Exploring New Physics Through Contact Interactions in Lepton Pair Production at a Linear Co

ExploringNewPhysicsThroughContactInteractionsinLeptonPairProduction

ataLinearCollider

GabriellaP´asztor∗

CERN,CH-1211Geneva23,Switzerland

MaximPerelstein†

TheoryGroup,LawrenceBerkeleyNationalLab,Berkeley,CA94720,USA(Dated:February1,2008)

IfacontactinteractiontypecorrectiontoaStandardModelprocessisobserved,studyingitsdetailedpropertiescanprovideinformationonthefundamentalphysicsresponsibleforit.Assumingthatsuchacorrectionhasbeenobservedinleptonpairproductionata500GeV−1TeVlinearcollider,weconsiderafewpossiblemodelsthatcouldexplainit,suchastheorieswithlargeandTeV-scaleextradimensionsandmodelswithleptoncompositeness.Weshowthatusingthemeasuredcross-sectionsandangulardistributions,thesemodelscanbedistinguishedwithahighdegreeofconfidence.

arXiv:hep-ph/0111471v2 4 Dec 2001I.INTRODUCTION

AllknownsolutionstothegaugehierarchyproblemoftheStandardModel(SM)requiretheappearanceofnewparticlesatenergyscalesaround1TeV.Itisnotguaranteed,however,thatthesenewparticlescanbeproduceddirectlyattheproposed500GeVlinearcollider(LC).Onlyforsupersymmetrictheoriesaretherestrongargumentsthatatleastsomesuperpartnersshouldbekinematicallyaccessibleatsuchacollider[1].InthecaseofcompositeHiggsmodelsandmodelswithextradimensions,thesituationisfarlesscertain.Itispossiblethatallthenewstatespredictedinthesetheoriesaretooheavyandcannotappearinthefinalstateata500GeVLC.Infact,formodelswithlargeextradimensions[2],currentexperimentalconstraintsmostlikelyruleoutthepossibilitythatstringReggeexcitationscouldbelighterthan500GeV.Inthiscase,theonlydirecteffectofextradimensionswouldbetheenhancedrateofeventswithmissingenergyduetogravitonemission.Theseevents,however,provideonlyverylimitedamountofinformationaboutthefundamentaltheory.Moreover,thissignaturecouldbemimickedbygravitinoemissionprocessesincertainsupersymmetricmodels,soonewouldneedadditionalhandlestodisentangletheunderlyingphysics[3].Inthissituation,itisimportanttolookforindirecteffectsofnewphysics,thatis,theeffectsofnewheavyparticlesappearingasvirtualstates.Forexample,processessuchasBhabhascatteringorotherleptonpairproduction,

e+e−→e+e−,µ+µ−,τ+τ−

(1)

couldreceiveanadditionalcontributionfromtheexchangeofaheavystateX.Becausesuchadditionalcon-tributionscomefromshort-distancephysicsanddonotpossesspolesintheaccessiblerangeofanykinematicvariables,theyarereferredtoascontactinteractions.Bycarefullyexaminingthetotalcrosssectionandangulardistributionoftheseprocesses,itshouldbepossibletonotonlyfinddeviationsfromtheStandardModel,butalsogainsomeinformationaboutthenatureofthestateX,suchasitsspinandcouplings.

Inthisreport,wewillassumethatthecrosssectionofprocess(1)wasfoundtodeviatefromtheStandardModelprediction.Wewillthenconsiderseveralpossibleexplanationsforthisdeviation,suchasmodelswithleptonsubstructure,modelswithTeV-scalestrings,andmodelsinwhichgaugefieldscanpropagateintheextradimensions.Ourmaingoalistodeterminehowwellonecandiscriminatebetweenthesepossibilities,giventhemeasurementofthetotalcrosssectionandangulardistributionsofthefinal-stateparticles.

II.

MODELSWITHCONTACTINTERACTIONS

TheunpolarisedcrosssectionformulaforBhabhascatteringcanbewrittenintheform

dσ

2s

󰀂

󰀃

u2(|ALL|2+|ARR|2)+2t2|ARL,s|2+2s2|ARL,t|2,

(2)

2

where

ALL=ARR=

11

󰀄

(11+tsin2θWcos2θW

sin2θW1++2ts−MZ−−(1

cos2θW(1

cos2θW

11

2t−MZ

󰀅

+∆LL,

st

αΛ

,2

∆RR=2

ηRR

αΛ2

.(4)

Hereηa={+1,0,−1}parametrisethehelicitystructureofthecontactinteractions,andΛisthescaleof

compositeness.Wewillstudytwopossibilities:

(VV)thevector-vectormodelwithηLL=ηRR=ηRL=+1,(AA)theaxial-axialmodelwithηLL=ηRR=−ηRL=+1.

