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Investigating the jet activity accompanying the production at the LHC of a massive scalar particle

decaying into photons

Benjamin Fuks, Dong Woo Kang, Seong Chan Park, Min-Seok Seo

To cite this version:

Benjamin Fuks, Dong Woo Kang, Seong Chan Park, Min-Seok Seo. Investigating the jet activity

accompanying the production at the LHC of a massive scalar particle decaying into photons. Physics

Letters B, Elsevier, 2016, 761, pp.344 - 349. �10.1016/j.physletb.2016.08.056�. �hal-01470394�

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Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Investigating the jet activity accompanying the production at the LHC of a massive scalar particle decaying into photons

Benjamin Fuks

a

,

b

, Dong Woo Kang

c

,

d

, Seong Chan Park

d

,

e

, , Min-Seok Seo

f

aSorbonneUniversités,UPMCUniv.Paris06,UMR7589,LPTHE,F-75005Paris,France bCNRS,UMR7589,LPTHE,F-75005Paris,France

cDepartmentofPhysics,SungkyunkwanUniversity,Suwon440-746, RepublicofKorea dDept.ofPhysics&IPAP,YonseiUniversity,Seoul03722, RepublicofKorea

eKoreaInstituteforAdvancedStudy(KIAS),Seoul02455, RepublicofKorea

fCenterforTheoreticalPhysicsoftheUniverse,InstituteforBasicScience,34051Daejeon,RepublicofKorea

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

Articlehistory:

Received30July2016

Receivedinrevisedform24August2016 Accepted26August2016

Availableonline29August2016 Editor:J.Hisano

We studythe jetactivity that accompanies the productionby gluon fusionof a new physics scalar particledecayingintophotonsatthe LHC.Intheconsideredscenarios,boththe productionand decay mechanismsaregovernedbyloop-inducedinteractionsinvolvingaheavycoloredstate.Weshowthatthe presence oflargenewphysics contributionstotheinclusivediphotoninvariant-massspectrumalways implies asignificantproduction rate ofnon-standard diphoton events containingextra hard jets. We investigate the existence of possible handles that could providea way to obtaininformation on the underlyingphysicsbehindthescalarresonance,andthisinawidemasswindow.

©2016TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introduction

The resonant productionofa highly massive diphoton system consists of a prediction of many theories beyond the Standard Model, in particular in the case where the Higgs sector is non- minimal. Scrutinizing LHC proton–proton collisions givingrise to events featuring two hard photons plays thus a key role in the LHCexperimentalprogram,inparticularasthediphotonchannelis experimentallyclean andassociatedwithasmallStandardModel background.TherelatedRun IATLASandCMSanalyseshavehence beencornerstonesfortheHiggsbosondiscoveryin2012[1,2],and the Run II has a great potential to observe a new massive par- ticle decaying into two photons formasses ranging up to a few TeV [3–6]. More precisely, such a new particle should appear as a resonant bump in the diphoton invariant-mass spectrum. Pre- vious hints at the 2

σ

-level for such a diphoton resonance have spurred an intense theoretical activity over the last few months, anddifferentattemptshavebeenperformedinordertocharacter- izetheexcessbothfromthetop-downandbottom-upapproaches.

In themeantime, updated LHC resultshave beenreported anda newphysicssignalnowturns outtobe statisticallydisfavored[7, 8].Inthiswork, wemotivate thestudyoflessinclusivechannels

*

Correspondingauthor.

E-mailaddress:sc.park@yonsei.ac.kr(S.C. Park).

in orderto verifythe compatibilityof theproperties ofanynew state thatwouldbedecayingintoadiphotonsystemwithrespect toQCDradiation.

As the Landau–Yang theorem [9,10] forbids the on-shell cou- plingofamassivevectorbosontoaphotonpairandtheoff-shell case doesnot give rise to anyresonant behavior, diphoton reso- nance searchesare usually interpreted aslimitson theexistence ofascalar(withaspins

=

0)oratensor(withaspins

=

2)state.

