The reconstruction of the Higgs potential in the Standard Model or
supersymmetric theories demands the measurement of the trilinear Higgs
couplings. These couplings affect the multiple production of Higgs bosons at
high energy colliders. We present a systematic overview of the cross sections
for the production of pairs of (light) neutral Higgs bosons at the LHC. The
analysis is carried out for the Standard Model and its minimal supersymmetric
extension.Comment: Latex, 11 pages, uses feynmp.sty [included]. The complete paper,
  including figures, is also available via anonymous ftp at
  ftp://ttpux2.physik.uni-karlsruhe.de/ttp99/ttp99-17/ or via www at
  http://www-ttp.physik.uni-karlsruhe.de/Preprints

Djouadi, A.

Kilian, W.

Muhlleitner, M.

Zerwas, P. M.

English

arXiv

The reconstruction of the Higgs potential in the Standard Model or supersymmetric theories demands the measurement of the trilinear Higgs couplings. These couplings affect the multiple production of Higgs bosons at high energy colliders. We present a systematic overview of the cross sections for the production of pairs of (light) neutral Higgs bosons at the LHC. The analysis is carried out for the Standard Model and its minimal supersymmetric extension

Mühlleitner, M.

Zerwas, Peter

DESY Publication Database

Production of neutral Higgs-boson pairs at LHC

Djouadi, Abdelhak

Kilian, W

Mühlleitner, M M

Zerwas, Peter M

CERN Document Server

hep-ph/9904287DESY 99/033TTP99-17PM/99-21Production of Neutral Higgs-Boson Pairs at LHCA. Djouadi1, W. Kilian2, M. Muhlleitner3 and P.M. Zerwas31Lab. de Physique Mathematique, Universite Montpellier, F-34095 Montpellier Cedex 52Institut fu¨r Theoretische Teilchenphysik, Universita¨t Karlsruhe, D-76128 Karlsruhe3Deutsches Elektronen-Synchrotron DESY, D-22603 HamburgAbstractThe reconstruction of the Higgs potential in the Standard Model or supersymmetric theoriesdemands the measurement of the trilinear Higgs couplings. These couplings aect the multi-ple production of Higgs bosons at high energy colliders. We present a systematic overview ofthe cross sections for the production of pairs of (light) neutral Higgs bosons at the LHC. Theanalysis is carried out for the Standard Model and its minimal supersymmetric extension.1. Introduction1. Self-interactions of the Higgs eld in the scalar sector induce the breaking of the elec-troweak symmetry SU(2)L  U(1)Y down to the electromagnetic symmetry U(1)EM of theStandard Model (SM). Gauge bosons and fermions acquire masses by interactions with thenon-zero Higgs eld v = 1/(p2GF )1/2 in the ground state of the scalar potential. It istherefore an important experimental task to reconstruct the elements of the Higgs potentialwhich gives rise to the spontaneous breaking of the electroweak symmetry. The shape of thepotential is determined by the mass MH of the physical Higgs boson eld, and its trilinearand quadrilinear couplings. The trilinear coupling [1],λHHH = 3M2H/M2Z (1)in units of λ0 = M2Z/v, can be measured directly in the production of Higgs-boson pairs athigh energy colliders. In proton collisions at the LHC, Higgs pairs can be produced throughdouble Higgs-strahlung o W and Z bosons [2], WW and ZZ fusion [3], and gluon-gluonfusion [4]; in generic notation:double Higgs-strahlung : qq! W /Z ! W/Z + HHWW/ZZ double-Higgs fusion : qq! qq + WW/ZZ! HHgluon fusion : gg! HHCharacteristic diagrams of the three processes are shown in Fig.1. With values typicallynear 10 fb, high integrated luminosities are needed to generate a suciently large ensembleof signal events and to cope with the large number of background events.2. The Minimal Supersymmetric extension of the Standard Model (MSSM) incorporates aquintet of Higgs bosons: h, H , A, H; the particles h, H are neutral and CP-even whileA is neutral and CP-odd. The mass of the light CP-even Higgs boson h is limited to lessthan about 130 GeV. The masses of the other Higgs bosons are typically of the order of theelectroweak symmetry breaking scale v, yet they