Triple Higgs coupling as a probe of the twin-peak scenario

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Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Triple Higgs coupling as a probe of the twin-peak scenario

Amine Ahriche

^a^,^b^,^c^,^∗

, Abdesslam Arhrib

^d

, Salah Nasri

^e

aDepartmentofPhysics,UniversityofJijel,PB98OuledAissa,DZ-18000Jijel,Algeria

bTheAbdusSalamInternationalCentreforTheoreticalPhysics,StradaCostiera11,I-34014,Trieste,Italy cFakultätfürPhysik,UniversitätBielefeld,33501Bielefeld,Germany

dUniversitéAbdelMalekEssaadi,FacultédesSciencesetTechniques,B.P416,Tangier,Morocco ePhysicsDepartment,UAEUniversity,POB17551,AlAin,UnitedArabEmirates

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received22November2014

Receivedinrevisedform16February2015 Accepted24February2015

Availableonline26February2015 Editor:J.Hisano

Keywords:

Higgs Singlets

di-Higgsproduction

Inthisletter,weinvestigatethecaseofatwinpeakaroundtheobserved125GeVscalarresonance,using di-HiggsproductionprocessesatbothLHCande⁺e⁻LinearColliders.WehaveshownthatbothatLHC andLinearColliderthetripleHiggscouplingsplayanimportantroletoidentifythisscenario;andalso thatthisscenariocanbedistinguishablefromanyStandardModelextensionbyextramassiveparticles whichmightmodifythetripleHiggscoupling.Wealsointroduceacriterionthatcanbeusedtorule out thetwinpeakscenario.

©²⁰¹⁵^TheÂuthors.^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

In July2012, ATLAS andCMS Collaborations[1,2] have shown theexistence ofaHiggs-likeresonancearound 125 GeVconﬁrm- ing thecornerstone of theHiggs mechanismthat predicted such particlelongtime ago. AllHiggscouplingsmeasured so farseem to be consistent, to some extent, with the Standard Model (SM) predictions.Moreover, inorderto establishtheHiggs mechanism asresponsibleforthephenomenaofelectroweaksymmetrybreak- ingonestillneedstomeasuretheselfcouplingsoftheHiggsand thereforetoreconstructitsscalarpotential.

RecentmeasurementsattheLHCshowthatthereisstilluncer- taintyontheHiggsmass;mh=125.3±0.4(stat.)±0.5(syst.)GeV for CMS [3] and mh=¹²⁵.0±⁰.5 GeV for ATLAS [4] from the diphoton channel and mh=¹²⁵.5±⁰.37(stat.)±⁰.18(syst.)GeV fromcombined channels.Despitethisrelativelylarge uncertainty, ascenariooftwodegeneratescalars around125.5 GeVresonance isneitherexcludednorconﬁrmed[5].

Inthe twin peak scenario (TPS); itis assumed that there are twoscalars h1,2 withalmost degeneratemassesaround 125 GeV.

Toourknowledge, there isno indication fromexperimental data whichdisfavorthisscenario.ThecouplingsofthetwinpeakHiggs toSMparticlesgh_iX X aresimplyscaledwithrespecttoSMrateby

*

Correspondingauthor.

E-mailaddresses:aahriche@ictp.it(A. Ahriche),aarhrib@ictp.it(A. Arhrib), snasri@uaeu.ac.ae(S. Nasri).

cosθ (forh₁) andsinθ (for h₂), whereθ isa mixingangle,such thatwehavethefollowingapproximatesumrule:

g²

h1f¯f

+

g²

h2f¯f

g²

hSMf¯f

,

g_h²

1V V

+

g²_h

2V V

g_h²

SMV V

,

(1)

where f canbeanyoftheSMfermionsandV =^W,Z vectorbo- son. Infact,thebranching ratiosoftheHiggs toSM particlesare SM-likeonlyiftheHiggsinvisibleisverysuppressedorkinemati- callyforbiddenaswillbeconsideredinourexample.Consequently, the single Higgs production such as gluon–gluon fusion at LHC, Higgs-strahlung,Vector BosonFusions, andtt H at¯ LHCande⁺e⁻ LinearColliders(LC)willobeythesamesumrule.Thesummation ofeventnumbers(bothforproductionanddecay)ofthetwopos- siblecases will be identicalto SM casesince cos²θ+^sin²θ=^1.

