Signature of the Maximally Symmetric 2HDM via W^{\pm}/Z-Quadruplet Productions at the LHC
SSignature of the Maximally Symmetric 2HDM via W ± /Z -Quadruplet Productions at the LHC N. Darvishi ∗ , † and M.R. Masouminia ‡ ∗ School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom † Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland ‡ Institute for Particle Physics Phenomenology, Department of Physics,Durham University, Durham DH1 3LE, United Kingdom
ABSTRACT
We consider the Maximally Symmetric Two-Higgs Doublet Model (MS-2HDM) inwhich the so-called Standard Model (SM) alignment can be achieved naturally by thevirtue of an SO(5) symmetry imposed on the 2HDM. We investigate the signature ofthe MS-2HDM via pp → HX → V V ∗ X and pp → HHX → V V ∗ V (cid:48) V (cid:48)∗ X processesat the LHC for different values of tan β . We perform our calculations with NLO QCDaccuracy, using the Herwig 7 multi-purpose event generator at √ s = 13 TeV center-of-mass energy. We show that the production of single SM-like Higgs bosons via W ± /Z -pairs is completely aligned with the SM. Interestingly, the presence of the heavy Higgsstates significantly enhances the cross-section for the W ± /Z -quadruplet productionchannels in the low- p ⊥ regions. These vital analyses may aid the future discovery ofthis minimal and very predictive extension of the SM and can be generalised to otherrealisations of the 2HDM. a r X i v : . [ h e p - ph ] D ec I. INTRODUCTION
For many years, the Standard Model (SM) has been the cornerstone for our understandingof the fundamental interactions of Particle Physics [2–5]. This was brought to its climax withthe discovery of the Higgs boson at CERN’s Large Hadron Collider (LHC) [6, 7]. The datacollected from this discovery imposes constraints over the coupling strengths of the Higgsboson, primarily to the electroweak (EW) gauge bosons ( V = W ± , Z ), which are very closeto SM predictions [8, 9]. Despite all these achievements, the SM still falls short of answeringsome of the most profound questions such as the origin of the observed matter-antimatterasymmetry and the dark matter relic abundance in the Universe. This has fueled numeroustheoretical and experimental scrutinise in the study of theories Beyond the SM (BSM),particularly for models with extended Higgs sectors. These new-born theories regardless oftheir motivational and structural differences must restore those predictions of the SM thatare consistent with the LHC observations. This is only possible within the so-called SMalignment limit [10–19].One of the simplest extensions of the SM is the Two-Higgs Doublet Model (2HDM), whichenriches the SM scalar sector by introducing a second complex scalar doublet [10, 11, 20–22].This extension can provide new sources of CP violation [20, 21], introduce stable scalar DMcandidates [23–25], and give rise to EW baryogenesis [26, 27]. Interestingly, the potentialof this model contains the maximum number of distinct SU(2) L -preserving accidentalsymmetries as subgroups of the maximal symmetry Sp(4) ∼ SO(5) [28, 29]. Thereby, themost minimal version of the 2HDM is an SO(5)-invariant potential, the so-called MaximallySymmetric 2HDM (MS-2HDM) [14, 28–36]. In MS-2HDM, the SM alignment can emergenaturally as a consequence of an accidental SO(5) symmetry in the Higgs sector. Thissymmetry can be broken explicitly by the renormalization group (RG) effects and softly bythe bilinear scalar mass term m . A remarkable feature of this model is that all quarticcouplings can unify at very large scales µ X ∼ – GeV, for a wide range of tan β values and charged Higgs-boson masses [31, 32]. This unique feature aids to gain a minimaland very predictive model which is governed only by three parameters: the quartic couplingunification scale µ X , the mass of charged Higgs M h ± (or m ) and the value of tan β . Thesethree parameters allow one to determine the entire Higgs-mass