Electroweak production of multiple (pseudo)scalars in the 2HDM
KKIAS-P18109
Electroweak production of multiple (pseudo)scalars in the 2HDM
Rikard Enberg a , William Klemm a,b , Stefano Moretti c and Shoaib Munir d,ea Department of Physics and Astronomy,Uppsala University, Box 516, SE-751 20 Uppsala, Sweden. b School of Physics & Astronomy,University of Manchester, Manchester M13 9PL, UK. c School of Physics & Astronomy,University of Southampton, Southampton SO17 1BJ, UK. d School of Physics, Korea Institute for Advanced Study,Seoul 130-722, Republic of Korea. e East African Institute for Fundamental Research (ICTP-EAIFR),University of Rwanda, Kigali, Rwanda.
Abstract
The two-Higgs Doublet Model (2HDM) is the most minimal extension of the Standard Model(SM) containing extra Higgs doublet fields. Given the multiplicity of Higgs states in a 2HDM,its Higgs potential is significantly more involved than the SM one. Importantly, it contains amultitude of Higgs triple self-couplings, unlike the SM, which only has one. These interactionsare key to understanding the phenomenology of the 2HDM, as they uniquely determine theform of the potential. Several studies analysing the prospects of measuring these couplings atthe Large Hadron Collider (LHC) have found them to be quite low generally. However, suchstudies have largely concentrated on Higgs pair-production induced by gluon-gluon scattering,either via direct annihilation or followed by their splitting into b -(anti)quark pairs, which inturn annihilate leaving behind spectator b -(anti)quarks. Both of these channels are thereforegoverned by QCD dynamics. We compare here the yields of such channels to those initiatedby (primarily) valence quarks, which involve Electro-Weak (EW) interactions only, for neutralmulti-Higgs final states. We find that EW production can be dominant over QCD productionfor certain final state combinations. We also illustrate that charged final states, which can onlybe produced via EW modes, could serve as important probes of some H ± triple couplings, thatare inaccessible in QCD-induced processes, during Run 2 and 3 of the LHC. Our analysis coversregions of the parameter space of the Type-I 2HDM that have escaped the most up-to-dateexperimental constraints coming from EW precision data, LHC measurements of the 125 GeVHiggs boson properties, searches for additional Higgs states, and flavour physics. We dedicate this work to the memory of Prof. W. James Stirling, an example to never forget. † E-mails: [email protected], [email protected], [email protected], [email protected] a r X i v : . [ h e p - ph ] J un Introduction
The 2012 discovery of a neutral Higgs boson [1, 2], H obs , with a mass near 125 GeV, is strongevidence for gauge boson masses being induced by the Higgs mechanism of Electroweak SymmetryBreaking (EWSB). While the Higgs boson data collected at the LHC is still consistent with theminimal EWSB dynamics of the SM, some other experimental results cannot be reconciled withit. In particular, certain anomalies in the flavour sector [3, 4, 5, 6, 7] are far more compatible withan extended Higgs sector [8, 9, 10, 11, 12] than with the SM. In view of this, as the H obs stateemerges from a Higgs doublet in the SM, the phenomenology of its minimal extension by anotherHiggs doublet, which results in the two-Higgs Doublet Model, deserves particular attention.In the 2HDM Higgs sector, five physical states emerge after EWSB: three neutral, of whichtwo are scalars ( h and H , with m h < m H ) and one a pseudoscalar ( A ), plus a charged pair( H ± ). The theory of this scenario is well-understood (see, e.g., [13, 14]), but its phenomenologicalinvestigation is far from complete at present. In particular, while there exist some indicationsof what the accessible discovery channels of the additional Higgs bosons of a 2HDM could be atthe LHC, little effort has been spent on assessing which are the most suitable channels to pindown the specific nature of the underlying Higgs dynamics. The reason is that there are severalincarnations of the 2HDM and, although each of them yields a different phenomenological patternin general, there exists a significant level of degeneracy among them if only the production anddecay channels of a single Higgs state are studied. Indeed, for an unequivocal extraction of a 2HDMscenario involved in EWSB, the various components of the scalar potential ought to be accessedexperimentally. This makes the study of multi-Higgs final states mandatory.In the context of the LHC, several analyses exist in literature, addressing double, or even triple,Higgs production, assuming a 2HDM to be the underlying framework (see, e.g., Ref. [15, 16] for areview). However, the majority of such analyses have concentrated on production modes inducedby QCD dynamics, notably gluon-gluon ( gg ) fusion into a (neutral) pair of Higgs states. Thesepairs emerge either from a primary Higgs state (resonantly or otherwise) or as Higgs-strahlung froma box diagram involving heavy fermion loops. Alternatively, because Higgs couplings to quarks areof Yukawa type (i.e., proportional to the quark mass), the b ¯ b scattering channel has also beenexploited. It should be noted that b -quarks are not valence partons and are therefore producedfrom a (double) gluon splitting. Hence this channel is also intrinsically gg -induced.While these QCD processes