However, for processes with di-Higgs final states (pp(e⁻e⁺)→ hh+^{X ),}^the^triple^Higgs^couplings^may^playânîmportant^role,ând thereforetheseprocessescanbeusefultodistinguishbetweenthe cases ofone scalar ortwo degenerate ones around theobserved 125 GeVresonance.

ItiswellknownthatthetripleHiggscouplingscanbe,inprin- ciple, measured directly at the LHC with highluminosity option through double Higgs production pp→^gg→^hh ^[6]. ^Such ^measurement is rather challenging at the LHC, and for this purpose several parton level analysis have been devoted to this process.

It turns out that hh→^b_b¯

γ γ

[7],hh→^b_b¯

τ

⁺

τ

⁻ [7,8] and hh→ b_bW¯ ⁺_W⁻_[8,9]_ﬁnal_states_are_very_promising_for_Highluminosity.

http://dx.doi.org/10.1016/j.physletb.2015.02.062

0370-2693/©²⁰¹⁵^TheÂuthors.^Published^byÊlsevier^B.V.^Thisîsânôpenâccessârticleûnder^the^CC^BY^license(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

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Recently,CMSreported apreliminaryresultonthesearchforres- onantdi-Higgsproductioninb_b¯

γ γ

channel[10].

The LC has also the capability of measuring with better pre- cision: theHiggsmass andsomeof theHiggscouplings together with the self coupling of the Higgs [11]. Using recoil technique fortheHiggs-strahlungprocess, theHiggsmasscanbe measured with an accuracy of about 40 MeV [11]. We note that at LHC withhighluminosity wecanmeasuretheHiggsmasswithabout 100 MeVuncertaintywhichisquitecomparabletoe⁺e⁻ colliders.

The triple Higgscoupling can be extractedfrom e⁺e⁻→^Zh^∗→ Zhh at 500 GeV andeven better from e⁺e⁻→

νν

h^∗→

νν

hh at

√s>800 GeV.Inthisregard,theLHCande⁺e⁻LCmeasurements arecomplementary[12].

InRef.[13],theauthorshaveprovidedatooltodistinguishthe two-degeneratestatesscenariofromthesingleHiggsone.Theap- proachof [13] applies only tomodels which enjoy modiﬁcations ofh→

γ γ

ratewithrespecttotheSM.However,accordingtothe latestexperimentalresults,bothforATLASandCMSthedi-photon channel seem to be rather consistent with the SM [3,4]. In this workweproposeanewapproachtodistinguishtheTPS.Thisap- proachis basedon the di-Higgs productionwhich issensitive to the tripleHiggs coupling,that is modiﬁed inthe majorityof SM extensions.

Here,asanexample,weconsider,theTwo-SingletsModelpro- posedin[14],wheretheSMisextendedwithtworealscalarﬁelds S0 and

χ

1; each oneis oddunder adiscrete symmetry Z⁽₂⁰⁾ ^and Z⁽₂¹⁾respectively.Theﬁeld

χ

1 hasanon-vanishing vacuumexpec- tationvalue,whichbreaks Z⁽₂¹⁾ spontaneously,whereas,^S0 =^0;

andhence,S0 isadarkmattercandidate.BothﬁeldsareSMgauge singletsandhencecaninteractwiththe‘visible’particlesonlyvia theHiggsdoubletH .Thespontaneousbreakingoftheelectroweak andthe Z⁽₂¹⁾ ^symmetries^introduces ^the ^two ^vacuumexpectation values

υ

and

υ

1 respectively. ThephysicalHiggsh1 andh2,with masses m₁ and m₂ ^m1, are related to the excitations of the neutral component of the SM Higgs doublet ﬁeld, Re(H⁽⁰⁾), and the ﬁeld

χ

1 through rotation with a mixing angle θ and, with a speciﬁc choice in the parameter space, could give rise to two degenerate scalars around 125 GeV. In what follows, we denote byc=^cosθ ands=^sinθ.Thequarticandtriplecouplingsofthe physicalﬁeldshi aregivenintheappendicesin[15].