spectrum of the model.The production of the EW gauge vector boson pairs and quadruplets have always beenamong the critical observations in the on-going attempts to probe the SM and search for signsof BSM physics at the LHC, within its high-energy hadronic scattering data. Also, theseevents have played a key role in the LHC precision measurements as well as the estimationof the irreducible backgrounds in Higgs boson searches. Moreover, since these processesare amongst the largest Higgs-tagged signatures at the current LHC energies, observing adistinct deviation from the SM theoretical predictions may be directly interpreted as a signalfor BSM physics [37, 38]. Therefore, it would be interesting to look for the possible signatureof the MS-2HDM at the LHC via W ± /Z -pair and -quadruplet production events. In thispaper, firstly we ensure that the predictions of the MS-2HDM for the pp → HX → V V ∗ X production rates are aligned with their SM counterparts. Then, we evaluate the signatureof the MS-2HDM via pp → HHX → V V ∗ V (cid:48) V (cid:48)∗ X events at the LHC for different values of tan β . We calculate these production rates up to one QCD loop and 2 jets, using Herwig 7 (v7.2.1) event generator [39–42]. The corresponding amplitudes are provided by
MadGraph5 (v2.7.3) [43] and matched to the NLO corrections using
Matchbox [44, 45]. The producedunderlying events are showered by an AO
MC@NLO matched
QCD+QED+EW partonshower [46, 47]. Finally, the results of these simulations have been analyzed using Rivet (v3.1.1) [48].The layout of the paper is as follows. After this introductory section, Section II brieflyreviews the basic features of the 2HDM and the naturally aligned MS-2HDM. We also outlinethe Higgs-mass spectrum and our misalignment predictions for Higgs-boson couplings togauge bosons. Section III shows the dominant channels for pp → HX → V V ∗ X and pp → HHX → V V ∗ V (cid:48) V (cid:48)∗ X production events at the LHC and highlights the sup-processeswhere the new heavy Higgs bosons can substantially modify these cross-sections. This sectionalso includes the calculation setup for our analysis. In Section IV, we discuss our numericalresults for single and double Higgs production events in the MS-2HDM. Particularly, weshow that the cross-section of the pp → HHX → V V ∗ V (cid:48) V (cid:48)∗ X processes is significantlyenhanced with respect to the SM. Finally, Section V contains our conclusions. II. TYPE-II 2HDM AND SM ALIGNMENT
The 2HDM contains two scalar iso-doublets, Φ , , with U(1) Y hypercharges Y Φ , = +1 / .In terms of these doublets, the most general renormalisable 2HDM potential may be conve-niently written as V = − µ (Φ † Φ ) − µ (Φ † Φ ) − (cid:104) m (Φ † Φ ) + H . c . (cid:105) + λ (Φ † Φ ) + λ (Φ † Φ ) + λ (Φ † Φ )(Φ † Φ ) + λ (Φ † Φ )(Φ † Φ )+ (cid:20) λ (Φ † Φ ) + λ (Φ † Φ )(Φ † Φ ) + λ (Φ † Φ )(Φ † Φ ) + H . c . (cid:21) , (1)where the mass terms µ , and quartic couplings λ , , , are real parameters. Instead, theremaining mass term m and the quartic couplings λ , , are complex. Out of these 14theoretical parameters, only 11 are physical, since 3 parameters can be transformed awayusing a SU(2) reparametrisation of the Higgs doublets. In the Type-II 2HDM, both scalardoublets Φ and Φ receive non-zero vacuum expectation values (VEVs). In detail, we have (cid:104) φ (cid:105) = v / √ and (cid:104) φ (cid:105) = v / √ , where t β ≡ tan β = v /v and v ≡ ( v + v ) / as the VEVof the SM Higgs doublet. After the spontaneous symmetry breaking, the standard W ± and Z bosons acquire their masses from the three would-be Goldstone bosons ( G ± , G ) [5, 49].Thereafter, the model remains with five physical scalar states: two CP-even scalars ( H and h ), one CP-odd scalar ( a ) and two charged bosons ( h ± ). The
QCD+QED+EW parton shower scheme is a new addition to
Herwig 7 which is introduced in [47]and will be available to the public with the v7.3.0 release.