may extend up to values of order 1 TeV.The MSSM Higgs system is described inherently by two parameters which are generallychosen as the mass MA of the pseudoscalar Higgs boson and the mixing parameter tan β,ratio of the vacuum expectation values of the two neutral Higgs elds. Radiative correctionsintroduce the mass and mixing parameters of the heavy t/~t and b/~b chiral multiplets intothe system.In CP-invariant theories, six types of trilinear couplings are realized among the neutralHiggs elds [1{5]:hhh, Hhh, HHh, HHHhAA, HAAThey can be expressed in terms of the two mixing angles β and α, mixing angle in the1double Higgs-strahlung: qq ! ZHH/WHHW/ZHqq¯HHW/ZHHW/ZHHW/ZWW/ZZ double-Higgs fusion: qq ! qqHHW/Z HW/ZqqHHW/ZHHHHgg double-Higgs fusion: gg ! HHtHggHHHHFigure 1: Processes contributing to Higgs-pair production in the Standard Model at the LHC:double Higgs-strahlung, WW/ZZ fusion, and gg fusion (generic diagrams).CP-even Higgs sector. The couplings involving two light Higgs bosons, for example, aregiven by the trigonometric functionsλhhh = 3 cos 2α sin(β + α) + 3M2Zcos αsin βcos2 α (2)λHhh = 2 sin 2α sin(β + α)− cos 2α cos(β + α) + 3 M2Zsin αsin βcos2 αThe couplings are dened in units of λ0. They are renormalized indirectly by the renorma-lization of the mixing angle α and directly by additive terms proportional to the radiativecorrection parameter  which, to leading order, is given by  = 3GF M4t /(p2pi2 sin2 β) ln(M2t˜/M2t ) [6]. In the subsequent numerical analysis the complete one-loop and the leadingtwo-loop corrections to the Higgs masses and couplings [7] are included . The size of thecouplings has been exemplied for a set of parameters in Ref.[1].The trilinear MSSM Higgs couplings are involved in a large number of multi-Higgs pro-2cesses at the LHC [8{9]:double Higgs-strahlung : qq !W/Z + HiHj and W/Z + AA [Hi,j = h, H ]triple Higgs production : qq ! AHiHj and AAAWW/ZZ double-Higgs fusion: qq ! qq + HiHj and qq + AAgg fusion : gg ! HiHj , HiA and AAIn this analysis we will restrict ourselves to a specic class of nal states while a comprehen-sive description of all processes will be deferred to a subsequent report [10]; we will studynal states involving two light Higgs bosons h:pp ! gg ! hh (3)pp ! Z/W + hh and A + hhThey are generated either in the continuum or, for moderate values of tan β, in cascadedecays, too [11]:H ! hh, A ! Zh and H !Wh (4)A set of typical diagrams is shown in Fig.2. We will also present selected results on cascadedecays involving heavy Higgs bosons H in the nal state; they can be generated in the chainsqq ! Z ! AH ! ZHh (5)qq ! W  ! HH !WHhThese chains give rise to large rates, yet they do not involve trilinear Higgs couplings butonly gauge couplings. The corresponding diagrams are shown in Fig.3.The cross sections for continuum production are generally small and it will be dicultto discriminate the signal from the background, after the decay of the Higgs particles intopairs of b quarks, for instance. Cascade decays, on the other hand, have been proposed tosearch for these particles at the LHC [12].The present paper has got a limited goal. We have built up the general theoreticalformalism for multiple Higgs production at the LHC in the Standard Model and the MSSM,and we discuss a few examples in detail, see also Ref.[10]. Just setting the base for theseprocesses we do not intend to consider background reactions in a systematic way; suchsimulations can only be carried out by taking proper account of detector properties, what isbeyond the scope of this paper.3double Higgs-strahlung: qq ! Zhh/WhhW/Zh, Hqq¯hhW/ZH±/AhhW/ZhhW/ZhhW/Ztriple Higgs production: qq ! AhhZH, hqq¯hhAAhhAhhAWW/ZZ double-Higgs fusion: qq ! qqhhW/Z H, hW/ZqqhhW/ZhhH±/Ahhhhgg double-Higgs fusion: gg ! hht, bh, HgghhhhFigure 2: Processes contributing to double and triple Higgs production involving trilinearcouplings in the MSSM.cascade decay: qq ! AH/HH ! ZHh/WHhW/ZH±/Aqq¯HhW/ZFigure 3: Processes which contribute to double light plus heavy Higgs