clearly afford one the possibility of the direct measurements of anumber of terms in the 2HDM Lagrangian, the complete list of these terms is much longer. Inorder to remedy this, we study here double and triple Higgs boson production in q ¯ q ( (cid:48) ) -induced EWinteractions, where q represents predominantly a valence u, d , in the Type-I 2HDM. This theoreticalscenario has been shown to yield spectacular signals involving light neutral Higgs states, with a masssmaller than that of H obs , that are potentially accessible at the LHC, see Refs. [17, 18, 19, 20]. Here,we assess the complementary portion of the Type-I 2HDM parameter space, wherein the lighterof the two scalar Higgs states has a mass of 125 GeV, along the lines of [21], which considereda similar setup but concentrated exclusively on charged Higgs boson signals. We will argue thatthe cross sections for the production of some of these double (and triple) Higgs final states couldbe accessible within the already scheduled LHC Runs. We will in particular show that in certaincases not only can these cross sections be larger for EW processes compared to the QCD-initiatedprocesses, but the former can also possibly provide access to some of the Higgs self-couplings thatnone of the latter can.The article is organised as fellows. In Sec. 2 we review in some detail the various types ofminimally flavour-violating 2HDM and identify the Higgs-Higgs and Higgs-gauge couplings availablein it. In Sec. 3 we discuss parameter space regions of the Type-I 2HDM which are amenable to LHCinvestigation in multi-Higgs final states, satisfying all the theoretical and experimental constraintsof relevance. In Sec. 4 we discuss our results. Finally, we present our conclusions in Sec. 5.2 The two-Higgs Doublet Model
The 2HDM contains two Higgs doublet fields, Φ and Φ , and its most general potential can bewritten as V = m Φ † Φ + m Φ † Φ − [ m Φ † Φ + h.c.]+ 12 λ (Φ † Φ ) + 12 λ (Φ † Φ ) + λ (Φ † Φ )(Φ † Φ ) + λ (Φ † Φ )(Φ † Φ )+ (cid:26) λ (Φ † Φ ) + (cid:2) λ (Φ † Φ ) + λ (Φ † Φ ) (cid:3) Φ † Φ + h.c. (cid:27) . (1)Upon EWSB, Φ and Φ are defined in terms of their respective vacuum expectation values v and v , the physical Higgs states h , H , A and H ± , and the Goldstone bosons G and G ± asΦ = 1 √ (cid:32) √ (cid:0) G + cos β − H + sin β (cid:1) v − h sin α + H cos α + i ( G cos β − A sin β ) (cid:33) , (2)Φ = 1 √ (cid:32) √ (cid:0) G + sin β + H + cos β (cid:1) v + h cos α + H sin α + i ( G sin β + A cos β ) (cid:33) , (3)where α is the mixing angle of the CP-even interaction states and tan β ≡ v /v . Upon minimisationof the Higgs potential in Eq. (1), after rewriting it in terms of these expanded fields, the bare masses m and m get replaced by v , . Similarly, the quartic couplings λ − in Eq. (1) can be tradedfor the masses of the four physical Higgs bosons as well as the mixing parameter sin( β − α ). Thefree parameters of a 2HDM thus include m h , m H , m A , m H ± , λ , λ , m , tan β and sin( β − α ).If all the SM fermions couple to both the Higgs fields of a 2HDM, it can lead to dangerousflavour-changing neutral currents (FCNCs). In order to avoid large FCNCs, the most generalapproach taken is to enforce a Z symmetry on the Lagrangian, so that each type of fermion onlycouples to one of the doublets [22, 23]. This symmetry is softly broken by the m term in theHiggs potential above and explicitly broken by the λ , terms. In the following we restrict ourselvesto the CP-conserving case λ = λ = 0.The Type-I 2HDM is obtained if (conventionally) Φ → − Φ under the Z symmetry, so that allthe quarks and charged leptons couple only to Φ . On the other hand, the Type-II 2HDM observesthe transformation property Φ → − Φ , d iR → − d iR , e iR → − e iR , so that only these mutuallycouple, while the up-type quarks couple instead to Φ . The Type-III (or Type Y or flipped) modelis built such that Φ couples to the up-type quarks and the leptons and Φ couples to the down-type quarks only while in the Type-IV (or Type X or lepton-specific) model Φ couples to all thequarks and Φ to all the leptons. In this study, we will concentrate on the Type-I 2HDM, forwhose allowed parameter space the relevance of the aforementioned EW processes with respect tothe QCD-induced ones is most pronounced. (We will defer the study of the other Types to futurepublications.)We are in particular interested in the couplings of the (pseudo)scalars to gauge bosons and thetriple-Higgs couplings. The (pseudo)scalar-gauge couplings λ HAZ and λ HH + W − are proportionalto sin( β − α ), and λ hAZ and λ hH + W − to cos( β − α ), while λ AH + W − is independent of the 2HDMangles. The LHC data requires at least one of h and H to have a mass near 125 GeV and SM-likecouplings. In order for h to satisfy this condition, | sin( β − α ) | ( | cos( β − α ) | ) should not be toofar from 1 (0). This implies that couplings proportional to sin( β − α ) should be larger than thoseproportional to cos( β − α ), which indeed vanishes in the decoupling limit [24]. However, given thecurrent measurements of the properties of the H obs , this limit need not be strictly adhered. Forthis reason, we treat sin( β − α ) as a free parameter here. The decoupling limit, cos( β − α ) →
0, means that h has a mass near 125 GeV and very SM-like coupling strengths,while all the other states are much heavier. B → X s γ ) × . ± .