The masses of the h ± and a scalars are given by M h ± = m s β c β − v λ + λ ) + v s β c β ( λ c β + λ s β ) ,M a = M h ± + v λ − λ ) , (2)where s β ≡ sin β , c β ≡ cos β . Moreover, the masses of the two CP-even scalars, H and h ,may be obtained by diagonalising the × CP-even mass matrix M S , M S = (cid:18) A CC B (cid:19) , (3)which may be explicitly written as M S = M a (cid:18) s β − s β c β − s β c β c β (cid:19) + v (cid:18) λ c β + λ s β + 2 λ s β c β λ s β c β + λ c β + λ s β λ s β c β + λ c β + λ s β λ s β + λ c β + 2 λ s β c β (cid:19) , with λ ≡ λ + λ . The mixing angle α is required for the diagonalization of M S , whichmay be determined by tan 2 α = 2 CA − B . (4)So, the CP-even mass matrix M S takes on the form (cid:99) M S = (cid:18) c β s β − s β c β (cid:19) M S (cid:18) c β − s β s β c β (cid:19) = (cid:32) (cid:98) A (cid:98) C (cid:98) C (cid:98) B (cid:33) , (5)with (cid:98) A = 2 v (cid:2) c β λ + s β c β λ + s β λ + 2 s β c β (cid:0) c β λ + s β λ (cid:1)(cid:3) , (cid:98) B = M a + λ v + 2 v (cid:2) s β c β ( λ + λ − λ ) − s β c β (cid:0) c β − s β (cid:1) ( λ − λ ) (cid:3) , (6) (cid:98) C = v (cid:2) s β c β (2 λ − λ ) − c β s β (2 λ − λ ) + c β (cid:0) − s β (cid:1) λ + s β (cid:0) c β − (cid:1) λ (cid:3) . The SM Higgs field may now be identified by the linear field combination, H SM = φ cos β + φ sin β = H cos( β − α ) + h sin( β − α ) . (7)Thus, the SM-normalised couplings of the CP-even H and h scalars to the EW gauge bosonsare given by g HV V = cos( β − α ) , g hV V = sin( β − α ) . (8)The SM alignment condition, cos( β − α ) = 1 (or sin( β − α ) = 1 ), can be realised in twodifferent ways: (i) (cid:98) C → and (ii) M h ± ∼ M a (cid:29) v . However, our primary interest lies innatural realisations of SM alignment by imposing the symmetries of model. The 2HDMpotential contains 13 accidental symmetries, which have been fully classified in [29, 30, 36].Of these, eight restrict the quartic couplings such that the alignment condition (cid:98) C → is met. However, only for three symmetries exact alignment can be achieved naturallywithout imposing any constraints on the values of tan β , nor on the bilinear mass terms µ , and m [31, 33]. In the simplest scenario, dubbed the MS-2HDM, the SM alignmentcan be naturally realised as a consequence of an accidental SO(5) symmetry in the Higgssector [14, 29, 32, 34]. In the MS-2HDM, the SO(5) symmetry puts severe restrictions onthe allowed form of the kinematic parameters of the 2HDM potential in (1), µ = µ , m = 0 ,λ = λ , λ = 2 λ , λ = Re ( λ ) = λ = λ = 0 . (9)These parameters produce one massive CP-even scalar with M H = 2 λ v . The other fourphysical scalars ( h, a, h ± ) become massless and would participate in decays of SM particles,which is inconsistent with observation. The custodial SO(5) symmetry could be realised atlarge RG scales µ X , where µ X lies between µ (1) X ∼ GeV and µ (2) X ∼ GeV, with theEW scale behaviour determined by the RG evolution of the parameters. This accompaniedby soft breaking term m lifts up the masses in a viable Higgs spectrum as M H = 2 λ v , M h = M a = M h ± = Re ( m ) s β c β . (10)In the EW scale, the H -boson couplings in terms of the light-to-heavy scalar-mixing param-eter may be expressed by θ S ≡ (cid:98) C/ (cid:98) B . So, the approximate analytic expressions may be givenby [32] g HV V (cid:39) − θ S , (11a) g hV V (cid:39) − θ S = v s β c β M a + v λ (cid:104) c β (2 λ − λ ) − s β (2 λ − λ ) (cid:105) . (11b)Given the narrow experimental limits on the deviation of g HV V from 1, one must have theparameter θ S (cid:28) .The MS-2HDM is a minimal and very predictive extension of the SM governed by onlythree additional parameters: the unification scale µ X , the charged Higgs mass M h ± (or m )and tan β , allowing one to determine the entire Higgs sector of the model. Previously, wepresented our MS-2HDM benchmarks in terms of these input parameters, for our misalign-ment predictions of the SM-like Higgs-boson couplings to the W ± and Z bosons [32]. Thesebenchmarks are given in Table I. Here, we intend to calculate the rate of W ± /Z -pair and-quadruplet productions through single a double SM-like Higgs boson decay modes basedon these benchmarks. III. W ± /Z -QUADRUPLET PRODUCTION AND EVEN GENERATIONFRAMEWORK The W ± /Z -pair and -quadruplet production events are amongst the largest Higgs-taggedsignatures at the current LHC energies. However, the best processes for probing the singsof an extended Higgs sector are the W ± /Z - quadruplet productions through double Higgsdecays, i.e. pp → HH → V V ∗ V (cid:48) V (cid:48)∗ . This is since, as we have shown in Section II, Couplings ATLAS CMS tan β = 2 tan β = 20 tan β = 50 | g low-scale HZZ | [0.86, 1.00] [0.90, 1.00] 0.9999 0.9999 0.9999 | g high-scale HZZ | | g low-scale Htt | . +0 . − . . +0 . − . | g high-scale Htt | | g low-scale Hbb | . +0 . − . . +0 . − . | g high-scale Hbb | Predicted values of the SM-like Higgs boson couplings to the Z boson and to top- andbottom-quarks in the MS-2HDM for both scenarios with low- and high-scale quartic coupling unifica-tion, assuming M h ± = 500 GeV. The corresponding central values for these couplings from ATLASand CMS are also given, including their uncertainties [50]. the SM-like Higgs boson in the MS-2HDM couples to the EW gauge bosons with couplingstrength exactly as that of the SM Higgs boson, while the other neutral heavy states donot couple to them at all [32]. On the other hand, because of the mixing between the lightand the heavy states, the W ± /Z - quadruplet production through double Higgs decays maybe enhanced. Henceforth, we calculate these processes within the MS-2HDM, which caninclude Higgs trilinear mixing channels, H/h/a → HH . Additionally, we check the W ± /Z -pair production events through single Higgs decays to ensure the MS-2HDM predictions arealigned with those of the SM. The exclusive production of the EW gauge boson pairs andquadruplets via single and double Higgs decays can be given as p ( p ) + p ( p ) → H ( p H ) + X → W + ( p W + ) + W − ( p W − ) + X → l +1 ν l + l − ν l + X, (12) p ( p ) + p ( p ) → H ( p H ) + X → Z ( p ,Z ) + Z ( p ,Z ) + X → l +1 l − + l +2 l − + X, (13) p ( p ) + p ( p ) → H ( p ,H ) + H ( p ,H ) + X → W + ( p ,W + ) + W − ( p ,W − ) + W + ( p ,W + ) + W − ( p ,W − ) + X, → l +1 ν l + l − ν l + l +3 ν l + l − ν l + X, (14) p ( p ) + p ( p ) → H ( p ,H ) + H ( p ,H ) + X → Z ( p ,Z ) + Z ( p ,Z ) + Z ( p ,Z ) + Z ( p ,Z ) + X, → l +1 l − + l +2 l − + l +3 l − + l +4 l − + X. (15)In the above processes, the Higgs boson production mechanism is dominated by the gluonfusion channels gg → H and gg → HH , which account for ∼ %95 of the Higgs productionrate at the LHC [37, 51]. Figure 1 displays all dominant sub-processes up to two jets that In [51], it has been shown that one can simply enhance the LO differential cross-sections of Higgsproduction with the use of a factorization-scale-dependant K-factor and forget about the higher-order and gggggg 𝑙 gggggg𝐻𝐻𝐻𝑡/𝑏𝑡/𝑏𝑡/𝑏 𝑡/𝑏𝑡/𝑏𝑡/𝑏 𝐻𝐻𝐻𝐻 g ggg gg𝑉𝑉 ∗ 𝑙 𝑙𝑙𝑙𝑙 𝑙 𝑙𝑙𝑙 𝑙 𝑙𝑉𝑉 ∗ 𝑉𝑉 ∗ 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑙𝑙 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝐻𝐻 𝑉𝑉 ∗ 𝑉′𝑉′ ∗ gggggg 𝑡/𝑏 𝑡/𝑏 𝑡/𝑏 g gg𝐻 𝐻𝐻/ℎ/𝑎 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑙𝑙 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝐻/ℎ/𝑎 𝐻𝐻𝐻/ℎ/𝑎𝐻𝐻 𝑉𝑉 ∗ 𝑉′𝑉′ ∗ (a) (b) (c) FIG. 1.
