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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 [1−4]. 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) [5−16], Next-to-MSSM (NMSSM) [17−32], Minimal Dilaton Model (MDM) [33−37], 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 , andhV , which are reviewed in [42, 43]. Recently, evidence for a new scalar around 151 GeV was accumulated with significances of4.3σ locally and3.9σ globally [44], subsequently revised to4.1σ locally and3.5σ 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 TeVpp 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 thepp→bˉbH/A→bˉbττ andpp→bˉbH/A→bˉbtˉt channels at a 100 TeVpp collider and proposed pushing the exclusion limits for heavy Higgs searches up toMH∼10TeV , with exceptions in regions of lowtanβ . Furthermore, the analysis in Ref. [13] explored thepp→H/A→˜χ01˜χ∓2 process, revealing the4ℓ+⧸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
pp→bˉbH/A→bˉbtˉt 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.
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The NMSSM extends the MSSM by introducing an additional singlet superfield, denoted as
ˆS , where the superpotential of theZ3 -symmetric NMSSM is defined asWNMSSM=WMSSM|μ=0+λˆSˆHu⋅ˆHd+κˆS33,
(1) where
WMSSM|μ=0 is the superpotential of the MSSM without the μ-term, λ and κ are coupling constants,ˆHu andˆHd are the doublet Higgs superfields, andˆS is the added singlet superfield. After electroweak symmetry breaking, the singlet scalar's vacuum expectation value (VEV), denoted asvs , dynamically generates the massive μ-term [55, 56]μ≡λvs.
(2) Concurrently, the scalar components
Hu andHd also attain VEVs, labeled asvu andvd , respectively. This leads to the introduction of a new parametertanβ , defined astanβ≡vu/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+λAλSHu⋅Hd+13κAκS3+h.c.,
(4) where
LsoftMSSM|μ=0 denotes the MSSM's soft SUSY breaking terms with the μ parameter set to zero. The symbolsHu andHd refer to the scalar components of the Higgs doublets,Aλ andAκ represent the trilinear coupling constants with mass dimension, andmS 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 , andm2S , can differ fromM20+μ2 . Furthermore, the trilinear coupling constantsAλ andAκ may vary independently fromA0 . 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 andM0 represent the universal sfermion mass and universal gaugino mass, respectively, whileA0 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 asH1=cosβHu+εsinβH∗d=(H+S1+iP1√2),
(6) H2=sinβHu−εcosβH∗d=(G+v+S2+iG0√2),
(7) H3=S=vs+S3+iP2√2,
(8) where
ε=(01−10) , andS1 ,S2 , andS3 create the CP-even basis, whileP1 andP2 establish the CP-odd basis.H2 is identified as the SM-like Higgs,H1 represents a new Higgs doublet field, andH3 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+(m2Z−λ2v2)sin22β,
(9) M2S,12=−12(m2Z−λ2v2)sin4β,
(10) M2S,13=−(M2A2μ/sin2β+κvs)λvcos2β,
(11) M2S,22=m2Zc o s22β+λ2v2sin22β,
(12) M2S,23=2λμv[1−(MA2μ/sin2β)2−κ2λsin2β],
(13) M2S,33=14λ2v2(MAμ/sin2β)2+κvsAκ+4(κvs)2−12λκv2sin2β,
(14) where
M2A is defined asM2A=2μ(ASUSYλ+κvs)sin2β.
(15) Notably,
ASUSYλ is the SUSY scale equivalent ofAλ , derived from the GUT scale parameters by running through RGEs.The CP-odd Higgs mass matrix
M2P in the basis(P1,P2) is expressed byM2P,11=M2A,
(16) M2P,12=λv(Aλ−2κvs),
(17) M2P,22=λ(Aλ+4κvs)vuvdvs−3κvsAκ.