Inouranalysiswerequirethat¹:(i) allthedimensionlessquar- tic couplings to be ⁴

π

for the theory to remain perturbative, (ii) thetwoscalareigenmassesshouldbeinagreementwithrecent measurements [3,4]: we have checked that for the Two-Singlets model,thesplittingbetweenm1 andm2 couldbe oftheorderof 40 MeV.(iii) thegroundstatestability tobeensured;and(iv) we allowtheDMmassm₀ tobeaslargeas1 TeV.

In our work, we consider di-Higgs production processes at the LHC and e⁺e⁻ LC, whose values of the cross section could be signiﬁcant, namely,

σ

^{L H C}(hh) and

σ

^{L H C}(hh+^t¯t) at 14 TeV;

σ

^LC(hh+^Z) at500 GeV and

σ

^LC(hh+^Emiss) at1 TeV.All these processesinclude,atleast,oneFeynmandiagramwithtripleHiggs coupling. For the TPS, the total cross section gets contributions fromtheﬁnal statesh₁h₁, h₁h₂ andh₂h₂.Therefore thequantity tobecomparedwiththestandardscenariocanbeexpressed as:

σ

^TPS

(

hh

+

^X

) = σ (

h₁h₁

+

^X

) +

²

σ (

h₁h₂

+

^X

) + σ (

h₂h₂

+

^X

) ,

(2) whichcanbeparameterizedas:

σ

^TPS

₌ σ

_aar₁

+ σ

_abr₂

+ σ

_bb

,

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1 Actually,weconsideredthatallquarticcouplingstobeoforderunity;andthe singletvevυ1= χ1 =²⁰∼^{2000 GeV.}

Fig. 1. Numericalvaluesoftheparametersriin(4)for600benchmarksthatfulﬁll theabovementionedrequirements.

with

σ

aa+

σ

ab+

σ

bb=

σ

^SM(hh+^X)and

σ

aa,

σ

bb and

σ

ab corre- spondtothecrosssectioncontributionscomingfromtripleHiggs diagrams (a), non-triple Higgs diagrams(b) and the interference termintheamplitude,respectively.Thecoeﬃcientsri aredimen- sionlessparameters,thatreceivecontributionsfromtheﬁnalstates hihj, which depend on the mixing angle θ and the Higgs triple couplingsλ⁽_{i jk}³⁾.

In the TPS, the amplitudes for di-Higgs production processes haveSMFeynmandiagramswheretheHiggsfieldh isreplacedby h_i.Tocomputetheparametersr_i,wefirstestimatehowdoeseach amplitudegetmodifiedwithrespecttothecorrespondingSM one for each case hihj. For example,in the case ofh1h1 production, there aretwo typesof diagrams:(1) The onesthat involvetriple scalarinteractionsh1h1h1 andh2h1h1,withcouplingsequaltothe one ofa SM timesa factorofcλ⁽₁₁₁³⁾/λ^SM_hhh andsλ⁽₁₁₂³⁾/λ^SM_hhh, respectively. We denotethe total amplitude of thesetwo contributions byM(a).(2) TheoneswithnotripleHiggscouplings.Theirampli- tude,denotedbyM(b),isgivenbytheoneoftheSM scaledbya factorof c².Therefore,theamplitudes M(a,b) (where a (b)stand fortriple Higgs(non-tripleHiggs) Feynman diagrams) forthedi- Higgs productioncan be written in terms oftheir corresponding SMvaluesas:

h1h1: M(a)= [(^cλ⁽₁₁₁³⁾ +^sλ⁽₁₁₂³⁾)/λ^SM_hhh]M^SM(a), M(b)=^c²M^SM(b),

h2h2: M(a)= [(^cλ⁽₁₂₂³⁾ +^sλ⁽₂₂₂³⁾)/λ^SM_hhh]M^SM(a), M(b)=^s²M^SM(b),

h1h2: M(a)= [(^cλ⁽₁₁₂³⁾ +^sλ⁽₁₂₂³⁾)/λ^SM_hhh]M^SM(a), M(b)=^csM^SM(b),

whereλ^SM_hhhistheSM tripleHiggscouplingcalculatedatone-loop.