15 [25]BR( B u → τ ± ν τ ) × . ± .
19 [25]BR( B s → µ + µ − ) × . ± .
85 [26] µ γγ . +0 . − . [27] µ ZZ . +0 . − . [27] µ W W . +0 . − . [27] µ ττ . +0 . − . [27] µ bb . +0 . − . [27]Table 1: Measured values of the B -physics observables and H obs signal rates imposed as constraintson the scanned points.As for the triple-Higgs couplings, the CP-conserving model we are considering here containseight of these, namely λ hhh , λ hhH , λ hHH , λ HHH , λ hAA , λ HAA , λ hH + H − and λ HH + H − . The explicitexpressions for these couplings are more complicated than for the (pseudo)scalar-gauge ones above.They are all functions of both sin( β − α ) and cos( β − α ), as well as of the quartic λ i parametersfrom the scalar potential in Eq. (1). However, all the λ i dependence can be written in terms oftheir combinations that are invariant under U (2) basis changes in the potential. Thus the onlybasis dependence of these couplings comes from the angles. For explicit expressions, see Ref. [24]. We numerically scanned the parameters of the Type-I 2HDM using the 2HDM Calculator (2HDMC) [28]in the ranges: m H : 150 – 750 GeV ; m H ± : 50 – 750 GeV ; m A : 50 – 750 GeV ;sin( β − α ): − m : 0 – m A sin β cos β ; tan β : 2 – 25 ,with m h fixed to 125 GeV and λ , λ to zero, such that each point satisfied the following set ofrequirements. • Unitarity (default unitarity limit is 16 π ), perturbativity (default perturbativity limit is 4 π )and Higgs potential stability conditions were enforced with methods provided by 2HDMC. • The oblique parameters S , T and U were calculated with 2HDMC methods and were requiredto fall within the 95% Confidence Level (CL) ellipsoid based on 2018 PDG values [29]: S = 0 . ± . , (4) T = 0 . ± . , (5) U = 0 . ± . , (6)with correlations ρ ST = 0 . ρ SU = − .
66 and ρ T U = − . • All scalar states in the models satisfied all (95% CL) constraints included in the programHiggsBounds 5.2.0 [30]. • The B -physics observables were calculated with SuperIso 3.4 [31]. They were required tomeet the limits from the SuperIso manual (95% CL), except for the three Branching Ratios(BRs) listed in Tab. 1, for which we applied the constraints on the m H ± , tan β plane derivedin [32]. 4
200 400 600 800 m h + m H ± [GeV]10 -1 σ ( qq → h H ± ) [ f b ] m H + m H ± [GeV]10 -1 σ ( qq → HH ± ) [ f b ] m A + m H ± [GeV]10 -1 σ ( qq → A H ± ) [ f b ] Figure 1: Cross sections for the three possible charged 2BFSs. • The signal strengths for h → γγ , ZZ , W W , τ τ and b ¯ b , calculated using HiggsSignals 2.2.0[33], were required to lie within 2 σ of the LHC measurements for H obs given in Tab. 1.We point out here that due to the absence of a dark matter (DM) candidate particle, theconstraints from the relic abundance of DM and from the experimental facilities for its detectionare irrelevant in the 2HDM. Such constraints would indeed apply in the case of the MinimalSupersymmetric Standard Model, which contains two Higgs doublets as well, and also predictsfermionic DM. The prospects of the pair-production of the heavy Higgs bosons in this model, withone of these decaying into the DM itself, have been studied in, e.g., [34]. For each scanned point, we calculated tree-level cross sections in pp collisions with √ s = 13 TeV forall possible q ¯ q ( (cid:48) ) → h i h j processes, with h i,j = ( h, H, A, H ± ). These cross sections were calculatedusing the 2HDMC model [28] with MadGraph5 aMC@NLO [35]. For the neutral 2-body final states(2BFSs), we also calculated the cross sections for b ¯ b → h i h j in the five flavour scheme using thesame methods and for gg → h i h j (gluon-gluon fusion) using MadGraph based codes [16].From these, we estimated cross sections for the 3-Body Final States (3BFSs) h i + h j + h k /V k ,with h i = ( h, H, A, H ± ) and V = ( W ± , Z ). This was done by multiplying the cross section for agiven 2 → Furthermore, while a fullanalysis would take into account all the contributions, including the interference effects amongdifferent channels, to the production of a given 3BFS simultaneously, we consider the contributionof each channel separately here. We are afforded this simplification by the fact that the 3BFS crosssections presented in the following sections are typically dominated by a single process.