Dominant sub-processes for W ± /Z -pair and -quadruplet productions through single anddouble Higgs boson decays at the LHC up to 2 jets; (a) W ± /Z -pair productions via single Higgsdecay channels. (b) W ± /Z -quadruplet productions through double Higgs boson decays. (c) DoubleHiggs production channels via H/h/a → HH decays. are mediated through the exchange of a heavy virtual top/bottom quark. The parts (a) and(b) of Figure 1 show the dominant single and double Higgs production channels, respectively.The part (c) showcases the contributions of the light and heavy Higgs bosons through thetrilinear Higgs vertices, where the signature of new physics would rise. Also, the leptonicdecay channels W + W − → l + ν l + l (cid:48)− ν l (cid:48) and ZZ → l + l − + l (cid:48) + l (cid:48)− have been considered to ensurea clean observable signature and to prevent the reconstruction of H → V V ∗ resonances.In our calculations for the production rates of the pp → HX → V V ∗ and pp → HHX → V V ∗ V (cid:48) V (cid:48)∗ events, we utilize the Herwig 7 (v7.2.1) event generator [39–42]. This will bedone for both the SM and the MS-2HDM, in the collinear factorization framework. Thecontributing matrix elements are generated with
MadGraph5 and convoluted by
MMHT2014 parton distribution function libraries [53] via
LHAPDF interface [54]. The underlying eventsare enhanced by an AO
QCD+QED+EW parton shower scheme [45, 47, 55] and the clustermodel hadronization [56]. The generated events are then analysed with
Rivet , based on theexisting analysis
MC_WWINC and
MC_ZZINC which are modified according to our needs.
IV. NUMERICAL RESULTS AND DISCUSSION
In this section, we present our results for W ± /Z -pair and quadruplet production throughthe single and the double Higgs bosons decays at √ s = 13 TeV. In the first step, we checkthe efficiency of our calculation setup by evaluating the single Higgs production results in virtual corrections to these processes, e.g. via the
W/Z
Higgs-strahlung sub-processes [52]. Nevertheless, forthe sake of completeness, we are considering the full range of real and virtual QCD and QED contributionsto (12), (13), (14) and (15), using the
Matchbox merging functionality within
Herwig 7 . b b b b b b pp → H SM → W + W − b CMS data − − − − Transverse momentum for H → W + W − at √ s =
13 TeV p H ⊥ [GeV] d σ / d p H ⊥ [ p b / G e V ] b b b b b b b b pp → H SM → ZZ b CMS data − − − − − Transverse momentum for H → ZZ at √ s =
13 TeV p H ⊥ [GeV] d σ / d p H ⊥ [ p b / G e V ] b b b b b b pp → H SM → ZZ b CMS data . . . − − − Pseudorapidity for H → ZZ at √ s =
13 TeV η H d σ / d η H [ p b ] FIG. 2.
Differential cross-section for single Higgs boson production as a function of its transversemomentum and pseudo-rapidity. The calculations are in the colliner framewok, using
Herwig 7 (v7.2.1) at √ s = 13 TeV. The top panel corresponds to the pp → HX → W + W − X channelwhile the bottom panels are for the pp → HX → ZZX channel. The data are from the CMScollaboration [57, 58]. To calculate the uncertainty region, we have manipulated the factorizationhard-scale by a factor of 2. the SM with the existing experimental observations from the CMS collaboration, includingtheir statistical and systematic uncertainties [38, 57, 58].In Figure 2, we exhibit the results of our analysis for single Higgs bosons production via H → V V ∗ decay channels. The top panel demonstrates the kinematically reconstructedtransverse momentum distribution of the exchanged Higgs boson from the H → W + W − decay mode while the bottom panels correspond to the transverse momentum and pseudo-rapidity from the H → ZZ decay mode. Figure 3 shows the fiducial cross-sections of singleHiggs production through W ± -pairs (left panel) and Z -pairs (right panel). The event selec-tion criteria for these calculations have been chosen in accordance with the reported condi-tions in [57, 58]. Despite the low precision of the experimental data, in both figures one canreadily observe that these predictions are perfectly capable of describing the experimentalmeasurements.In the next step, we calculate the single and the double Higgs production events within theMS-2HDM. According to our discussion in Section II, the MS-2HDM has two conformally- b pp → H SM → W + W − b CMS data − − Total cross-section for Higgs production via H → W + W − at √ s =
13 TeV √ s [TeV] σ ( pp → H ) [ p b ] b pp → H SM → ZZ b CMS data − − Total cross-section for Higgs production via H → ZZ at √ s =