In this paper, we focus on new physics setupsfeaturing a mas- sive scalarparticlethatwe denoteby R andrefertoRef. [11]for information onthespin-two case. Inorder forthisparticleto be producedwithasufficientlylargeratetobeobservedinthedipho- ton mode,we assume that thecouplingsofthe R particleto the Standard Model gluonsand photonsare issued frominteractions with anew colored andelectrically chargedparticle. Weinvesti- gate twosimplifiedmodelswherethiscoloredparticleiseithera heavyquark Q oraheavyscalarquarkq.

˜

Bothscenariosyieldthe loop-inducedproductionoftheR stateviathegluon-fusionmech- anism gg

R,asdepictedinFig. 1fortheheavyquarkcase,and the R-decaymodeintoaphotonpair R

γ γ

.

As shownin Fig. 2where we presenttheleading-order Feyn- man diagramscorresponding to theproductionof thescalarpar- ticle R with an additionalgluon via a loop containing theheavy quarkstateQ,theinteractionsunderconsiderationalsoinducethe associatedproductionoftheRparticlewithadditionaljets.Were- http://dx.doi.org/10.1016/j.physletb.2016.08.056

0370-2693/©2016TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.

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Fig. 1. Feynman diagram representing the loop-induced production of a scalar R-particleviagluonfusionwhenaheavyquarkQrunsintotheloop.

Fig. 2.Feynmandiagramsrepresentingtheloop-inducedproductionofascalarpar- ticleRinassociationwithahardjet,viagluonfusionandwhenaheavyquarkQ runsintotheloop.Thetwodiagramsinthefirstrowaretriangle()diagramsand theoneinthesecondrowisabox()diagram.

strict ourstudyto a configuration featuring one extrajet with a transverse-momentumofatleast50–100 GeV,asthemagnitudeof thecrosssectionrelatedtotheproductionoftheRstatewithtwo ormoresuch hard jetsis estimatedtobe too smallto yieldany statisticallymeaningfuldeviationwithinthecontextofthecurrent amountofrecordedLHCdata.Therearetwocategoriesofdiagrams contributingtothegg

R gprocessrespectivelycontainingatri- angularloop (the so-calledtriangle diagrams

presentedin the upperpanel of the figure) and a rectangular loop (the so-called boxdiagram

ofthelower panelofthefigure), thetriangledia- gramssharingthesamevertexstructureasforsingle Rproduction.

Since this process is loop-induced, the corresponding scattering amplitude isultraviolet finite.It nonethelessexhibits infrareddi- vergencesrelatedtotheextragluonthatcouldbesoft,collinearor both.Thephasespaceintegrationcanhoweverbesafelyperformed thankstotherequirementofthisgluonbeinghard,whichprevents fromenteringtheinfraredsensitivephasespaceregions.Inthefol- lowing,weinvestigatehowmeasurementsofthepropertiesofthe jetsproducedinassociationwitha scalardiphotonresonancecan providenew handles to probethe underlying physics. Ourstudy complementsrecentworksinwhichthejetmultiplicity spectrum associatedwiththeproductionoftheR particlewithamassfixed to750 GeVhasbeenprobedtogetinformationontheproduction mechanismfromwhich thediphotonsignal originates[11–13] or inwhicheffectivefieldtheorylimitsarestudied[14].

While the latter work mostly focuses on non-renormalizable dimension-fiveoperators describing the newphysics, we incon- trastconsider a theoretical framework containing onlyrenormal- izable four-dimensional operators. By performing exact one-loop calculations,weprobeboththestructureoftheloop-diagramsgiv-

ingrisetoadiphotonsignalwithandwithoutextrahardjetsand the structure of the couplings of the R particle to the Standard Model.

In the next section (Section 2), we describe the theoretical setupemployedforouranalysisandthenpresentourphenomeno- logicalresultsinSection3.Weconcludeandsummarizeourfind- ingsinSection4.