(18) Three CP-even mass eigenstates
h1 ,h2 , andh3 (mh1<mh2<mh3 ) are derived from the mixture of(S1,S2,S3) , and two CP-odd mass eigenstatesa1 anda2 (ma1<ma2 ) are derived from(P1,P2) . This can be represented as(h1h2h3)=Sij(S1S2S3),
(19) (a1a2)=Pij(P1P2),
(20) where
Sij andPij are the mixing matrices that diagonalize the mass matricesM2S andM2P , 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 theNMSSMTools-6.0.2 package.Among the three CP-even Higgs bosons (
hi , wherei=1,2,3 ), the125GeV SM-like Higgs could be eitherh1 orh2 , 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 , wherei=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 (tanβ≫1 ),M2S,11 closely approximatesM2A . In addition, the Higgs bosons H and A become degenerate, which implies that they have the same mass and exhibit identical couplings to quarks. -
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 [58−61] 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 [62−65]; (iii) 123−127 GeV Higgs boson with signal predictions that are globally consistent with LHC Higgs data [3, 4, 66−69]; (iv) constraints from searches for additional Higgs bosons and exotic decays of the SM-like Higgs, usingHiggsBounds-5.5.0 , including a limit of 10.7% on invisible Higgs decay [69−74]; (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 packageSModelS-v2.2.1 [83−89].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 , exceeding1TeV . 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 exceed340GeV and620GeV , respectively.● The mass range for the lightest neutralino varies from
4GeV to4TeV , 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:
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h1 is the125GeV SM-like Higgs.h2 andh3 are heavy CP-even Higgs bosons, whilea1 anda2 are heavy CP-odd Higgs bosons.-
h2 is the125GeV SM-like Higgs. The light CP-even Higgsh1 and light CP-odd Higgsa1 are typically singlet-dominant. The heavy CP-even Higgsh3 and light CP-odd Higgsa2 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 eitherh2 orh3 being doublet-dominant; the same is valid fora1 anda2 , 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, withh3 anda2 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 from0.6TeV to10TeV , we calculate their production cross sections and decay branching ratios. We also compare thepp→bˉbH→bˉbtˉt 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 versusmH (left), reduced couplingCAuu versusCHuu (middle), and reduced couplingCAdd versusCHdd (right). From left to right, the colors representMA ,1/tanβ , andtanβ respectively. Samples with larger values oftanβ are plotted on top of those with smaller values.● In the left panel, the surviving samples are plotted on the
mA versusmH plane, with colors indicatingMA . H and A have nearly identical masses, approximately equal to the parameterMA . 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 thatmA≈MA . Furthermore,S1 is the CP-even doublet-dominated Higgs, labeled here as H. According to Eq. (9), whentanβ≫1 ,mH≈MA . The mass of H and A is between0.6TeV and10TeV .● 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 andCHuu are approximately equal to1/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 couplingsCHuu andCAuu 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 andCHdd approximatetanβ . 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 couplingsCHdd andCAdd 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 thatBr(A→VV/˜V˜V)=0 . However, this difference is minimal due to the small coefficientCHVV . 