production in the MSSMbut which do not involve trilinear couplings.490 100 120 140 160 180 1900.1110100MH[GeV]SM: pp → HH +XLHC: σ [fb]WHH+ZHHWW+ZZ → HHgg → HHWHH:ZHH ≈ 1.6WW:ZZ ≈ 2.3Figure 4: The cross sections for gluon fusion, WW/ZZ fusion and double Higgs-strahlungWHH, ZHH in the SM. The vertical arrows correspond to a variation of the trilinear Higgscoupling from 1/2 to 3/2 of the SM value.2. Higgs Pairs in the Standard ModelThe cross sections for double Higgs-strahlung o W/Z bosons and for vector-boson fusioncan be evaluated, mutatis mutandis, at the quark level for the LHC in the same way asfor e+e− collisions, cf. Ref.[1]; just the couplings have to be adjusted properly. The protoncross sections are derived by folding the parton cross sections σ^(qq0 ! HH ; s^) of the quarksubprocesses with the appropriate luminosities dLqq′/dτ :σ(pp! HH) =∫ 14M2H/sdτdLqq′dτσ^(qq0 ! HH ; s^ = τs) (6)wheredLqq′dτ=∫ 1τdxxq(x; Q2)q0(τ/x; Q2) (7)with q and q0 denoting the parton densities in the proton [13], taken at a typical scaleQ  MH .The large number of gluons in high-energy proton beams provides an additional mecha-nism for the production of Higgs pairs: gluon fusion gg ! HH [4]. The proton cross sectionis derived by folding the parton cross section σ^(gg ! HH) with the gluon luminosity. Thecoupling between gluons and SM Higgs bosons is mediated by heavy top-quark loops. As5expected from single Higgs production [14], QCD radiative corrections are particularly im-portant for this channel. They have been determined in the low-energy limit of small Higgsmasses M2H  4M2t , leading to a K factor K  1.9 [15]. A K factor of similar size isgenerally expected for Higgs masses beyond the top-quark threshold.The cross sections are shown in Fig.4 for the intermediate Higgs mass range discussedabove. Gluon fusion dominates over the other mechanisms. The WW/ZZ fusion mechanismsare the next important channels. In addition to the four b jets, the four WW ()WW () bosonsor the mixed bbWW () pairs generated in the decays of the two Higgs bosons, the light-quark jets associated with the equivalent W/Z bosons in the fragmentation, q ! W/Z + qcan be exploited to tag fusion events; these jets are emitted at average transverse momentapT  1/2MW/Z . WW fusion dominates over ZZ fusion at a ratio WW :ZZ  2.3. Thecross sections for double Higgs-strahlung are relatively small. This follows from the scalingbehavior of the cross sections which drop  1/s^. The cross sections for Higgs-strahlungo W and Z bosons are combined in Fig.4; their relative size is close to W/Z  1.6. Thevertical arrows indicate the sensitivity of the cross sections to the size of the trilinear Higgscoupling; they correspond to a modication of the trilinear SM coupling λHHH by the adhoc rescaling coecient κ = 1/2 ! 3/2.3. Higgs Pairs in Supersymmetric TheoriesWith appropriate modications, the pattern of MSSM Higgs pair-production at the LHC issimilar to the characteristics in e+e− collisions [1,5]. An important exception however is theadditional gluon-fusion channel [9].1. We will focus on the production of pairs of light Higgs bosons: pp ! hh. For moderatevalues of tanβ, the hh production channels follow the pattern of the Standard Model, withgluon fusion being dominant, Fig.5a. However, within the cascade-decay regions of the heavyHiggs bosons H , H the cross sections rise dramatically. These domains are marked in thegures explicitly by arrows. Large contributions to the cross sections are generated by heavyHiggs formation gg/V V ! H ! hh in the fusion channels, and H ! Wh decay inHiggs-strahlung W ! Hh ! Whh. As expected [9], the gluon-fusion hh cross sectionbecomes very large in the H decay region, giving rise to a sample of about a million hhevents. This process therefore provides an important channel for searching for MSSM Higgsbosons at the LHC [12]. The sensitivity of the cross sections with regard to a variation ofλhhh by the rescaling factor κ = 1/2 to 3/2 is close to ten per-cent in the continuum whilethe