2. Theoreticalframework

In our study, we assume the existence of a real scalar field R with a mass mR whose interactions withthe Standard Model are mediated viathe exchange ofa heavy quark Q ofmassmQ. Vector-like quarksare importantinmanyextensionsofthe Stan- dard Model (e.g. in theories with extra dimensions [15,16] or composite-Higgsmodelswithpartialcompositeness [17]) andare generallyconsideredaslyinginthefundamentalrepresentationof the QCD gauge group SU

(

3

)

c. Although they can possibly lie in manydifferentrepresentationsoftheelectroweaksymmetrygroup SU

(

2

)

L

×

U

(

1

)

Y,we focusonaminimalsetupwherethe Q quark is a weak isospin singlet with an hypercharge quantum number set to2/3. Inaddition, we neglectany mixingwiththe Standard Modelup-typequark sector,so thatwe relyontheeffectivenew physicsLagrangian

L

(NP1)

=

iQ

¯

D Q

/

mQQ Q

¯ +

1

2

μR

μR

1 2m2RR2

+ ˆ κ

QR Q Q

¯ ,

(1)

that issupplementedtotheStandardModelLagrangian

L

SM.The interaction strength between the heavy quark and R is denoted by

κ ˆ

Q,andthegaugecovariantderivativeisgivenby

DμQ

=

μQ

igsTaGaμQ

i2

3e AμQ

,

(2)

with gs ande denoting the strong andelectromagnetic coupling constants,andthegluonandphotonfieldsandTathefun- damentalrepresentationmatricesof SU

(

3

)

.Since theextraquark Q doesnot mix withthe Standard Modelquark sector, our new physics model evades by construction all existing searches for vector-like quarksattheLHC[18–22].Asa result,oursimplepa- rameterization alsoembeds modelsinwhichtherearemorethan onestateconnectingtheR scalartotheStandardModel.Thiscan beaccountedforbyastronger

κ ˆ

Q coupling.

Alternatively,onemayconsiderthat themediationofthenew physicsinteractionsoftheRparticlewiththeStandardModelpro- ceedsviatheexchangeofascalarquarkq

˜

ofmassmq˜.Forthesake ofminimalityandsimplicity,thesquarkq

˜

isconsideredasaweak isospin singlet andlies inthe fundamental representation ofthe SU

(

3

)

cgroup.ThenewphysicssectoristhendescribedbytheLa- grangian

L

(NP2)

=

Dμq

˜

Dμq

˜ −

mq2˜q

˜

q

˜ +

1

2

μR

μR

1 2m2RR2

+ ˆ κ

q˜Rq

˜

q

˜ .

(3)

In thenext section, we will investigatethe effects relatedto the nature of the particle connecting the new physics to the Stan- dardModelsectors, andmakepredictionsby usingeithertheLa- grangian

L

(NP1) ortheLagrangian

L

(NP2).Asforthevector-like quark case,thesquarkq

˜

doesnotsinglycoupletotheStandardModelso thatournewphysicsmodelingcannotbeprobedbytypicalsquark searchesattheLHC.

Inordertocalculate(loop-induced) differentialandtotal cross sections related to processes involving an R scalar in the final state, we make use of the MadGraph5_aMC@NLO platform [23]

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Fig. 3.Totalproductioncrosssectionsfortheproductionofa750 GeVscalarresonance,possiblyinassociationwithajetwhosetransversemomentumisimposedtobe aboveaspecificthreshold.Intherightpanelofthefigure,wepresenttheproductionratesrelativelytotheppRtotalproductioncrosssection.Allresultsarepresented asfunctionofthemassofthevector-likequarkQrunningintotheloopmQ.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothe webversionofthisarticle.)

whoseloop-module[24] hasbeenrecentlyextendedto dealwith loop-inducedprocesses[25].Thisrelies onthe numericalevalua- tion of loop integralsin four dimensions, which necessitates the calculation of rational terms associated with the

-dimensional components ofthe loop-integralsthat should be normally evalu- ated in D

=

4

2

dimensions. Theserationaltermscan besplit into two ensembles, the first one being connected to the loop- integraldenominators(R1)andthesecondonetotheloop-integral numerators(R2).Whilethe R1 termsare universal,the R2 terms are model-dependent and process-dependent. They can however be cast as a finite number of counterterm Feynman rules de- rived from the bare Lagrangian [26]. Starting from the two

L

(NPi) Lagrangians, we translate, by a joint use of the FeynRules [27]

and NLOCT [28] packages, the model informationinto a UFO li- brary [29] that contains all relevant R2 counterterms and thatis readytobeusedinMadGraph5_aMC@NLO.