13 TeV √ s [TeV] σ ( pp → H ) [ p b ] FIG. 3.
Feducial cross-section for W ± ( Z ) -pair productions through single SM Higgs boson decays atthe LHC for √ s = 13 TeV displayed in left (right) panel. The data are from the CMS collaboration,including their statistical and systematic uncertainties [57, 58]. To calculate the uncertainty region,we have manipulated the factorization hard-scale by a factor of 2. invariant quartic coupling unification points µ (1) X (low-scale) and µ (2) X (high-scale), for a givenchoice of the charged Higgs-boson mass M h ± and tan β [31, 32]. Thus, we perform theseanalysis for both unification points. In Figures 4 and 5, we display the differential cross-sections for pp → H → V V ∗ production as a function of pseudo-rapidity of the producedgauge bosons in the MS-2HDM. The results for the low-scale (LS) and the high-scale (HS)points are shown in the left and the right panels, respectively. The top panels correspondto the kinematic properties of the EW bosons while the bottom panels depict the behaviourof gauge boson pairs. The calculations have been done at TeV center-of-mass energy for M h ± = 500 GeV and the typical values of tan β , such as tan β = 2 , and , relevant tothe benchmarks of Table I. By analogy, Figures 6 and 7 show the transverse momentumdistributions for W ± and Z bosons production through single SM-like Higgs bosons.As expected, we observe that the results of pp → H → W + W − and pp → H → ZZ forboth lower- and higher-scale quartic coupling unification points are in excellent agreementwith the SM and the experimental data. Obviously, this is since the normalised couplings g HV V approaches the SM value g H SM V V = 1 for both points. However, the deviation of theMS-2HDM results from the SM predictions is higher because the degree of misalignmentreaches its maximum value for tan β = 2 , while still remaining within their σ uncertainty.Now, let us turn our attention to the W ± /Z -quadruplet production events through doubleHiggs decay channels, i.e. pp → HH → V V ∗ V (cid:48) V (cid:48)∗ . Here, the sub-processes involving H/h/a → HH decays may have large contributions into the pp → HH production rate,as shown in Figure 1(c). In Figures 8 and 9, we exhibit our results for the production ofthese events with tan β = 2 , and at TeV center-of-mass energy. In both figures, thetop panels represent the reconstructed kinematics of the exchanged H scalars while bottomplots show the rates of production as functions of the pseudo-rapidity of the gauge bosons.These are shown for both the low-scale and the high-scale unification points. From theseplots, we observe a substantial increase in the production rate of the SM-like Higgs bosons0 H SM → W + W − H → W + W − with tan β = H → W + W − with tan β = H → W + W − with tan β = − − − W ± pseudo-rapidity in H → W + W − at √ s =
13 TeV for LS η W d σ / d η W [ p b ] H SM → W + W − H → W + W − with tan β = H → W + W − with tan β = H → W + W − with tan β = − − − W ± pseudo-rapidity in H → W + W − at √ s =
13 TeV for HS η W d σ / d η W [ p b ] H SM → W + W − H → W + W − with tan β = H → W + W − with tan β = H → W + W − with tan β = − − − Pseudo-rapidity of W -pair in H → W + W − at √ s =
13 TeV for LS η WW d σ / d η WW [ p b ] H SM → W + W − H → W + W − with tan β = H → W + W − with tan β = H → W + W − with tan β = − − − Pseudo-rapidity of W -pair in H → W + W − at √ s =
