Bounds on the electromagnetic interactions of excited spin-32 leptons

R.Walsh∗andA.J.Ramalho†

InstitutodeF´ısica,UniversidadeFederaldoRiodeJaneiro,CaixaPostal68528,IlhadoFund˜ao,

21945-970RiodeJaneiro,RJ,BrazilWediscusspossibledeviationsfromQEDproducedbyavirtualexcitedspin-3/2√leptoninthe+−

reactionee−→2γ.DatarecordedbytheOPALCollaborationatac.m.energy

arXiv:hep-ph/9907364v1 14 Jul 1999Lint=

(2)

Λe

µν¯∗Ψ,µγν(cLψL+cRψR)F

s=183GeVandtotalintegratedluminosityof56.2pb−1to

obtainlowerboundsonthemassscaleΛ,aswellasonthespin-3/2excited-leptonmassM3/2andcouplingstrengthscL,R.Thecalculationofthedifferentialcrosssectionfortwo-photonproductionwasperformedattreelevel,taking

(2)(1)

intoaccountthenonstandardcouplingsspecifiedbyLintandLint.Theresultingexpressionsaregivenby

dσ(i)

dΩ󰀈

+α2

QED

∗†

e-mailaddress:walsh@if.ufrj.bre-mailaddress:ramalho@if.ufrj.br

1

TABLEI.Coefficientsan(y)forthepolynomialsofthecorrectionsF±.

a8

(1)A+

(i)

a70

a6−1

a52y+4

a4

−10y2+2y

−53y+13

a3

−32y2−28y

a28y3+48y2+52y+5−4y2−8y−14−11y−12

a1

−16y3−32y2−38y−4

0

a0

80y3+26y2+10y+140y2+5y

+13y−2

0

B+

(1)

00000

C(1)

0000−2y+87y+8

A−

(2)

1−620y+14−96y−14

84y2+180y

−264y2−160y

+1472y3+288y2+60y−14−144y3−120y2

+672y3+12y2−4y−1

C(2)

000−13−2y−26y−2−6y+32y−1

Λ4Λ8

22

(c2R±cL)22(c2R±cL)

(1−y−x)

+

2yB±(x,y)

Λ2

4yB(2)(x,y)

(1)

2

(c2R+cL)

(1−y−x)

cRcL

++

D(1)(x,y)D(2)(x,y)

(1−y−x)

+

Λ4(1−y−x)

s=183GeV,alongwith

thecorrespondingpredictionforQEDandOPALexperimentaldata.InlinewithOPALexperimentalprocedure,weconsidertheeventangleθdefinedsothatcosθispositive,sincethetwophotonsareidentical,andanexperimentalcutcosθ<0.97.ThecompositenessscaleΛwastakentobeequaltotheexotic-leptonmass,withnumericalvaluesconsistentwiththe95%confidencelevellowerboundsthatwederivedforeachinteraction,asdiscussedinthefollowing.

10dσ/dΩ [pb/sr]10,00,20,40,60,81,0cos θFIG.1.Angulardistributionat

√Wederivedlowerboundsontheexotic-leptonmassandcouplingsbyaχ2fit,defining

χ(i)=

2

󰀃󰀅σ(i)−σexp

k

k

k

160140M3/2 [GeV]120exdclued100800,00,51,01,522,0cLFIG.3.SameasFig.2butforinteractionLint.s=183GeV.

(2)Thenextgenerationoflineare+e−colliders(NLC)willgiveimportantcontributionstothesearchofnonstandard(2)(1)physics.Angulardistributionsfora500GeVNLCareshowninFigs.4and5,consideringinteractionsLintandLintrespectively,andassuminganinputmassM3/2=250GeVorthelowerboundwhichweobtainedfromtheOPALdata.Weconsidredacutinthepolarangleθsuchthat5o<θ<175o.Asexpected,crosssectionsgrowfaster

(2)

withenergyinthepresenceofthenonstandardinteractionsunderdiscussion,themoresointhecaseofLint,whichcontainsahigher-dimensionaloperator.Inordertoestimatelowerboundsinthiscase,wedefinedχ2functions

χ(i)=

2

󰀃󰀅N(i)k−NSM

k

k

SM+(NSMδ)2Nkk

thecorrespondingerror,inwhichthePoisson-distributedstatisticalerroriscombinedinquadraturewiththesystem-aticerror.Weconsideredaconservativeintegratedluminosityof10fb−1andatypicalsystematicerrorδ=2%forameasurementina500GeVNLC.Theresultsofthisχ2analysisaredisplayedinFigs.6and7.Clearly,thelowerboundscanbeconsiderablyimprovedbytheexperimentsinthefuturee+e−colliders.

3

10dσ/dΩ [pb/sr]10,10,00,20,40,60,81,0cos θFIG.4.Angulardistributionat√s=500GeV.The

solidlinerepresentstheQEDprediction,whereasthedashed(dottted)curveshowsthetotalangularspectruminthe

(2)

presenceofthenonstandardinteractionLint,foraninputmassM3/2=142GeV(250GeV).

550500450M3/2 [GeV]4003503002502000,00,5exdclued1,01,522,0cL√

FIG.6.SameasFig.2butforaNLCenergys=500GeV.

WethankK.SachsfromOPALforthedatausedinthispaper.ThisworkwaspartlysupportedbyCNPqandFINEP.(1985).

[4]OPALCollaboration,K.Ackerstaffetal.,Phys.Lett.B438,379(1998).

[5]ALEPHCollaboration,R.Barateetal.,Phys.Lett.B429,201(1998);DELPHICollaboration,P.Abreuetal.,ibid.B

433,429(1998).