3. Phenomenologicalresults

As afirst benchmark scenario,we focuson the possiblechar- acterizationofthe750 GeVresonancewhosehintshavebeenre- centlyobserved by both theATLAS andCMS collaborations[3,4].

To this aim, it is useful to study its production together with a possibleadditionalhardjet.

In Fig. 3, we consider a model where the coupling of the R scalar with the Standard Model occurs via heavy Q-quark ex- changes (the modeldescribed by the

L

(NP1) Lagrangian ofEq.(1)), andwe evaluatetotal crosssectionsfor R productionpossibly in association with a jet whose transverse momentum pT is con- strained tobe above some threshold pTj. In ourcalculations, the loop-inducedhardmatrixelementshavebeenconvolutedwiththe next-to-leading orderset of NNPDF 3.0 partondistribution func- tions [30] accessed via the LHAPDF 6 library [31], and we have fixedboththefactorizationandrenormalizationscalestohalfthe transverse mass of all final state particles. The results are pre- sented withthe

κ ˆ

Q dependence of the cross sectionsfactorized out, since the latter parameter can always be tuned so that the rateforpp

R accommodates anydiphotonexcessthatwouldbe observed,andasafunctionofthemassoftheheavyquark Q that runsinto the loops. Focusing, forthe sake ofthe example, on a benchmarkscenarioinwhichmR

=

750 GeV andthatcorresponds

to theRun II ATLASandCMSpast observations,vector-likequark massesrangingup toatmost2 TeV couldaccommodate a signal cross section ofthe orderof 10–20 fb andsimultaneously forbid the

κ ˆ

Q value to be such that perturbation theory breaks down (

κ ˆ

Q

10).

Comparingthepp

R tothepp

R jpredictions,weobserve that any sign for a large beyond the Standard Model contribu- tion to the diphoton production cross section

σ (

pp

R

γ γ )

isalways accompaniedwithsignificant newphysics effectsinthe productionrateofdiphotoneventswithextrahardjets.Inourpa- rameterization of Eq. (1), we have considered vector-like quarks lyinginthefundamentalrepresentationoftheSU

(

3

)

group.How- ever,thecrosssectionratios(rightpanelofFig. 3)areindependent ofthecolorrepresentationthatcouldbechosendifferently,result- ing in larger rates. The effect of a different color representation choice for the heavy quark is relatedto the SU

(

3

)

group theory factorsofthedifferentscatteringamplitudes,

A (

gagb

R

)

Tr

(

TaTb

) = δ

ab

/

2

,

(4)

A

(

gagb

R gc

)

d

fabdTr

(

TdTc

)

1

2fabc

,

(5)

A

(

gagb

R gc

)

Tr

(

Ta

[

Tb

,

Tc

]) ∝

1

2fabc

,

(6)

wherea,b andc are thecolorindicescarriedby theinitial-state and final-stategluons, and

A

and

A

are theone-loop ampli- tudes related to the gg

R g process when considering either the triangleortheboxdiagramsrespectively. Theamplitudes are hence all independent of the specific color representationof the heavyquark.