Thentheparametersriaregivenby:

r₁

=

c²

[λ

⁽₁₁₁³⁾²

+ λ

⁽₁₂₂³⁾²

+

²

λ

⁽₁₁₂³⁾²

] +

^s²

[λ

⁽₁₁₂³⁾²

+ λ

⁽₂₂₂³⁾²

+

²

λ

⁽₁₂₂³⁾²

] +

^2cs

[ λ

⁽₁₁₁³⁾

λ

⁽₁₁₂³⁾

+

²

λ

⁽₁₁₂³⁾

λ

⁽₁₂₂³⁾

+ λ

⁽₁₂₂³⁾

λ

⁽₂₂₂³⁾

]

/

λ

^SM_hhh

2

,

r₂

= {

^c³

λ

⁽₁₁₁³⁾

+

^3c²^s

λ

⁽₁₁₂³⁾

+

^3cs²

λ

⁽₁₂₂³⁾

+

^s³

λ

⁽₂₂₂³⁾

}/λ

^SM_hhh

.

(4) Thus,thevaluesofri quantifybyhowmucheachdi-Higgsprocess deviatesfromtheSMcase.InFig. 1,weshowtheparametersrias afunctionofsinθ forabout600chosensetsofthemodelparam- eters withinthecondition (1).Weseethat forverysmallmixing angle ri’s are approximately equal to unity, while for sinθ >0.8 andsinθ <−⁰.2,theparameterr₁ becomeslargerthanunityand

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Table 1

Differentcontributionstotheconsideredprocessescrosssections.NumbersforLHC aretakenfrom[16]atNLO.

σaa(fb) σab(fb) σbb(fb) σ^SM(fb)

hh 9.66 −49.9 70.1 29.86

hh+^t¯t 3.3164×¹⁰⁻² ⁰.13952 0.84731 1.02 hh+^Z ⁹.0206×¹⁰⁻³ ⁴.6999×¹⁰⁻² ⁹.005×¹⁰⁻² ⁰.14607 hh+^Emiss 5.1631×¹⁰⁻² −⁰.20867 0.29708 0.14004

r₂ acquires negative values. This behavior could lead to an en- hancement/reduction to the cross section depending on thesign oftheinterferencecontribution,

σ

ab,tothetotalcrosssection.This meansthatthemeasurementofthefollowingratio:

ξ (

hh

+

^X

) = σ

^TPS

pp

(

e⁻e⁺

) →

hh

+

X

σ

^SM

pp

(

e⁻e⁺

) →

^hh

+

^X

,

(5) couldbeveryusefultoconﬁrmorexclude thisscenariobasedon thedeviationofanyoftheparametersri fromunity.Forinstance, theratioξ (hh+^X)candeviatefromunityiftheSM isextended withmassiveparticles(SM+^MP)^that^couple^to^the^Higgs^doublet andcontributetothetripleHiggscouplingaswelltheHiggsmass.

In this case, r1=(1+)² and r2=¹+, where represents therelativeenhancementofthetripleHiggscouplingduetoSM+ MP.As we will show later, our considered scenario forsmall or

largemixingcouldbedistinguishedfromthecaseofSM+^MP^by combiningtheratio(5)fordifferentprocesses.

In Table 1, we give the values of

σ

aa,

σ

ab and

σ

bb for the corresponding di-Higgs production processes. We note that their contributions to the LHC process pp→^{hh and} ^to ^the ^LC ^one e⁺e⁻→^{Zhh seem} ^to ^be uncorrelated, which makes the Higgs triplecouplingusefultoprobethisscenarioanddistinguishitfrom (SM+^MP).