Modelswithlargeextradimensionshavetwosourcesfromwhichcontactinteractionsmayarise.Thefirst

contributionisfromthevirtualeffectofstringReggeexcitationsofthephotonandtheZboson.Thishasbeencomputedin[5]usingasimplestringtoymodel.ThecorrectedBhabhascatteringcrosssectionisgivenby

󰀁󰀄󰀅2󰀁πdσ󰀁×1−+...,(5)4dcosθ󰀁SMMs

whereMsisthestringscale.Thesecondcontributioncomesfromvirtualgravitonexchange,andwas

analysedin[6,7,8].ThiseffectcouldbesizablebecauseofthelargenumberofKaluza-Klein(KK)modesofthegravitonthatcontribute.The∆afunctionsinthiscasearegivenby

∆LL=∆RR=

4παMH

λ

4

s)+(u+

3

(s+

3

(t+

3

4παMH

1

2

2MW

,

1cos2θW

2

MW

∆RR=−2V

1

2MW

,

∆RL,s=∆RL,t=−

3

3

Analogousformulascanbeobtainedforµ+µ−andτ+τ−finalstates.Sincephenomenologyofstringmodelswithmultiplegenerationshasnotbeenstudiedindetail,wewillnotconsidertheeffectsofReggestatesinthesechannels.

III.

ANALYSIS

Thetheoreticalformulas(2)–(7)havebeenimplementedinPANDORA[10]toscanthescaleparametersofourmodels(referredtoasVV,AA,SR,KK+,KK−andTeVinthefollowing).Ateachscanpointtheangulardistributionoftheproducedleptonsisstudiedcalculatingtheexpectednumberofeventsin10binsofcosθ,withacutof|cosθ|<0.9imposedontheoutgoingelectronpolarangleinthecaseofBhabhascattering.Theratioofthepredictednewphysicscross-sectiontotheSMcross-sectionforelectronandmuonpairproductionisshowninFigure1forallthemodelsconsideredata500GeVLC.

1.041.031.021.0110.990.980.97

(a)

ee

-1-0.500.5

1cosθ

1.041.031.021.0110.990.980.97

σ/σSMσ/σSM(b)

AAVVTeVKK−KK+SR

µµ

-1-0.500.5

1cosθ

FIG.1:Ratioofthepredictednewphysicscross-sectiontotheSMcross-sectionfor(a)electronand(b)muonpairproductionasafunctionoftheleptonpolarangleforthemodelsAA(Λ=71TeV),VV(Λ=85TeV),TeV(Mc=14TeV),KK+(MH=3.4TeV),KK−(MH=3.4TeV)andSR(Ms=1.7TeV)ata500GeVLC.Thescaleparametershavebeenchosentobeatthesensitivityreachwith100fb−1integratedluminosity.

Foreachconsideredmodelandparametervalue100−1000MonteCarlo(MC)experimentsaregeneratedusingPoissonstatistics.Theseareinturncomparedtoalltheoreticalmodels(includingSM)bycalculatingtheχ2oftheMCandthepredictedtheoreticaldistributions,accountingforafullycorrelatedsystematicerrorof2%aswell.(Wewillusethetermtruemodelforthemodelwhichisassumedtobetrue,ie.whichwasusedtogeneratetheMCexperiments.)Wedefinetheconfidencelevel(CL)atwhichamodelwithagivenparametercanbeexcludedbytheratioofitsχ2probabilitytothehighestχ2probabilityforanymodelwithanyparameterconsidered:

1−CL=P(χ2)/max(P(χ2))

(9)

TheexpectedCLiscomputedasthemedianvalueforalltheMCexperimentsgeneratedwiththesamemodelandparametervalue.

IV.

RESULTS

Foreachnewphysicsmodelconsidered,wehavecalculatedthemaximumvalueofthescaleparameterforwhichtheStandardModelhypothesisisexpectedtobeexcludedatthe95%CL.Welisttheselimits,forthreesamplevaluesoftheLCenergyandluminosity,inTableI.Thecorrespondinglimitsfortheexclusionofallmodelsbutthetrueoneareinevitablysomewhatlower,asshownintheTableII.Thiseffectismorepronouncedwhenonlyonechannelisanalysed,asisnecessarilythecasefortheSRmodelwhereatpresenttheoreticalcalculationsonlyexistforBhabhascattering.Inmostcases,however,combiningallthechannelsallowsonetodistinguishbetweenthetheoreticalmodelsalmostuptotheSMsensitivityreachofTableI,withthemodelselectionsensitivityreachofTableIIbeingonlyabout5-15%lower.InFigure2weplot1−CLcorrespondingtothebestfitforeachtestedmodelintheelectronpairfinalstateasafunctionofthescaleparameterofthetruemodelforthecaseofa500GeVLCwith100fb−1luminosity.