Investigating the pp

R j process, it turns out that the full amplitude exhibits a t-channel enhancement such that the con- tributions fromthetrianglediagramsdominateoverthe boxdia- gram ones, especially when the mass ofthe quark Q is not too large. This‘triangledominance’ consequently impliesthatthe ra- tio

σ (

pp

R j

)/ σ (

pp

R

)

is insensitive to the quark massmQ in themasswindowof interest,sincethe sametriangleloop ap- proximately factorizes fromthe two amplitudes

A(

gg

R

)

and

A(

gg

R g

) = A

(

gg

R g

) + A

(

gg

R g

)

. The dependence of the resultson the vector-like quark mass mQ therefore stems

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Fig. 4.Totalproductioncrosssectionsfortheproductionofamassivescalarresonance,possiblyinassociationwithajetwhosetransversemomentumisimposedtobeabove aspecificthreshold.Intherightpanelofthefigure,wepresenttheproductionratesrelativelytotheppRtotalproductioncrosssection.Wefocusonthreescenariosfor whichmR=750 GeV,1500 GeVand2000 GeVrespectively.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionof thisarticle.)

fromtheformofthetriangle-loopamplitude

A

(1)thatisgiven,in thelargemQ limit,by

A

(1)

(

mQ

,

mR

)

1

mQ

+

7m2R

120m3Q

+

m4R

168m5Q

+ O

m6

R

m7Q

.

(7)

InFig. 4, westudythe dependenceofthe previous resultson themassoftheresonancemR,andfocusontwoextrabenchmark scenarios wheremR is fixed to 1500 GeV and2000 GeV respec- tively.Ontheleftpanel ofthefigure,we showthatthetotalrate is reduced when considering heavier R states, as could be ex- pected fromthe corresponding phase space suppression andthe dependence of

A

(1) on mR. We can also observe the presence of threshold effects related to the imaginary part of the loop- amplitude when the vector-like quark mass is about half the R scalar mass. Such setups will nevertheless not be considered in the following, as in this case the scalar particle preferably de- caysbackintoapairofvector-like quarks(thatoccursatthetree level)andnotintoaphoton pair(thatisaloop-inducedprocess).

On the right panel of the figure, we present the dependence of the

σ (

pp

R j

)/ σ (

pp

R

)

ratiointermsofthevector-likequark mass.Wefindthatthecrosssectionforproducingthescalarstate in association with a hard jet is relatively larger and larger for heavier and heavier R states. This property originates from two contributions,therenormalizationscalechoice(andtheassociated

α

s value)that dependsonmR aswell asthemR functionalform ofthetriangleloop-amplitude(seeEq.(7)).The

α

s dependenceis howeverreducedwhencomparingthetwolarge R-massvalues.

Similarconclusionscould beobservedforthenewphysics pa- rameterizationofEq.(3)astheresultsofEq.(4),Eq.(5)andEq.(6) aregeneralenoughtoholdregardlessofthenatureoftheparticle mediatingthe RcouplingtotheStandardModel.

Theloopamplitude ishoweversuppressedby oneextrafactor ofthemassofthescalarquarkrunningintotheloop,

A

(2)

(

mq˜

,

mR

)

1

4m2q˜

+

m2R

30m4q˜

+

3m4R

560mq6˜

+ O

m6

R

m8q˜

,

(8)

sothat it is not possible tosimultaneously explain any potential excessofabout10–20 fbinthediphotonspectrum andmaintain theperturbativityofthetheory.Scenarioswithextrasquarkswill thereforenotbeconsideredintherestofthiswork.

Inordertostudythepropertiesofascalardiphotonresonance, it maybe usefulto investigateeventswhere thenewheavy par- ticle recoils against a hard jet. For a proper description of such an eventconfiguration,itisnecessary toincludeatleastone ex- tra radiation at the level of the matrix element and match the fixed-order results to parton showers for a correct modeling of theremaining jetactivity.We makeuseoftheMadSpin[32] and MadWidth [33] programs to simulate the decay ofthe scalar R particleonthebasisoftheassociatedmatrixelement,aftershrink- ing the R

γ γ

loop-inducedinteraction to a point-like vertex. We theninterfacethepartoniceventsobtainedinthiswaytothepar- ton showering and hadronization infrastructure implemented in the Pythia 8 package [34], andreconstruct all final state jetsby meansoftheanti-kT algorithm[35]witharadiusparameterfixed to0.4asimplementedinFastJet[36].Wefinallyanalyzethegen- eratedeventsbymeansoftheMadAnalysis5platform[37].

