraints from direct SUSY searches at the LHC and LEP, using the package SModelS-v2.2.1 [8389].

      For the samples satisfying the above theoretical and experimental constraints, we observe the following properties.

      ● The squarks of the first two generations are heavier than 2.2TeV, with the lightest squark, ˜t1, exceeding 1TeV. These mass limits are a direct result of constraints from LHC searches and naturalness requirements.

      ● The third-generation sleptons can be as light as approximately 170GeV, constrained by LHC search data.

      ● The gluino mass exceeds 2TeV, constrained by LHC search data. Consequently, given the universal gaugino mass condition at the GUT scale, the bino and wino masses exceed 340GeV and 620GeV, respectively.

      ● The mass range for the lightest neutralino varies from 4GeV to 4TeV, typically dominated by bino and singlino compositions, with some higgsino admixture. This range is constrained by dark matter experiments, such as relic density and direct searches, and by the composition of the neutralino itself.

      ● In the Higgs sector, we categorize the samples into two types, a classification emerging from the extended Higgs sector of the NMSSM:

      - h1 is the 125GeV SM-like Higgs. h2 and h3 are heavy CP-even Higgs bosons, while a1 and a2 are heavy CP-odd Higgs bosons.

      - h2 is the 125GeV SM-like Higgs. The light CP-even Higgs h1 and light CP-odd Higgs a1 are typically singlet-dominant. The heavy CP-even Higgs h3 and light CP-odd Higgs a2 are typically doublet-dominant.

      In this study, we focus on doublet-dominant heavy Higgs due to the difficulty of detecting singlet-dominant Higgs. There are two types to consider. In the first type, h1 resembles the SM-like Higgs, with either h2 or h3 being doublet-dominant; the same is valid for a1 and a2, where one of them is doublet-dominant. We label the heavy CP-even and CP-odd doublet-dominant Higgs bosons as H and A, respectively. In the second type, h2 acts as the SM-like Higgs, with h3 and a2 typically being doublet-dominant, also denoted as H and A. Thus, H and A represent the heavy CP-even and CP-odd doublet-dominant Higgs bosons in subsequent discussions. For the heavy Higgs bosons H and A, which have masses ranging from 0.6TeV to 10TeV, we calculate their production cross sections and decay branching ratios. We also compare the ppbˉbHbˉbtˉt signal with simulation results in Ref. [52].

      In Fig. 1, we show the mass and reduced coupling of the heavy doublet-dominated Higgs bosons H and A in the scNMSSM. The observations from these figures can be summarized as follows.

      Figure 1.  (color online) Surviving samples are shown in the planes of mA versus mH (left), reduced coupling CAuu versus CHuu (middle), and reduced coupling CAdd versus CHdd (right). From left to right, the colors represent MA, 1/tanβ, and tanβ respectively. Samples with larger values of tanβ are plotted on top of those with smaller values.

      ● In the left panel, the surviving samples are plotted on the mA versus mH plane, with colors indicating MA. H and A have nearly identical masses, approximately equal to the parameter MA. This similarity arises because, according to Eq. (16), P1 is the CP-odd doublet-dominated Higgs; as A is also denoted as the CP-odd doublet-dominated Higgs, it follows that mAMA. Furthermore, S1 is the CP-even doublet-dominated Higgs, labeled here as H. According to Eq. (9), when tanβ1, mHMA. The mass of H and A is between 0.6TeV and 10TeV.

      ● In the middle panel, the surviving samples are displayed on the plane of reduced coupling with up-type fermions for A versus H, with the colors indicating 1/tanβ. For most samples, CAuu and CHuu are approximately equal to 1/tanβ. This approximation arises because the doublet components of H and A are neither exactly equal nor exactly equal to 1. Furthermore, the values of the reduced couplings CHuu and CAuu range from 0 to 0.8.

      ● In the right panel, the surviving samples are plotted on the plane of reduced coupling with down-type fermions for A versus H, with colors representing tanβ. The results are similar to those in the middle panel; for most samples, CAdd and CHdd approximate tanβ. This approximation is also due to the doublet components of H and A not being exactly equal or exactly equal to 1. Additionally, the values of the reduced couplings CHdd and CAdd vary from 0 to 50.