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 representingtanβ . The branching ratios pertain to the decays of the heavy CP-even Higgs H intotˉt ,bˉb ,τ+τ− , all possible lighter Higgs bosons, and all possible SUSY particles, respectively. Samples with larger values oftanβ 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 totanβ ; that is, a smallertanβ corresponds to a larger branching ratioBr(H→tˉt) . This relationship is due toCHuu being directly proportional to1/tanβ . Consequently, whentanβ<10 , the branching ratioBr(H→tˉt) exceeds 0.2. Astanβ approaches 1, the branching ratioBr(H→tˉt) tends toward 1.● In the upper middle and right panels, the branching ratios of H to
bˉb andτ+τ− are proportional totanβ ; a largertanβ corresponds to higher branching ratiosBr(H→bˉb) andBr(H→τ+τ−) . This proportionality is due toCHdd being directly proportional totanβ . Additionally, whentanβ exceeds 40, the maximum branching ratioBr(H→bˉb) can reach 0.8, while the maximum branching ratioBr(H→τ+τ−) can reach only 0.2. Furthermore, the branching ratioBr(H→τ+τ−) is generally lower thanBr(H→bˉb) 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 ratioBr(H→light 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 ratiosBr(H→SUSY) can approach this maximum value of 0.8, remaining above 0.5. Whentanβ is smaller than 10, the heavy Higgs H predominantly decays intotˉt ; conversely, whentanβ exceeds 30, it primarily decays intobˉb .We calculate the cross sections for the process
pp→bˉbH in the SM withmH ranging from0.5 to10TeV 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 formH ormA in our samples is multiplied by the square of the reduced couplingCHbb and branching ratioBr(H/A→tˉt) . As the masses and various couplings of the heavy Higgs bosons H and A are very similar, along with nearly identical branching ratiosBr(H→tˉt) andBr(A→tˉt) and similar reduced couplingsCHbb andCAbb , the heavy Higgs bosons H and A are considered degenerate in the detection channelpp→bˉbH/A→bˉbtˉt . Therefore, the cross section for thepp→bˉbH/A→bˉbtˉt channel is twice that of the individual H or A channels. Production rates for our samples in thepp→bˉbH/A→bˉbtˉt channel are presented in the left panel of Fig. 3, where colors indicatetanβ . The red and green curves represent the model-independent exclusion and discovery reaches, respectively, with an integrated luminosity of3ab−1 at100TeV , 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) versusBr(H→tˉt) (left), heavy Higgs total decay widthΓtot(H) versus heavy Higgs massmH (middle), and cross section ofpp→bˉbH→bˉbtˉt versus heavy Higgs massmH (right), where the colors of the samples indicatetanβ . The red and green curves represent the model-independent exclusion and discovery ranges, respectively, for thepp→bˉbH/A→bˉbtˉt channel, with an integrated luminosity of3ab−1 at100TeV , according to Fig. 9 in Ref. [52]. Samples with larger values oftanβ 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
pp→bˉbH/A→bˉbtˉt channel of the CP-even doublet-dominated heavy HiggsH/A in the scNMSSM, with colors representingtanβ . As the heavy Higgs A and H are considered degenerate, the cross sectionσ(pp→bˉbH/A→bˉbtˉt)=2σ(pp→bˉbH→bˉbtˉt) . The observations from these plots can be summarized as follows.● In the left panel,
1/tan2β/Γtot(H) appears to be directly proportional toBr(H→tˉt) , because the decay diagram forBr(H→tˉt) includes a coupling vertexCHuu . In the calculation of the decay cross-section, aC2Huu term is introduced. Thus,Br(H→tˉt) is proportional to1/tan2β . Additionally, the branching ratioBr(H→tˉt) is inversely proportional to the total decay widthΓtot(H) , which is represented asBr(H→tˉt)=σ(H→tˉt)Γtot(H)∼1/tan2βΓtot(H).