For the benchmarksconsidered previously inFig. 1, we illus- trate in Fig. 2 the production cross section of di-Higgs at e⁺e⁻ LC andLHC and in Fig. 3 the ratio ξ. As it can be seen, in the TPS,thecrosssectionoftheprocessespp→^hh, ^pp→^hh+^tt and¯ e⁻e⁺→^hh+^Emissaremostlyenhanced,whilefore⁻e⁺→^hh+^Z itisenhancedjustforthemixingvalues0.5<sinθ <0.8.

Nowletusdiscussthepossibilityofdisentanglingthe TPS from the SM+^MP. Ît îs ^clear ^from ^{Fig. 3} ^that ^for ^both ^LHC ând ^LC processeswithlargemixing,0.35<cos²θ <0.65,theTPSmayco- incidewithSM+^MP.^However,^fornon-maximalmixingvaluesthe TPSisclearlydifferentthanSM+^MP^whereâll^benchmarks^have thefollowingfeature

ξ

₁^{T P S}

+ ξ

₂^{T P S}

> ξ

₁^SM⁺^MP

() + ξ

₂^SM⁺^MP

() ,

(6) where ξ_i^{T P S} the ratio in (5) for any LHC or LC processes and ξ_i^SM⁺^MP() is the same ratio due the existence of massive par- ticles. Therefore,when measuring the quantities (5)for both the LHC ande⁺e⁻ LC processes,and one ﬁnds that the criterion (6) is not fulﬁlled,then it is a certain exclusion for thisscenario. In

Fig. 2. The cross section values(2)for the di-Higgs production processes for the 600 benchmarks used previously. The solid lines correspond to the SM cross sections.

Fig. 3. Theratiosξgivenin(5)forthedi-Higgsproductionprocessesforthe600benchmarkusedpreviously.Thegreenbenchmarkscorrespondtothelargemixingcase where0.35<cos²θ <0.65,andthebluepointrepresentstheSM;andthesolidcurverepresentsthecaseofaSMextension,wherethenewphysicsaffectsthetripleHiggs couplingasλhhh=λ^SM_hhh(1+);andthevalueoftherelativeenhancementcanbereadfromthepalette.(Forinterpretationofthereferencestocolorinthisﬁgurelegend, thereaderisreferredtothewebversionofthisarticle.)

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Table 2

Differentvaluesoftheratios(4)and(5)forthethreechosenbenchmarks.

B1 B2 B3

sinθ 0.53555 0.90126 −0.39802

r1 2.95386 2.88466 5.62286

r2 1.31634 0.28189 −1.26011

ξ (hh) 1.10345 2.80975 6.27248

ξ hh+tt¯

2.69728 2.51821 4.66603

ξ (hh+Z) 1.22243 0.88532 0.55827

ξ (hh+Emiss) 1.24900 2.76488 6.07213

Table 3

Theeventsnumberforthedifferentprocesseswithintheluminosityvaluesmen- tionedabovefortheSMandthebenchmarksshowninTable 2.

Events number Channel SM B1 B2 B3

pp→hh 4b 966.75 1066.8 2716.3 6063.9

2b2τ 106.70 117.74 299.8 669.27 2b2γ 3.89 4.29 10.93 24.4

pp→hh+t¯t 4b 33.02 89.06 83.15 154.07

e⁻e⁺→^hh+^Z ^4b ²³.65 28.91 20.94 13.2

e⁻e⁺→hh+Emiss 4b 45.34 56.63 125.36 275.31

case where the criterion (6) is fulfilled, detailed analysis is re- quired forin order to identify the mixing angle, the parameters r_i andthereforetheHiggstriplecouplings.Infact,bystudyingall thedi-HiggsproductionchannelsatbothLHCande⁺e⁻LConenot onlyconfirm/excludethisscenario, butalsodistinguished it from models where only one type of processes gets modified by new physicssuch as:itmanifests asnewsourcesofmissingenergyin e⁻e⁺→^hh+Êmiss [17],new colored scalar singlets contribution to pp→^{hh (or}^hh+^t¯t)[18],orthepresenceofaheavyresonant Higgs[19].