13 TeV for HS η WW d σ / d η WW [ p b ] FIG. 4.
Differential cross-section as a function of pseudo-rapidity for W ± -pair productions throughsingle SM-like Higgs boson ( H ) events displayed for lower-scale (higher-scale) quartic couplingunification point in left panels (right panels). These are shown for different values of tan β at √ s = 13 TeV. The top panels correspond to the kinematic properties of the W ± bosons while thebottom panels depict the behaviour of W ± -pairs. Note that, these results are compared with relevanttheoretical predictions in the SM within its uncertainty bounds. compared to their SM counterparts. This becomes more pronounced for the smaller valuesof tan β , which has a nearly 2-fold increase compared to similar SM prediction. Despitethe fact that these processes have expectedly smaller cross-sections in comparison with thesingle Higgs production events, they have substantial deviance from the SM and may bedirectly observed at the LHC data.In a similar fashion, Figures 10 and 11 demonstrate the transverse momentum distribu-tions of the differential cross-section for the double Higgs production events. Observe that,the peaks in the Higgs and W ± /Z bosons p ⊥ distributions are increased by a factor ∼ p ⊥ < GeV. However, the p ⊥ distribution’s tails converge to theSM predictions in the high- p ⊥ regions. Therefore, the signature of the MS-2HDM may beobserved in the low- p ⊥ regions of the W ± /Z -quadruplet production events through doubleHiggs decay channels. Our observations can be readily generalised to other realisations ofthe 2HDM in their alignment limits.1 H SM → ZZH → ZZ with tan β = H → ZZ with tan β = H → ZZ with tan β = − − − − Z pseudo-rapidity in H → ZZ at √ s =
13 TeV for LS η Z d σ / d η Z [ p b ] H SM → ZZH → ZZ with tan β = H → ZZ with tan β = H → ZZ with tan β = − − − − Z pseudo-rapidity in H → ZZ at √ s =
13 TeV for HS η Z d σ / d η Z [ p b ] H SM → ZZH → ZZ with tan β = H → ZZ with tan β = H → ZZ with tan β = − − − − Pseudo-rapidity of Z -pair in H → ZZ at √ s =
13 TeV for LS η ZZ d σ / d η ZZ [ p b ] H SM → ZZH → ZZ with tan β = H → ZZ with tan β = H → ZZ with tan β = − − − − Pseudo-rapidity of Z -pair in H → ZZ at √ s =
13 TeV for HS η ZZ d σ / d η ZZ [ p b ] FIG. 5.
The same as in Figure 4, but for Z -pair productions . V. CONCLUSIONS
The data collected from CERN’s LHC impose constraints over the coupling strengthsof the Higgs boson, primarily to the EW gauge bosons ( V = W ± , Z ), which are veryclose to the SM predictions. This simple fact severely restricts the form of possible scalar-sector extensions of the SM. In this study, we have considered the MS-2HDM where theSM alignment can be achieved naturally by the virtue of an SO(5) symmetry imposed onthe 2HDM. The MS-2HDM is a minimal and very predictive extension of the SM governedby only three parameters: the unification scale µ X , the charged Higgs mass M h ± and tan β which allow one to determine the entire Higgs sector of the model.Given the remarkable features of the MS-2HDM [31, 32], we have investigated the possiblesignature of this model via W ± /Z -quadruplet productions at the LHC. We have performedour calculations with NLO QCD accuracy for pp → HX → V V ∗ X and pp → HHX → V V ∗ V (cid:48) V (cid:48)∗ X processes for different values of tan β , using the Herwig 7 multi-purpose eventgenerator at √ s = 13 TeV center-of-mass energy. The corresponding amplitudes are providedby
MadGraph5 , up to one QCD loop and two jets. The produced underlying events areshowered by an AO
MC@NLO matched
QCD+QED+EW parton shower and the resultshave been analysed using
Rivet .We have shown that the predictions for W ± /Z -pair productions through single SM-like2 H SM → W + W − H → W + W − with tan β = H → W + W − with tan β = H → W + W − with tan β =
100 200 300 400 500 600 700 80010 − − − − − − − W ± transverse momentum in H → W + W − at √ s =
13 TeV for LS p W ⊥ [GeV] d σ / d p W ⊥ [ p b / G e V ] H SM → W + W − H → W + W − with tan β = H → W + W − with tan β = H → W + W − with tan β =
100 200 300 400 500 600 700 80010 − − − − − − − W ± transverse momentum in H → W + W − at √ s =
13 TeV for HS p W ⊥ [GeV] d σ / d p W ⊥ [ p b / G e V ] H SM → W + W − H → W + W − with tan β = H → W + W − with tan β = H → W + W − with tan β =
100 200 300 400 500 600 700 80010 − − − − − − Transverse momentum of W -pair in H → W + W − at √ s =
13 TeV for LS p WW ⊥ [GeV] d σ / d p WW ⊥ [ p b / G e V ] H SM → W + W − H → W + W − with tan β = H → W + W − with tan β = H → W + W − with tan β =
100 200 300 400 500 600 700 80010 − − − − − − Transverse momentum of W -pair in H → W + W − at √ s =