sensitivity of H cascade decays to a variation of λHhh is indicated by arrows.For large tan β, a huge ensemble of hh continuum events is generated by gluon fusion,Fig.5b. The enhancement is due to the large hbb Yukawa coupling,  mb tan β, in the b-quarkloops connecting the gluons with the Higgs bosons. Since the box diagrams are enhanced6SM9590 100 1050.010.11101001000104Mh[GeV]MSSM: pp→hh+Xtanβ=3LHC: σ[fb]Whh:Zhh ≈ 1.8WW:ZZ ≈ 2.6Whh+ZhhWW+ZZ→hhAhhgg→hhH±→W±hH → hhFigure 5a:Total cross sections for MSSM hh production via double Higgs-strahlung Whh andZhh, WW/ZZ fusion and gluon fusion at the LHC for tan β = 3, including mixing eects(A = 1 TeV, µ = −1 TeV).90 100 1100.11101001000104Mh[GeV]MSSM: pp→hh+Xtanβ=50LHC: σ[fb]Whh+ZhhWW+ZZ→hhgg→hhWhh:Zhh≈1.7WW:ZZ≈1.8SMFigure 5b:Total cross sections for MSSM hh production via double Higgs-strahlung Whh,Zhh, WW/ZZ fusion and gluon fusion at the LHC for tan β = 50, including mixing eects(A = 1 TeV, µ = 1 TeV).79590 100 1050.010.1110Mh[GeV]MSSM: pp→Hh+Xtanβ=3LHC: σ[fb]WHhZHhH±→W±hA→ZhFigure 6: Total cross sections for MSSM Hh production in the processes WHh and ZHhfor tanβ = 3, including mixing eects (A = 1 TeV, µ = −1 TeV).quadratically compared to the triangle diagrams, the sensitivity to the trilinear coupling issmall.1 The continuum cross sections of the V V fusion and Higgs-strahlung channels aresuppressed with respect to the Standard Model until the decoupling limit is reached. Forlarge tan β cascade decays do not play a role in hh pair production; the kinematical decaythresholds are reached only for masses for which the decoupling limit is being approached.2. Two processes involve Higgs-pair nal states including a light plus a heavy Higgs boson.However for cross sections in excess of 1 fb, Fig.6, the nal states are generated in cascadedecays by gauge interactions:pp ! AH ! ZHhZpp ! HH! WHhW(8)These processes are therefore not suitable for measuring trilinear Higgs couplings.4. ConclusionsIn the present paper we have analyzed the production of neutral Higgs-bosons pairs invarious channels at the LHC which can eventually be used to measure fundamental trilinear1The multi-b final states pp ! hh ! (bb¯)(bb¯) with two resonance structures and large transverse momentaprovide an outstanding signature which may be exploited to search for h Higgs bosons in the range of largetan β (and moderate MA) not covered hitherto at LHC in standard channels.8Higgs self-couplings. In a rst step we have compared the production cross sections in theStandard Model, assuming a Higgs-boson mass in the intermediate range. Moreover, we havecalculated the cross sections for pairs of light Higgs bosons in the Minimal Supersymmetricextension of the Standard Model. Earlier results haven been combined with new calculationsin these analyses.The continuum cross sections are generally small in the SM and MSSM, yet not for gluonfusion. The trilinear SM Higgs coupling and the trilinear coupling λhhh in the MSSM maythus be accessible experimentally, provided the backgrounds can be rejected suciently well.If Higgs cascade decays H ! hh occur in the MSSM, they can be exploited to measure oneof the couplings between light and heavy CP-even neutral Higgs bosons, λHhh.AcknowledgementsWe are grateful to M. Spira for discussions and for providing us with a source code for gluonfusion of Higgs pairs.9References[1] A. Djouadi, W. Kilian, M. Muhlleitner and P.M. Zerwas, Report DESY 99/001 [hep-ph/9903229] and Eur. Phys. J. in press.[2] V. Barger, T. Han and R.J.N. Phillips, Phys. Rev. D38 (1988) 2766.[3] A. Dobrovolskaya and V. Novikov, Z. Phys. C52 (1991) 427; D.A. Dicus, K.J. Kallianpurand S.S.D. Willenbrock, Phys. Lett. B200 (1988) 187; K.J. Kallianpur, Phys. Lett.B215 (1988) 392; A. Abbasabadi, W.W. Repko, D.A. Dicus and R. Vega, Phys. Rev.D38 (1988) 2770; Phys. Lett. B213 (1988) 386.[4] E.W.N. 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Production of Neutral Higgs-Boson Pairs at LHC

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