The charged 2BFSs, each containing the H ± along with one neutral Higgs state, are shown in Fig. 1.These are all necessarily produced by an initial q ¯ q (cid:48) state, having no counterpart in gg/b ¯ b production,and each shows a maximum cross section of at least 10 fb in some kinematic regions. Whereas thecross sections for HH ± and AH ± states are strongly correlated with their cumulative masses,those of hH ± show greater variation. We find that this variation is correlated with sin( β − α ),with maximal cross sections corresponding to minimal sin( β − α ). This is consistent with a cross Our scan does contain a minority of points for which A and/or H ± have large widths. However, the large crosssections highlighted in the following sections all correspond to decays of states with narrow widths.
00 400 600 800 1000 m h + m H ± [GeV]10 -1 σ × B R [ f b ] hhH ± σ ( HH ± ) BR ( H → hh )
200 400 600 800 m h + m H [GeV]10 -1 σ × B R [ f b ] hHW ± σ ( HH ± ) BR ( H ± → W ± h ) σ ( hH ± ) BR ( H ± → W ± H ) m h + m A [GeV]10 -1 σ × B R [ f b ] hAW ± σ ( AH ± ) BR ( H ± → W ± h ) σ ( hH ± ) BR ( H ± → W ± A ) m h + m H ± [GeV]10 -1 σ × B R [ f b ] hH ± Z σ ( AH ± ) BR ( A → Zh ) m A [GeV]10 -1 σ × B R [ f b ] AAW ± σ ( AH ± ) BR ( H ± → W ± A ) m H ± [GeV]10 -1 σ × B R [ f b ] H ± H ± W ∓ σ ( HH ± ) BR ( H → W ± H ∓ ) σ ( AH ± ) BR ( A → W ± H ∓ ) m H + m A + m H ± [GeV]10 -1 σ × B R [ f b ] hhW ± σ ( hH ± ) BR ( H ± → W ± h ) m H [GeV]10 -1 σ × B R [ f b ] HHW ± σ ( HH ± ) BR ( H ± → W ± H ) m H + m A [GeV]10 -1 σ × B R [ f b ] HAW ± σ ( HH ± ) BR ( H ± → W ± A ) σ ( AH ± ) BR ( H ± → W ± H ) m H + m H ± [GeV]10 -1 σ × B R [ f b ] HH ± Z σ ( AH ± ) BR ( A → ZH ) m A + m H ± [GeV]10 -1 σ × B R [ f b ] AAH ± σ ( HH ± ) BR ( H → AA ) m A + m H ± [GeV]10 -1 σ × B R [ f b ] AH ± Z σ ( HH ± ) BR ( H → ZA ) Figure 2: Cross sections of qq (cid:48) -initiated subprocesses for selected charged 3BFSs.section dominated by an s -channel W ± , whose coupling to hH ± is proportional to cos( β − α ), asnoted earlier. Because the h is required to have very SM-like properties, the points selected byour scans have | sin( β − α ) | close to 1, which means that cos( β − α ) may span several orders ofmagnitude, resulting in large variation in possible hH ± cross sections. Conversely, the λ HH + W − coupling varies as sin( β − α ) and the λ AH + W − coupling has no dependence on sin( β − α ), so thecross sections for other charged 2BFSs are also consistent with dominant s -channel W ± production,being determined almost entirely by the final state kinematics.If we consider the possibility of either the charged or neutral Higgs in a 2BFS decaying, wecan have final states containing either three Higgs bosons or two Higgs bosons accompanied by onegauge boson. The cross sections for such 3BFSs, for processes where it exceeds 1 fb for at leastone point from the scan, are shown in Fig. 2. The maximal cross sections for all such 3BFSs aresummarised in Tab. 2. We note that there are several possible processes which would lead to crosssections of this size, and all of the possible h i → h j + h k /V k decays are represented, excepting one;6 -4 -3 -2 -1 σ ( gg/b ¯ b → H ± H ± ) [fb]10 σ ( q ¯ q → H ± H ± ) [ f b ] -3 -2 -1 σ ( gg/b ¯ b → hA ) [fb]10 -1 σ ( q ¯ q → h A ) [ f b ] -4 -3 -2 -1 σ ( gg/b ¯ b → HA ) [fb]10 σ ( q ¯ q → H A ) [ f b ] Figure 3: Neutral 2BFSs for which the cross sections for qq (cid:48) production can exceed those for gg/b ¯ b -initiated processes. The dashed line indicates where the cross sections are of equal magnitude. σ ( gg/b ¯ b → hh ) [fb]10 -5 -3 -1 σ ( q ¯ q → hh ) [ f b ] -4 -2 σ ( gg/b ¯ b → HH ) [fb]10 -10 -8 -6 -4 -2 σ ( q ¯ q → HH ) [ f b ] -4 -2 σ ( gg/b ¯ b → AA ) [fb]10 -9 -7 -5 -3 -1 σ ( q ¯ q → AA ) [ f b ] -3 -2 -1 σ ( gg/b ¯ b → hH ) [fb]10 -7 -5 -3 σ ( q ¯ q → h H ) [ f b ] Figure 4: Neutral 2BFSs for which gg/b ¯ b production by far dominates over qq (cid:48) -initiated production.The dashed line indicates where the cross sections are of equal magnitude. H → H + H − does not appear because our scan did not select any points meeting the condition m H > m H ± required for this decay. We also note in Fig. 2 that there are very few points selectedby our scan with large cross sections involving H ± → W ± A , H → AA , or H → AZ decays. Again,this is simply because most points do not have masses which satisfy the kinematic requirements forthese decays. However, our broad scan did find some points where the cross sections containing thesedecays are very substantial and a more comprehensive scanning should find additional candidates. The neutral final states may be produced by q ¯ q -induced processes as well as via loop-inducedprocesses initiated by a pair of gluons. The cross sections for the 2 → q ¯ q and gg/b ¯ b production. We find that, for H + H − , hA and HA final states, the q ¯ q cross sections can all exceed 10 fb and, for some regionsof the parameter space, dominate the combined gg + b ¯ b production, as shown in Fig. 3. While theremaining neutral 2BFSs, namely hh , HH , AA and hH , have EW cross sections unlikely to berelevant at the LHC, their gg/b ¯ b production can be significant, as seen in Fig. 4, so these are still7 -3 -2 -1 Σ σ ( gg/b ¯ b ) × BR [fb]10 -1 σ ( qq ) × B R [ f b ] hH ± W ∓ σ ( H + H − ) BR ( H ± → W ± h ) σ ( hA ) BR ( A → W ± H ∓ ) -3 -2 -1 Σ σ ( gg/b ¯ b ) × BR [fb]10 -1 σ ( qq ) × B R [ f b ] HHZ σ ( HA ) BR ( A → ZH ) -3 -2 -1 Σ σ ( gg/b ¯ b ) × BR [fb]10 -1 σ ( qq ) × B R [ f b ] AAA σ ( HA ) BR ( H → AA ) -3 -2 -1 Σ σ ( gg/b ¯ b ) × BR [fb]10 -1 σ ( qq ) × B R [ f b ] AAZ σ ( HA ) BR ( H → ZA ) -3 -2 -1 Σ σ ( gg/b ¯ b ) × BR [fb]10 -1 σ ( qq ) × B R [ f b ] AH ± W ∓ σ ( HA ) BR ( H → W ± H ∓ ) σ ( H + H − ) BR ( H ± → W ± A ) -3 -2 -1 Σ σ ( gg/b ¯ b ) × BR [fb]10 -1 σ ( qq ) × B R [ f b ] hhA σ ( HA ) BR ( H → hh ) -3 -2 -1 Σ σ ( gg/b ¯ b ) × BR [fb]10 -1 σ ( qq ) × B R [ f b ] hhZ σ ( hA ) BR ( A → Zh ) -3 -2 -1 Σ σ ( gg/b ¯ b ) × BR [fb]10 -1 σ ( qq ) × B R [ f b ] hHZ σ ( HA ) BR ( A → Zh ) σ ( hA ) BR ( A → ZH ) -3 -2 -1 Σ σ ( gg/b ¯ b ) × BR [fb]10 -1 σ ( qq ) × B R [ f b ] HH ± W ∓ σ ( HA ) BR ( A → W ± H ∓ ) σ ( H + H − ) BR ( H ± → W ± H ) Figure 5: Comparison of the cross sections for the qq (cid:48) -initiated subprocesses and their gg/bb -initiated counterparts, for selected neutral 3BFSs. The dashed line indicates where the crosssections are of equal magnitude.the more useful modes.For the neutral 2BFSs too we consider the possibility of one of the Higgs bosons decaying, andthe resulting 3BFSs for which q ¯ q cross sections exceed 1 fb are shown in Fig. 5 and Tab. 2. Again,we see some cross sections dominated by q ¯ q production. Here too all of the possible Higgs-to-Higgsdecays are included, apart from H → H + H − , which is not kinematically available to any of ourpoints. As with the charged 3BFSs, plots involving H ± → W ± A , H → AA , or H → AZ aresparsely populated, since these decays are only allowed for a small number of scanned points. Evidently, based on our results so far, several different processes and final states could poten-tially be observed at the LHC, thus serving as probes of the various couplings appearing in the2HDM Lagrangian. In Tab. 3 we have listed the ten triple-Higgs couplings (a – h) and the six(pseudo)scalar-gauge couplings (i – n) that appear in the 2HDM Lagrangian (assuming minimalflavour violation) row-wise and all the possible di-Higgs 2BFS combinations column-wise. If acoupling can potentially enter the secondary vertex of both gg/b ¯ b - and q ¯ q -initiated s -channel pro-duction processes of a given 2BFS at the LHC, the corresponding cell is checked.In Tab. 4 we similarly show possible 3BFSs, comprising of at least two Higgs bosons and atmost one gauge boson, that can originate from the 2BFS at the top of a column. For a given 3BFS,the coupling at the start of the corresponding row appears in, instead of the secondary vertex in the8rocess 1 Process 23BFS 2BFS BR σ max qq (cid:48) σ max qq (cid:48) σ max gg/bb AAW ± AH ± ( H ± → W ± A ) 322 − H ± H ± W ± HH ± ( H → W ± H ∓ ) 103 AH ± ( A → W ± H ∓ ) 94 − AAH ± HH ± ( H → AA ) 95 − HAW ± HH ± ( H ± → W ± A ) 91 AH ± ( H ± → W ± H ) 12 − hH ± Z AH ± ( A → Zh ) 22 − HHW ± HH ± ( H ± → W ± H ) 18 − hHW ± HH ± ( H ± → W ± h ) 16 hH ± ( H ± → W ± H ) 1 − hAW ± AH ± ( H ± → W ± h ) 15 hH ± ( H ± → W ± A ) 6 − AH ± Z HH ± ( H → ZA ) 13 − HH ± Z AH ± ( A → ZH ) 8 − hhH ± HH ± ( H → hh ) 7 − hhW ± hH ± ( H ± → W ± h ) 2 − AAA HA ( H → AA ) 135 4 AH ± W ± H + H − ( H ± → W ± A ) 58 HA ( H → W ± H ∓ ) 19 14 HH ± W ± HA ( A → W ± H ∓ ) 23 H + H − ( H ± → W ± H ) 4 3 AAZ HA ( H → ZA ) 23 1 hHZ HA ( A → Zh ) 12 4 HHZ HA ( A → ZH ) 11 5 hH ± W ± H + H − ( H ± → W ± h ) 6 hA ( A → W ± H ∓ ) 1 9 hhA HA ( H → hh ) 3 0.3 hhZ hA ( A → Zh ) 2 4Table 2: Maximum cross sections for each process, in fb. Only cross sections above 1 fb are included.production process of its parent 2BFS, the tertiary vertex between one of the two incoming Higgsbosons and an outgoing Higgs+Higgs/gauge state. A 3BFS has a ‘ ∗ ’ next to it if the incoming Higgsstate is necessarily off-shell, i.e., if its mass, m x , is smaller than the sum of the masses, m j + m k , ofthe two outgoing particles. In such a case, the cross section for the corresponding process cannotbe evaluated in the σ ( gg/b ¯ b/q ¯ q ( (cid:48) ) → h i h x ) × BR( h x → h j + h k /V k ) approach adopted here, and ittherefore does not contribute to the cumulative cross section shown for a given 3BFS in the scatterplots in the previous sections. The rightmost graph in Fig. 6 illustrates this scenario. In boththe tables, charged final states are typeset in bold and a box appears around those for which thetotal ( q ¯ q ) production cross section can be larger than 1 fb, while a box around a neutral final stateindicates that the cross section for q ¯ q production can exceed that for gg/b ¯ b production (for certainparameter space configurations).There are some important inferences that can be drawn from the table (note again that allthe statements regarding the 3BFSs are valid only in the parameter space regions that satisfy m x > m j + m k ). One can notice many instances where a coupling appears in more relevant 3BFSsthan 2BFSs. While a given 2BFS typically reflects contributions from several diagrams containingdifferent couplings, the 3BFSs often arise from multiple initial 2BFSs, and the decays leading to We note that virtual exchanges could also be potentially relevant for the cases where m x > m j + m k , especiallyjust above threshold. However, we again expect that the cross sections highlighted here will receive relatively smallcorrections from such contributions owing to the narrow widths of the intermediate states. oupling 1. hh HH AA H + H − hH hA hH ± HA H H ± AH ± a. λ hhh (cid:88) b. λ hhH (cid:88) (cid:88) c. λ hHH (cid:88) (cid:88) d. λ hAA (cid:88) (cid:88) e. λ hH + H − (cid:88) (cid:88) f. λ HHH (cid:88) g. λ HAA (cid:88) (cid:88) h. λ HH + H − (cid:88) (cid:88) i. λ hAZ (cid:88) j. λ HAZ (cid:88) k. λ H + H − Z (cid:88) l. λ hH + W − (cid:88) m. λ HH + W − (cid:88) n. λ AH + W − (cid:88) Table 3: The ten 2BFS combinations available in the 2HDM. Charged 2BFSs, which can onlybe q ¯ q ( (cid:48) ) -produced, are typeset in bold in the top row, while a box around a neutral 2BFS impliesthat the cross section for its production from q ¯ q ( (cid:48) ) -initiated processes can exceed that from gg/bb -initiated processes. A (cid:88) appears in a cell if the coupling at the start of the corresponding row mayenter the s -channel production of the given 2BFS. Coupling 1. hh HH AA H + H − hH hA hH ± HA H H ± AH ± a. λ hhh ( hhh ) ∗ ( hhH ) ∗ ( hhA ) ∗ ( hhH ± ) ∗ b. λ hhH hhH hhh hhA hhH ± c. λ hHH ( hHH ) ∗ ( hhH ) ∗ ( hHA ) ∗ ( hHH ± ) ∗ hH + H − d. λ hAA ( hAA ) ( hAA ) ∗ ( hH + H − ) ∗ HAA ( hhA ) ∗ ( AAH ± ) ∗ ( hHA ) ∗ AAA e. λ hH + H − hH + H − ( hH + H − ) ∗ HH + H − AH + H − ( hhH ± ) ∗ ( hHH ± ) ∗ ( hAH ± ) ∗ H + H − H ± f. λ HHH ( HHH ) ∗ ( hHH ) ∗ ( HHA ) ∗ ( HHH ± ) ∗ g. λ HAA