InFig. 5,westudythepropertiesofthediphotonsystemorigi- natingfromthedecayoftheRparticle(whenproducedinassocia- tionwithahardjet)whosemasshasbeenfixedtomR

=

750 GeV both in thecase wherethe heavy quark massis set to500 GeV (solid blue curve) and when it is set to 1500 GeV (solid red line).Ourresultsincludeaselectionontheleading final-statejet, its transverse momentum pT being imposed to be larger than 150 GeV and the absolute value of its pseudorapidity

| η |

to be smallerthan2.5.Ontheupperpanelofthefigure,wepresentthe transversemomentum distributionofthetwofinal-statephotons, andtheirangulardistancesinthetransverseplaneandinazimuth are shownin the lower panel of the figure. Except the normal- ization, the shapes of the spectra are very similar regardless of thevector-likequarkmasschoice,andthisforallrepresenteddis- tributions. Althoughaninclusivediphotonsignal isingeneralac- companiedbyadiphotonplusahardjetsignal,itisveryunlikely that the photon properties could help on getting informationon thevector-like quark staterunning intotheloop.We additionally studytwoscenariosforwhichmQ

=

1500 GeV andmR isrespec- tivelyfixedto1.5 TeV(greendottedline)and2 TeV(purpledotted line).Theconclusionsaresimilar,withthedifferenceintheshapes ofthedistributionsbeingdrivenbythe Rstatemass.

4. Conclusion

Wehave studiedan extensionofthe StandardModelcontain- ing a singlet scalar particle R interactingwith a newheavy col-

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Fig. 5.Propertiesofthephoton-pairoriginatingfromthedecayofanR-particleproducedinassociation withahardjet.Wepresentthetransversemomentumspectrumof theleadingandnext-to-leadingphotons(toppanel),theirangulardistanceinthetransverseplane(lowerleftpanel)andtheirangulardistanceinazimuth(lowerrightpanel).

Thevector-likequarkmassisfixedeitherto500 GeV(solidblue)orthe1500 GeV(solidred)formR=750 GeV,andto1500 GeVforscenariosinwhichmR=1500 GeV (greendotted)and2000 GeV(purpledotted).Thenormalizationassumes10 fb1of13 TeVLHCcollisions.(Forinterpretationofthereferencestocolorinthisfigurelegend, thereaderisreferredtothewebversionofthisarticle.)

ored quark Q (with a spin s

=

1

/

2) or squark q

˜

(with a spin s

=

0) through which the singlet scalar can be produced at the LHCby gluon fusionanddecayinto adiphoton system. Wehave pointedout that theobservationof additionaljet activityaround an R-induced photon pair is important for checking the consis- tencyoftheunderlyingphysics,assignificantextrajetproduction isalsopredicted.

TherateforproducinganadditionalhardjetattheLHC,evalu- ated relativelyto the R single productioncross section hasbeen found to be around 20–40%, the exact value depending on the mass of the resonance particle mR that we have varied in the 750–2000 GeV mass window. It is howeverless sensitive to the massoftheparticlerunningintotheloopamplitude,mQ andmq˜ forscenarioswithavector-likequarkandscalarquarkrespectively.

Thepropertiesoftheprimaryandsecondaryphotonsissuedfrom the R decayhavealsobeeninvestigated,andwe havefoundthat theydonotseemtoprovideadditionalinformationonthecolored particlerunningintotheloopotherthanrelatedtotheoverallnor- malization of the considered distributions, which is expected in the caseofa scalar particledecay. We thereforestrongly recom- mendto correlatethefuture inclusiveanalysesof highly massive diphotonsystemsattheLHCwithlessinclusiveanalysesimposing strongrequirementsontheunderlyingjetactivity.

Acknowledgements

BF has been supported by the Théorie LHC France initiative of the CNRS (INP/IN2P3), SC by the National Research Founda-

tion of Korea (NRF) grant funded by the Korean government (MSIP)(No.2016R1A2B2016112)andMSbyIBS(ProjectCodeIBS- R018-D1).

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