      In Fig. 2, we show the decay properties of the CP-even doublet-dominated heavy Higgs H in the scNMSSM, with colors representing tanβ. As both heavy Higgs bosons A and H are doublet-dominated, their couplings to fermions show a very small difference. The only difference is that Br(AVV/˜V˜V)=0. However, this difference is minimal due to the small coefficient CHVV. Consequently, the decay properties of the CP-odd doublet-dominated heavy Higgs A are very similar to those of H. Therefore, the plot for A is omitted. The observations from these figures can be summarized as follows.

      Figure 2.  (color online) Surviving samples in the planes of branching ratios versus mH, with colors representing tanβ. The branching ratios pertain to the decays of the heavy CP-even Higgs H into tˉt, bˉb, τ+τ, all possible lighter Higgs bosons, and all possible SUSY particles, respectively. Samples with larger values of tanβ are plotted over those with smaller values.

      ● The dominant branching ratios consistently arise from the decays to tˉt, bˉb and SUSY particles. These branching ratios reach values close to 1.

      ● In the upper left panel, the branching ratio of H to tˉt is inversely proportional to tanβ; that is, a smaller tanβ corresponds to a larger branching ratio Br(Htˉt). This relationship is due to CHuu being directly proportional to 1/tanβ. Consequently, when tanβ<10, the branching ratio Br(Htˉt) exceeds 0.2. As tanβ approaches 1, the branching ratio Br(Htˉt) tends toward 1.

      ● In the upper middle and right panels, the branching ratios of H to bˉb and τ+τ are proportional to tanβ; a larger tanβcorresponds to higher branching ratios Br(Hbˉb) and Br(Hτ+τ). This proportionality is due to CHdd being directly proportional to tanβ. Additionally, when tanβ exceeds 40, the maximum branching ratio Br(Hbˉb) can reach 0.8, while the maximum branching ratio Br(Hτ+τ) can reach only 0.2. Furthermore, the branching ratio Br(Hτ+τ) is generally lower than Br(Hbˉb) due to the lower mass of τ compared to b, as the coupling strength of Higgs with fermions is proportional to their mass.

      ● In the lower left panel, the branching ratios of H to light Higgs bosons are relatively small, reaching a maximum of approximately 0.6. Additionally, for samples where tanβ exceeds 40, the maximum branching ratio Br(Hlight Higgs) is only 0.1.

      ● In the lower right panel, the maximum branching ratios of H to SUSY particles can approach 0.8. Additionally, when tanβ ranges from 10 to 30, the branching ratios Br(HSUSY) can approach this maximum value of 0.8, remaining above 0.5. When tanβ is smaller than 10, the heavy Higgs H predominantly decays into tˉt; conversely, when tanβ exceeds 30, it primarily decays into bˉb.

      We calculate the cross sections for the process ppbˉbH in the SM with mH ranging from 0.5 to 10TeV at s=100TeV using MG5_aMC_v2.6.7 [90, 91]. We used the "SM" model in MadGraph to conduct these calculations. The calculated cross section for mH or mA in our samples is multiplied by the square of the reduced coupling CHbb and branching ratio Br(H/Atˉt). As the masses and various couplings of the heavy Higgs bosons H and A are very similar, along with nearly identical branching ratios Br(Htˉt) and Br(Atˉt) and similar reduced couplings CHbb and CAbb, the heavy Higgs bosons H and A are considered degenerate in the detection channel ppbˉbH/Abˉbtˉt. Therefore, the cross section for the ppbˉbH/Abˉbtˉt channel is twice that of the individual H or A channels. Production rates for our samples in the ppbˉbH/Abˉbtˉt channel are presented in the left panel of Fig. 3, where colors indicate tanβ. The red and green curves represent the model-independent exclusion and discovery reaches, respectively, with an integrated luminosity of 3ab1 at 100TeV, as depicted in Fig. 9 of Ref. [52]. In the calculation of the SM cross section, we employed both four-flavor scheme (4FS) and five-flavor scheme (5FS) cross sections [92], and combined them using the formula from Ref. [93]:

      Figure 3.  (color online) Surviving samples are shown in the planes of 1/tan2β/Γtot(H) versus Br(Htˉt) (left), heavy Higgs total decay width Γtot(H) versus heavy Higgs mass mH (middle), and cross section of ppbˉbHbˉbtˉt versus heavy Higgs mass mH (right), where the colors of the samples indicate tanβ. The red and green curves represent the model-independent exclusion and discovery ranges, respectively, for the ppbˉbH/Abˉbtˉt channel, with an integrated luminosity of 3ab1 at 100TeV, according to Fig. 9 in Ref. [52]. Samples with larger values of tanβ are plotted on top of those with smaller values.