HAA ( HAA ) ∗ hAA ( hHA ) ∗ ( HHA ) ∗ AAH ± HAH ± AAA h. λ HH + H − HH + H − ( HH + H − ) ∗ ( hHH ± ) ∗ AH + H − ( HHH ± ) ∗ ( HAH ± ) ∗ H + H − H ± i. λ hAZ hAZ hAZ HAZ hhZ AH ± Z hHZ hH ± Z AAZ j. λ HAZ
HAZ HAZ hAZ hHZ HHZ AH ± Z H H ± Z AAZ k. λ H + H − Z H + H − Z l. λ hH + W − hH + W − hH + W − HH + W − hH + W − hhW ± hH W ± hAW ± AH + W − H + H − W ± m. λ HH + W − HH + W − HH + W − hH + W − hH W ± HH + W − HH W ± HAW ± AH + W − H + H − W ± n. λ AH + W − AH + W − AH + W − hAW ± HAW ± AAW ± H + H − W ± Table 4: 3BFSs that can result from the decay, via a vertex involving the coupling at the start ofa given row, of one of the Higgs bosons in the 2BFS at the top of the column. Again, a charged3BFS has a box around it if its total cross section can exceed 1 fb, while a box around a neutral3BFS indicates that its q ¯ q ( (cid:48) ) production can dominate over gg/bb production. A ‘ ∗ ’ next to a 3BFSimplies that its cross section has not been calculated in this study. See text for more details.10 qq H ( ∗ ) h hAA ¯ qq A ∗ A hhZ ¯ qq H h ∗ hhh Figure 6: Examples of s -channel diagrams considered for the production of three-body final states.Processes like the one on the right are not taken into account in the scatter plots shown above, as twoof the three final state particles result from an incoming Higgs state that is necessarily off-shell.Thus the corresponding cross sections cannot be calculated as σ ( gg/b ¯ b/q ¯ q ( (cid:48) ) → h i h x )*BR( h x → h j + h k /V k ). Such 3BFSs have therefore been typeset in grey colour in Tab. 4. m A [ G e V ] m H [GeV] λ ( hh H ) m A [ G e V ] m H [GeV] λ ( H AA ) Figure 7: The triple-Higgs couplings λ hhH and λ HAA , in units of the value of the Higgs tripleself-coupling in the SM, shown by the color scale in the plane of the masses of the heavy CP-evenand CP-odd neutral scalars.3BFSs reflect not only the relevant coupling, but also all other couplings and masses involved indetermining the width of the decaying particle. A careful kinematical selection of events mighthelp disentangle (some of) these couplings from each other, and complementary analyses of the twotypes of states can greatly enhance the potential of the LHC to probe such couplings.While only q ¯ q ( (cid:48) ) -production is available at leading order for charged 3BFSs, it is clearly thepreferred mode also for several neutral 3BFSs, especially those involving the λ hAZ , λ HAZ and λ hH + W − , λ HH + W − couplings. Additionally, we see that all of the charged 3BFSs that include a W ± can have a cross section in excess of 1 fb, which is a consequence of the cross section for the HH ± and AH ± q ¯ q ( (cid:48) ) -productionof the relevant 3BFSs, if observed, could prove crucial for pinning down the λ hH + W − , λ HH + W − and λ AH + W − couplings at the LHC. Of particular relevance for disentangling the underlying Higgs dynamics are the triple-Higgs cou-plings. In Tab. 4, rows b and g, we see that the couplings λ hhH and λ HAA enter, respectively, inprocesses for which EW production dominates for neutral 3BFSs hhA and
AAA , and at the sametime, also in EW processes giving substantial cross sections for charged 3BFSs hhH ± and AAH ± .In order to give an impression of the possible sizes of the λ hhH and λ HAA couplings, the colourheat map in Fig. 7 shows them in units of the SM-like Higgs self-coupling λ hhh , as functions ofthe neutral scalar masses m H and m A . We further show the cross sections for hhH ± and AAH ± production as functions of λ hhH and λ HAA , respectively, in Fig. 8.The λ hhH and λ HAA couplings range from essentially zero up to several times larger than the11 σ ( hh H + ) [f b ] λ hhH σ ( AA H + ) [f b ] λ HAA