13 TeV for HS p WW ⊥ [GeV] d σ / d p WW ⊥ [ p b / G e V ] FIG. 6.
The same as in Figure 4, but for differential cross-section as a function of transversemomentum for W ± -pair productions. Higgs boson events are aligned with their SM counterparts, while the presence of the heavyHiggs states significantly enhances the W ± /Z -quadruple productions. Particularly, we havefound that the cross-section for these events is increased by a factor ∼ p ⊥ < GeVregion with respect to the SM. However, these distributions converge to the SM predictionsin the high- p ⊥ regions. Therefore, the signature of the MS-2HDM may be observed inthe low- p ⊥ regions of the W ± /Z -quadruplet production events through double Higgs decaychannels. These observations are very helpful toward the possible future discovery of thismodel. ACKNOWLEDGMENTS
The authors would like to thank Prof. A. Pilaftsis and Prof. P. Richardson for theirinstructive discussions. ND is supported by the Lancaster-Manchester-Sheffield Consortiumfor Fundamental Physics, under STFC research grant ST/P000800/1. The work of ND isalso supported in part by the Polish National Science Centre HARMONIA grant undercontract UMO- 2015/20/M/ST2/00518 (2016-2020). MRM is supported by the UK Scienceand Technology Facilities Council (grant numbers ST/P001246/1). This work has receivedfunding from the European Union’s Horizon 2020 research and innovation program as part3 H SM → ZZH → ZZ with tan β = H → ZZ with tan β = H → ZZ with tan β =
100 200 300 400 500 600 700 80010 − − − − − − − − Z transverse momentum in H → ZZ at √ s =
13 TeV for LS p Z ⊥ [GeV] d σ / d p Z ⊥ [ p b / G e V ] H SM → ZZH → ZZ with tan β = H → ZZ with tan β = H → ZZ with tan β =
100 200 300 400 500 600 700 80010 − − − − − − − − Z transverse momentum in H → ZZ at √ s =
13 TeV for HS p Z ⊥ [GeV] d σ / d p Z ⊥ [ p b / G e V ] H SM → ZZH → ZZ with tan β = H → ZZ with tan β = H → ZZ with tan β =
100 200 300 400 500 600 700 80010 − − − − − − Transverse momentum of Z -pair in H → ZZ at √ s =
13 TeV for LS p ZZ ⊥ [GeV] d σ / d p ZZ ⊥ [ p b / G e V ] H SM → ZZH → ZZ with tan β = H → ZZ with tan β = H → ZZ with tan β =
100 200 300 400 500 600 700 80010 − − − − − − Transverse momentum of Z -pair in H → ZZ at √ s =
13 TeV for HS p ZZ ⊥ [GeV] d σ / d p ZZ ⊥ [ p b / G e V ] FIG. 7.
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13 TeV for HS η H d σ / d η H [ p b ] pp → H SM H SM pp → HH , tan β = → HH , tan β = → HH , tan β = . . . . − − − W pseudo-rapidity in HH → WWWW with at √ s =
13 TeV for LS η W d σ / d η W [ p b ] pp → H SM H SM pp → HH , tan β = → HH , tan β = → HH , tan β = . . . . − − − W pseudo-rapidity in HH → WWWW with at √ s =
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13 TeV for HS η H d σ / d η H [ p b ] pp → H SM H SM pp → HH , tan β = → HH , tan β = → HH , tan β = − − − Z pseudo-rapidity in HH → ZZZZ with at √ s =
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13 TeV for HS p H ⊥ [GeV] d σ / d p H ⊥ [ p b / G e V ] pp → H SM H SM pp → HH , tan β = → HH , tan β = → HH , tan β =
100 200 300 400 500 600 700 80010 − − − − − W transverse momentum in HH → WWWW with at √ s =
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13 TeV for LS p Z ⊥ [GeV] d σ / d p Z ⊥ [ p b / G e V ] pp → H SM H SM pp → HH , tan β = → HH , tan β = → HH , tan β =
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13 TeV for HS p Z ⊥ [GeV] d σ / d p Z ⊥ [ p b / G e V ] FIG. 11.
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