      σ=σ4FS+ωσ5FS1+ω,

      (30)

      where ω=ln(mH/mb)2.

      In Fig. 3 we show the cross section for the ppbˉbH/Abˉbtˉt channel of the CP-even doublet-dominated heavy Higgs H/A in the scNMSSM, with colors representing tanβ. As the heavy Higgs A and H are considered degenerate, the cross section σ(ppbˉbH/Abˉbtˉt)=2σ(ppbˉbHbˉbtˉt). The observations from these plots can be summarized as follows.

      ● In the left panel, 1/tan2β/Γtot(H) appears to be directly proportional to Br(Htˉt), because the decay diagram for Br(Htˉt) includes a coupling vertex CHuu. In the calculation of the decay cross-section, a C2Huu term is introduced. Thus, Br(Htˉt) is proportional to 1/tan2β. Additionally, the branching ratio Br(Htˉt) is inversely proportional to the total decay width Γtot(H), which is represented as

      Br(Htˉt)=σ(Htˉt)Γtot(H)1/tan2βΓtot(H).

      (31)

      ● In the middle panel, the total decay width Γtot(H) of the heavy Higgs increases exponentially with tanβ. Additionally, when tanβ remains constant, Γtot(H) increases with the mass of the heavy Higgs mH.

      ● In the right panel, the cross section σ(ppbˉbH/Abˉbtˉt) decreases rapidly as the mass of the heavy Higgs mH increases. The cross section for ppbˉbHbˉbtˉt can be approximated as follows:

      σ(ppbˉbHbˉbtˉt)σSM(ppbˉbH)C2HddBr(Htˉt)σSM(ppbˉbH)Γtot(H)

      (32)

      This decline is because σ(ppbˉbHbˉbtˉt) is proportional to σSM(ppbˉbH), and the production cross section σSM(ppbˉbH) diminishes with an increase in mass. Samples with the smaller tanβ values have larger cross sections σ(ppbˉbHbˉbtˉt), because σ(ppbˉbHbˉbtˉt) is inversely proportional to the total decay width Γtot(H), and Γtot(H) exponentially increases as the tanβ increases.

      ● In the right panel, the regions above the green and red curves indicate where the samples can be covered by 2 σ and 5 σ, respectively, with an integrated luminosity of 3ab1 at 100TeV. This implies that, through the ppbˉbH/Abˉbtˉt channel in the scNMSSM, samples with a heavy Higgs mass mH<2TeV can be tested at the 100TeV collider with an integrated luminosity of 3ab1. Samples with the heavy Higgs mass mH>7TeV are below the exclusion and discovery curves, and thus, they cannot be discovered or excluded. Samples with the heavy Higgs mass in the range of 27TeV and tanβ<20 can be tested at the 100TeV collider with an integrated luminosity of 3ab1.

      In Table 1, we present four benchmark samples detailing the Higgs sector, where σ(X) represents the cross section σ(ppbˉbXbˉbtˉt). The heavy Higgs bosons H and A, corresponding to h3 and a2, respectively, are doublet-dominated, while S233 and P222 indicate the singlet components in H and A. H and A have minimal singlet components, which suggests that h2 and a1 are primarily singlet-dominated. Owing to their weak coupling to fermions, these singlet-dominated bosons, h2 and a1, are difficult to detect at colliders.