Inordertoshowwhetherthisscenariocanbetestedatcollid- ers,weconsiderthreebenchmarksthatmaybedistinguishedfrom SM+^MP^(i.e.,^three ^red^points ^from^{Fig. 3),}^and^compare^the ^di- Higgsdistribution(of thedi-Higgs invariantmassasan example) withtheSM one.Thecorrespondingvaluesofratiosri andξi are giveninTable 2,andinTable 3,wepresenttheexpectednumber ofeventsatboththeLHCandLC.Weseethatforbenchmark B2, theeventsnumberissigniﬁcantlylargerthantheSMforthechan- nelspp→2b2

τ

attheLHCande⁻e⁺→4b+EmissatLC’s,whileit isreducedfortheprocesses pp→^4b+^t¯t ande⁻e⁺→^4b+^{Z .}^For benchmark B1, the events number of the processes pp→^2b2

τ

ande⁻e⁺→^4b+^Emiss is SM-like butit is reduced forthe processes pp→^4b+^tt and¯ e⁻e⁺→^4b+^{Z .}^For^benchmark ^B3,the eventsnumberisreducedfortheconsideredprocesses.

InFig. 4,we illustratethedi-Higgs invariantmassdistribution (Mh,h)fortheprocess e⁻e⁺→^hh+^Emiss.Clearly,the TPS canbe easily distinguished from the SM, especially in the case of non- maximalmixing.However,thefullconﬁrmationofthe TPS requires theenlargementoftheinvestigationby takingintoaccount other di-Higgs productionchannels such ashhj j, hhW^±,hh Z and hht j attheLHC[20]andthee⁺e⁻ LC[11].

In conclusion, we have investigated the caseof twin-peak at the 125 GeV observed scalar resonance by considering different di-HiggsproductionprocessesatbothLHCande⁺e⁻ LC.Wehave introduced acriterion whose violationexcludestheTPS scenario, otherwise thisscenario can be surely distinguished fromthe SM andSMextendedbymassiveﬁeldsincaseofnon-maximalmixing.

Fig. 4. Normalizeddi-Higgsinvariantmassdistributionfortheprocesse⁻e⁺→hh+ Emissforthebackground(BG)andtheconsideredbenchmarksinTable 2.

Last butnotleast, we should note that thisscenariocould be realized within SM+(real/complex) singlet scalar, or any larger scalar field content. Thisincludes neutralor chargedscalars that are members anymultiplets, wheretwo degenerate scalareigen- states h1,2 at 125 GeV, do couple to the SM gauge fields and fermions by more than ∼^90%, î.e., ^the ^sum ^rule ⁽¹⁾ îs ^fulfilled.² Ifthe measurementofdi-Higgs processesatLHCand/or e⁺e⁻ LC turnouttobeconsistentwithSMpredictions,thenitwillbevery challengingtodistinguishthe TPS scenario.

If the measurement of the couplings hf ¯f and hV V become much more precise from the future experiment data, it may be possiblethatonecouldbesensitivetotheradiativecorrectionsef- fecttothesecouplings.Suchradiativecorrectionstohf¯f andhV V couplings ina variety ofextended Higgssector havebeen evalu- atedin[22–24].Theseone-loopeffectsare oftheorderof2–10%

andeven morein some specialcases.The presentLHC measure- mentsarenotyetsensitivetosucheffects.

Acknowledgements

WewouldliketothankA.DjouadiandR.Santosforthevalu- able comments; and E. Vryonidou for sharing with us her code and for manyuseful discussions. A. Ahriche is supported by the AlgerianMinistry ofHigher EducationandScientificResearch un- dertheCNEPRUProjectNo.D01720130042;andpartiallybyDAAD andICTP.A.ArhribissupportedinpartbytheMoroccanMinistry ofHigherEducationandScientificResearch:“projetdesdomaines prioritairesdelarecherchescientifiqueetdudeveloppementtech- nologique”.

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