QCD-corrected spin analysing power of jets in decays of pola

We present results for the differential distributions of jets from non-leptonic decays of polarized top quarks within the Standard Model, including QCD radiative corrections. Our work extends existing results which are only available for semileptonic top q

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aPITHA02/07April2002DESY02-055TTP02-04QCD-correcteddecaysofspinpolarizedanalysingtoppowerquarksofjetsinA.Brandenburga, ,Z.G.Sib, andP.UwercabDESY-Theorie,22603Hamburg,GermanyInstitutf.TheoretischePhysik,RWTHAachen,52056Aachen,GermanycInstitutf.TheoretischeTeilchenphysik,UniversitätKarlsruhe,76128Karlsruhe,GermanyAbstract:Wepresentresultsforthedifferentialdistributionsofjetsfromnon-leptonicdecaysofpolarizedtopquarkswithintheStandardModel,includingQCDradiativecorrections.Ourworkextendsexistingresultswhichareonlyavailableforsemileptonictopquarkdecaysatthepartonlevel.Fort(↑)→b-jet+2lightjetswecomputeinparticulartheQCD-correctedtop-spinanalysingpoweroftheb-quarkjetandtheleastenergeticlight

jet.Thedependenceoftheresultsonthechoiceofthejetrecombinationschemeisfoundtobesmall.Inadditionwecomputethespinanalysingpowerofthethrustaxis.Ourresultsconstituteasofarmissingingredienttoanalysetopquarkproductionandsubse-quentnon-leptonicdecayatnext-to-leadingorderinαs,keepingthefullinformationonthetopquarkpolarization.

PACSnumber(s):12.38.Bx,13.88.+e,14.65.Ha

Keywords:topquarks,polarization,QCDcorrections,jets

We present results for the differential distributions of jets from non-leptonic decays of polarized top quarks within the Standard Model, including QCD radiative corrections. Our work extends existing results which are only available for semileptonic top q

1Introduction

Thedetailedanalysisofthedynamicsoftopquarkproductionanddecayisamajorobjec-tiveofexperimentsattheTevatron,theLHC,andapossiblefuturelineare+e collider.Aspecialfeatureofthetopquarkthatmakessuchstudiesveryattractiveisitslargedecaywidth:IncontrasttothelightquarksthelargetopdecaywidthΓt≈1.5GeVservesasacut-offfornon-perturbativeeffectsintopquarkdecays.Asaconsequenceprecisetheo-reticalpredictionsofcrosssectionsanddifferentialdistributionsinvolvingtopquarksarepossiblewithintheStandardModelanditsextensions.Aconfrontationofsuchpredic-tionswithforthcominghigh-precisiondatawillleadtoaccuratedeterminationsofStan-dardModelparametersandmaybehintstonewphenomena.Inparticular,observablesrelatedtothespinofthetopquarkcanbestudiedandutilizedtosearchfornewinterac-tionsofthetopquark[1].Ine+e collisions,topquarksareproducedhighlypolarized,especiallyifonetunesthepolarizationoftheincomingbeams,aspossiblee.g.attheTESLAcollider[2].Furthermore,evenforpurelyQCD-inducedproductionoftopquark

¯areingeneralhighlycorrelated[3].pairs,thespinsoftandt

Thepolarizationandspincorrelationsoftopquarksmustbetracedinthedifferentialdistributionsofthedecayproducts.Thisispossiblesincetheinformationonthetoppolarizationistransferredtotheangulardistributionofthedecayproductsthroughitsweak,parityviolatingdecays.Tobemoreprecise:ConsiderapolarizedensembleoftopquarksatrestwithpolarizationvectorP,0≤|P|≤1.Thedifferentialdecaydistribution

ofagivendecayproductreads:withrespecttotheangle betweenPandthedirectionp

1

dcos =1

We present results for the differential distributions of jets from non-leptonic decays of polarized top quarks within the Standard Model, including QCD radiative corrections. Our work extends existing results which are only available for semileptonic top q

non-factorizablecontributions,seeref.[7].)QCDcorrectionstotheproductionoftopquarkpairs,includingthefullinformationabouttheirspins,canbefoundinref.[8]fore+e collisionsandinref.[9]forhadron-hadroncollisons.Inthecaseofe+e collisions,alsofullyanalyticresultsforthetopquarkpolarization[10]andaspeci cspincorrelation

¯Xproduction[11]toorderαsareavailable.Inref.[12],helicityamplitudesfore+e →tt

andsemileptonicdecaysarecomputedtoorderαsandareusedtoconstructanevent¯istreatedinref.[13],includingboth¯→W+bW bgenerator.Thereactione+e →tt

factorizableandnon-factorizableQCDcorrections.Thetheoreticalstatusofpolarizedtopquarkdecayisasfollows:Acompletecalculationoftheangulardecaydistributionfort(↑)→W+btoorderαscanbefoundinref.[14].TheQCDcorrectionsforsemileptonicpolarizedtopquarkdecayshavebeencomputedinref.[15].Wewillcompareourresults,fromwhichthesemileptoniccasecanbeeasilyderived,tothoseofref.[15]insection3.Theoutlineofthispaperisasfollows:Inthenextsectionweshortlyreviewthetreelevelresultsforthedecayofpolarizedtopquarks.Insection3wediscussthecalculationoftheQCDcorrections.Section4containsournumericalresults,whichwediscussinsection5.

2Kinematicsandtreelevelresults

ConsideraninitialstateconsistingoftopquarksatrestwithpolarizationP.Forthenon-leptonicdecay

t(pt)→b(pb)+u(pu)+d¯(pd¯),(2)

thephasespaceR3ofthe nalstatemaybeparametrizedbytwoscaledenergiesandtwoangles:

dR3=mt2

2mt|M(pb,pu,pd¯)|2dR3,(4)

where|M(pb,pu,pd¯)|2standsforthesquaredmatrixelementaveragedoverthecolouroftheinitialstateandsummedovercolourandspinsofthe nalstate.Thefullydifferentialdistributionforreaction(2)readsattreelevel:

dΓ0

(1 xb+zb ξ)2+η2ξ2

(1+|P|cosθ),(5)

We present results for the differential distributions of jets from non-leptonic decays of polarized top quarks within the Standard Model, including QCD radiative corrections. Our work extends existing results which are only available for semileptonic top q

where

c=NC|Vud|2e4|Vtb|2mt

4,(6)

with4(2π)

m2

ξ=W

mW,zb=m2b

Γ dΓcos =κp|P|

(k2 m2)2+m2Γ2→π

WWW

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