Figure 8: Cross-sections σ ( hhH ± ) and σ ( AAH ± ) plotted against the triple-Higgs couplings λ hhH and λ HAA , respectively, with the couplings plotted in units of the value of the Higgs triple self-coupling in the SM, 3 m h /v . The cross sections are the same as those plotted in Fig. 2.Higgs self-coupling in the SM. The λ HAA coupling in particular can be sizeable, and may lead to alarge σ ( AAH ± ), although a relatively small portion of the scanned parameter space lies above thethreshold for this process, as was previously also noted in the central panel of the lowermost rowin Fig. 2. On the other hand, the production of hhH ± , which is sensitive to the λ hhH coupling, iskinematically allowed over a much larger portion of our scanned parameter space. While the crosssection for this 3BFS is generally smaller than σ ( AAH ± ), it can still reach upto 10 fb. In order to fully establish the EWSB mechanism, whether in the SM theory or beyond it, a fullreconstruction of the Higgs potential is required. This entails measuring experimentally the triple-Higgs couplings, which can only be achieved if scattering processes yielding two or more Higgsbosons can be isolated in the detector. Historically, most studies of these couplings have exploitedproduction modes that are enhanced in the hadronic environment of the LHC, primarily gluon-gluon fusion. Such studies have covered both the SM as well as extended Higgs sectors, chiefly2HDMs, with and without Supersymmetry. In such beyond-the-SM scenarios, couplings of theHiggs bosons to b -(anti)quarks can be enlarged with respect to the SM case, so that b ¯ b -inducedproduction can be relevant in onsetting final states with two or more Higgs bosons. This approachis somewhat limited, though, on two accounts. Firstly, these subchannels cannot lead to electricallycharged final states. Hence, they necessarily miss out on some couplings involving a charged Higgsboson, in parameter space regions of the 2HDMs where the neutral final state production processesthese couplings might alternatively enter are kinematically unavailable. Secondly, there could existfurther production channels (for neutral final states) offering access to many other triple-Higgscouplings, also needed to reconstruct the full EWSB potential.In this paper, we have therefore concentrated on EW-induced channels, where the initial stateconstitutes (primarily) of valence quark flavours, which annihilate via both electrically neutraland charged currents into neutral and charged 2-Higgs (and up to 3-Higgs) final states. We haveshown that the production cross sections for several charged final states (precluded to the gg and b ¯ b production modes) are large enough to be potentially accessible at the LHC, either duringthe Runs 2 and 3 or at its High Luminosity (HL-LHC) stage (depending on the parameter spaceconfiguration). We have also illustrated that such EW-induced channels can often be competitivewith, when not overtaking, those induced by gg and b ¯ b fusion, other than offering more probes ofvarious triple-Higgs couplings. Finally, as these EW channels are often mediated by weak gaugebosons (i.e., W ± and Z states), they can provide sensitivity to couplings involving one of these and12wo Higgs bosons.We have come to these conclusions after studying, as a preliminary step of a long-term investi-gation that will eventually include a complete detector simulation, the fully inclusive parton-levelyield of the aforementioned EW channels. This study tackled the phenomenology of the so-calledType-I 2HDM, as illustrative for conditions which may emerge in other possible non-minimal Higgsconstructs, in the presence of standard theoretical constraints as well as the latest experimentallimits coming from EW precision data, collider searches for the Higgs boson(s), and measurementsof the heavy flavour observables.In short, we advocate, alongside the time-honoured analyses based on QCD-induced processes,investigations of EW processes as well, which we have shown to offer improved and expandedsensitivity to both Higgs and gauge-Higgs structure of the underlying EWSB dynamics, which mayor may not be the same as the SM one. Acknowledgements
SMo is supported in part through the NExT Institute and the STFC Consolidated Grant ST/L000296/1.RE, WK and SMo are partially supported by the H2020-MSCA-RISE-2014 grant no. 645722 (Non-MinimalHiggs).
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