      P1 P2 P3 P4
      λ 0.61 0.21 0.10 0.10
      κ 0.36 −0.21 −0.42 0.67
      tanβ 2.07 4.98 20.02 47.91
      μ/GeV 361 345 295 498
      M0/GeV 8072 1506 5811 9596
      M12/GeV 3402 5569 3017 9289
      A0/GeV 7306 −6275 539 9862
      Aλ/GeV 4961 1230 4983 2357
      Aκ/GeV 2720 252 3769 −3588
      mh1/GeV 124 124 124 125
      mh2/GeV 341 648 1942 6796
      mH/GeV 720 2025 4030 7950
      ma1/GeV 512 277 2920 1860
      mA/GeV 716 2026 4031 7950
      S231 0.99 1.00 1.00 1.00
      S232 0.00 0.00 0.00 0.00
      S233 0.01 0.00 0.00 0.00
      P221 1.00 1.00 1.00 1.00
      P222 0.00 0.00 0.00 0.00
      Ch2uu 0.1 0.0 0.0 0.0
      CHuu −0.5 −0.2 −0.1 0.0
      Ca1uu 0.0 0.0 0.0 0.0
      CAuu 0.5 0.2 0.0 0.0
      Ch2dd 0.4 0.1 0.0 0.3
      CHdd 2.0 5.0 20.0 47.9
      Ca1dd 0.0 −0.2 −0.3 0.1
      CAdd 2.1 5.0 20.0 47.9
      Br(h2tˉt) 0 0.01 4.4×104 7.9×108
      Continued on next page

      Table 1.  Four benchmark points for surviving samples, where σ(X) denotes the cross section σ(ppbˉbXbˉbtˉt). H and A represent the doublet-dominated heavy Higgs bosons, while S233 and P222 indicate the singlet components in H and A, respectively.

    IV.   CONCLUSION
    • In this study, we explored the potential for detecting heavy Higgs bosons in the ppbˉbH/Abˉbtˉt channel at a 100 TeV hadron collider within the semi-constrained NMSSM. First, we scanned the relevant parameter space with the NMSSMTools package, which includes theoretical constraints such as vacuum stability and Landau poles, as well as experimental constraints such as Higgs data, B physics, sparticle searches, dark matter relic density, and direct detection experiments. We observed that singlet-dominated Higgs bosons S are difficult to detect due to their limited interactions outside the Higgs sector. Therefore, our analysis primarily focused on the more detectable heavy doublet-dominated CP-even Higgs H and CP-odd Higgs A, limiting their masses to below 10TeV to remain detectable. The presence of a CP-even Higgs (h1 or h2) resembling the 125 GeV SM-like Higgs does not affect these findings. As the heavy Higgs H and A are nearly identical in mass and couplings, the cross section for the combined channel ppbˉbH/Abˉbtˉt is effectively double that of the single H channel.

      We calculated their decay branching ratios and production rates, and compared them with the simulation results in Ref. [52]. We can summarize the following conclusions about the heavy Higgs bosons A and H, with masses ranging from 0.6 to 10 TeV, in the semi-constrained NMSSM.

      ● When the heavy Higgs bosons are doublet-dominated, their reduced couplings with up-type fermions, CHuu and CAuu, are approximately equal to 1/tanβ. This relationship causes the branching ratio of H/A to tˉt to be inversely proportional to tanβ; a smaller tanβ results in a larger branching ratio Br(Htˉt). Conversely, the reduced couplings with down-type fermions, CHdd and CAdd, approximate to tanβ, leading to branching ratios of H to bˉb and τ+τ that are directly proportional to tanβ.

      ● When tanβ is smaller than 10, the heavy Higgs H predominantly decays into tˉt, with the branching ratio Br(Htˉt) reaching 1. When tanβ exceeds 30, it primarily decays into bˉb, with a branching ratio Br(Hbˉb) up to 0.8 and Br(Hτ+τ) up to 0.2. For tanβ values between 10 and 30, the branching ratio Br(HSUSY) is dominant, reaching 0.8.

      ● The branching ratio Br(Htˉt) is proportional to 1/tan2β and inversely proportional to the total decay width Γtot(H). Furthermore, the total decay width of the heavy Higgs, Γtot(H), increases exponentially with tanβ.

      ● The cross section σ(ppbˉbH/Abˉbtˉt) decreases rapidly as the mass of the heavy Higgs (mH) increases and is inversely proportional to the total decay width Γtot(H). Consequently, this cross section also decreases exponentially with an increase in tanβ.

      ● For the ppbˉbH/Abˉbtˉt channel at a 100 TeV collider with an integrated luminosity of 3 ab1 in the semi-constrained NMSSM.

      ● Heavy Higgs bosons with a mass mH<2 TeV can be tested.

      ● Heavy Higgs bosons with a mass mH>7TeV are below the exclusion and discovery thresholds and therefore cannot be discovered or excluded.

      ● For heavy Higgs masses in the range of 2−7 TeV, those with tanβ20 can be tested, while those with tanβ20 cannot be discovered or excluded.

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