4

1−CL1

1−CL(a)

1

(b)

0.750.50.2500

50

true model: AA100150scale (TeV)

0.750.50.2500

50

true model: VV100150scale (TeV)

1−CL1

1−CL(c)

1

(d)

0.750.50.2500

10

true model: TeV20

30scale (TeV)

0.750.50.2500

5

true model: KK+1015scale (TeV)

1−CL1

1−CL(e)

1

(f)

AAVVTeVKK+KK−SRSM

0.750.50.2500

5

true model: KK−1015scale (TeV)

0.750.50.2500

2

true model: SR46scale (TeV)

FIG.2:Bestexpected1−CLforeachtestedmodel,usingtheelectronpairfinalstateonly,asafunctionofthescaleparameterofthetruemodel(a)AA,(b)VV,(c)TeV,(d)KK+(e)KK−and(f)SRata500GeVLCwithanintegratedluminosityofL=100fb−1.

TABLEI:HighestscaleparametervaluesofthetruemodelforwhichtheSMhypothesisisexpectedtobeexcludedatthe95%CLfordifferentLCenergiesandluminosities.Thefirstnumberscorrespondtotheresultsusingallfinalstatesandthesecondusingonlyelectronpairs.

trueAA(Λ)VV(Λ)TeV(Mc)KK+(MH)KK−(MH)SR(Ms)

√

71/4185/5614/8.53.4/3.43.4/3.4-/1.7

s=500GeV105/61128/8321/134.1/4.14.2/4.2-/2.1

√149/86178/11829/18.57.1/7.07.1/7.1-/3.5

5

TABLEII:Highestscaleparametervaluesofthetruemodelforwhichallothermodelhypothesesareexpectedtobeexcludedatthe95%CLfordifferentLCenergiesandluminosities.Thefirstnumberscorrespondtotheresultsusingallfinalstatesandthesecondusingonlyelectronpairs.Thesecondbestmodelisgiveninthelastcolumn.

true√

s=500GeV√

AA(Λ)68/32101/48142/70KK+/SRVV(Λ)74/26111/37157/54KK+TeV(Mc)12/4.218/6.525.5/9.5KK−KK+(MH)3.2/2.33.9/2.76.7/4.8VVKK−(MH)3.2/2.43.9/3.06.6/5.1TeVSR(Ms)

-/1.3

-/1.6

-/2.7KK−

6

V.

CONCLUSIONS

ManymodelsofphysicsbeyondtheStandardModelpredictnewparticlesattheTeVscale.Evenifthecolliderenergyisnotsufficienttoproducetheseparticlesdirectly,theirvirtualexchangescanstillleadtoobservableeffects,suchascontact-interactiontypecorrectionstoStandardModelprocesses.Ifsuchacorrectionisobserved,studyingitcarefullycanprovideimportantinformationaboutthephysicsatandabovetheTeVscale.Inthisstudy,wehaveconsideredafewwell-motivatedtheoreticalmodelswhichpredictcontactinteractioncorrectionstoleptonpairproductionprocesses.Wehaveshownthatforawiderangeofmodelparameters,measuringleptonpairproductioncross-sectionsandangulardistributionsata500GeV−1TeVlinearcolliderwithrealisticintegratedluminositieswillallowtounambiguouslydeterminewhichofthecandidatemodelsiscorrect.Infact,wefindthatwheneverasignificantdeviationfromtheStandardModelisseen,themodelselectioncanbeperformedwithahighdegreeofcertainty.Combiningthemeasurementswithelectron,muonandtaufinalstatesiscrucialformodelselection.

Acknowledgments

G.P.waspartiallysupportedinSnowmassbyaDPFSnowmassFellowshipandbytheHungarianScientificResearchFundunderthecontractnumbersOTKAT0292andT029328.M.P.issupportedbytheDirector,OfficeofScience,OfficeofHighEnergyandNuclearPhysics,oftheU.S.DepartmentofEnergyunderContractDE-AC03-76SF00098.

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