(31) ● In the middle panel, the total decay width
Γtot(H) of the heavy Higgs increases exponentially withtanβ . Additionally, whentanβ remains constant,Γtot(H) increases with the mass of the heavy HiggsmH .● In the right panel, the cross section
σ(pp→bˉbH/A→bˉbtˉt) decreases rapidly as the mass of the heavy HiggsmH increases. The cross section forpp→bˉbH→bˉbtˉt can be approximated as follows:σ(pp→bˉbH→bˉbtˉt)≈σSM(pp→bˉbH)⋅C2Hdd⋅Br(H→tˉt)≈σSM(pp→bˉbH)Γtot(H)
(32) This decline is because
σ(pp→bˉbH→bˉbtˉt) is proportional toσSM(pp→bˉbH) , and the production cross sectionσSM(pp→bˉbH) diminishes with an increase in mass. Samples with the smallertanβ values have larger cross sectionsσ(pp→bˉbH→bˉbtˉt) , becauseσ(pp→bˉbH→bˉbtˉt) is inversely proportional to the total decay widthΓtot(H) , andΓtot(H) exponentially increases as thetanβ 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
3ab−1 at100TeV . This implies that, through thepp→bˉbH/A→bˉbtˉt channel in the scNMSSM, samples with a heavy Higgs massmH<2TeV can be tested at the100TeV collider with an integrated luminosity of3ab−1 . Samples with the heavy Higgs massmH>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 of2−7TeV andtanβ<20 can be tested at the100TeV collider with an integrated luminosity of3ab−1 .In Table 1, we present four benchmark samples detailing the Higgs sector, where
σ(X) represents the cross sectionσ(pp→bˉbX→bˉbtˉt) . The heavy Higgs bosons H and A, corresponding toh3 anda2 , respectively, are doublet-dominated, whileS233 andP222 indicate the singlet components in H and A. H and A have minimal singlet components, which suggests thath2 anda1 are primarily singlet-dominated. Owing to their weak coupling to fermions, these singlet-dominated bosons,h2 anda1 , 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(h2→tˉt) 0 0.01 4.4×10−4 7.9×10−8 Continued on next page Table 1. Four benchmark points for surviving samples, where
σ(X) denotes the cross sectionσ(pp→bˉbX→bˉbtˉt) . H and A represent the doublet-dominated heavy Higgs bosons, whileS233 andP222 indicate the singlet components in H and A, respectively. -
In this study, we explored the potential for detecting heavy Higgs bosons in the
pp→bˉbH/A→bˉbtˉt channel at a 100 TeV hadron collider within the semi-constrained NMSSM. First, we scanned the relevant parameter space with theNMSSMTools 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 below10TeV to remain detectable. The presence of a CP-even Higgs (h1 orh2 ) 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 channelpp→bˉbH/A→bˉbtˉt 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 andCAuu , are approximately equal to1/tanβ . This relationship causes the branching ratio ofH/A totˉt to be inversely proportional totanβ ; a smallertanβ results in a larger branching ratioBr(H→tˉt) . Conversely, the reduced couplings with down-type fermions,CHdd andCAdd , approximate totanβ , leading to branching ratios of H tobˉb andτ+τ− that are directly proportional totanβ .● When
tanβ is smaller than 10, the heavy Higgs H predominantly decays intotˉt , with the branching ratioBr(H→tˉt) reaching 1. Whentanβ exceeds 30, it primarily decays intobˉb , with a branching ratioBr(H→bˉb) up to 0.8 andBr(H→τ+τ−) up to 0.2. Fortanβ values between 10 and 30, the branching ratioBr(H→SUSY) is dominant, reaching 0.8.● The branching ratio
Br(H→tˉt) is proportional to1/tan2β and inversely proportional to the total decay widthΓtot(H) . Furthermore, the total decay width of the heavy Higgs,Γtot(H) , increases exponentially withtanβ .● The cross section
σ(pp→bˉbH/A→bˉbtˉt) decreases rapidly as the mass of the heavy Higgs (mH ) increases and is inversely proportional to the total decay widthΓtot(H) . Consequently, this cross section also decreases exponentially with an increase intanβ .● For the
pp→bˉbH/A→bˉbtˉt channel at a 100 TeV collider with an integrated luminosity of 3 ab−1 in the semi-constrained NMSSM.● Heavy Higgs bosons with a mass
mH<2 TeV can be tested.● Heavy Higgs bosons with a mass
mH>7 TeV 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
tanβ≲20 can be tested, while those withtanβ≳20 cannot be discovered or excluded.
Exploration of heavy Higgs bosons at a 100 TeV hadron collider withinthe semi-constrained next-to-minimal supersymmetric standard model
- Received Date: 2024-04-19
- Available Online: 2024-09-15
Abstract: In this study, we explore the detectability of heavy Higgs bosons in the