Top quark associated production of topcolor pions at hadron colliders

FERMILAB-Pub-01/295-Thep-ph/0110218

Topquarkassociatedproductionoftopcolorpionsathadroncolliders

AdamK.LeibovichandDavidRainwater

TheoryDept.,FermiNationalAcceleratorLaboratory,Batavia,IL,USA

arXiv:hep-ph/0110218v2 23 Oct 2001Abstract

Weinvestigatetheassociatedproductionofaneutralphysicalpionwithtopquarksinthecontextoftopcolorassistedtechnicolor.Wefindthatsingle-topassociated

¯-associatedproductiondoesnotyieldviableratesateithertheTevatronorLHC.tt

¯H,butattheproductionattheTevatronissuppressedrelativetoStandardModeltt

LHCisstronglyenhancedandwouldallowforeasyobservationofthemaindecaychannelstobottomquarks,andpossibleobservationofthedecaytogluons.

I.INTRODUCTION

Hadroncollidersaremachinesextremelywell-suitedtostudytheforefrontproblemofelectroweaksymmetrybreaking(EWSB)andfermionmassgeneration.Fermilab’sTevatron,nowengagedinRunII,hassignificantpotentialtodiscoveralightStandardModel(SM)orMinimalSupersymmetric

<130GeV[1].However,itwillStandardModel(MSSM)Higgsboson,withmassuptoaboutMH∼

haveverylittlecapabilitytodeterminetheoverarchingmodelthatgovernsEWSBifaHiggscandidateisobserved.TheCERNLargeHadronCollider(LHC),ontheotherhand,willhaveconsiderablyexpandedcapabilitytodiscoverandmeasurealmostallthequantumpropertiesofaSMHiggsofanymassorseveraloftheMSSMHiggsbosonsovertheentireMSSMparameterspace[2–6].WhilethisiscertainlyverypromisingforfuturestudiesofEWSB,verylittleattentionhasbeengivenrecentlytonon-SM/MSSMtheoriesofgaugebosonandfermionmassgeneration.

OfparticularconcerntousarethemoremoderndynamicalmodelsofEWSB.Whiledynamicalmodelshavehistoricallyhadmanytheoreticalproblemsaswellasconflictswithdata,andbroadclasseshavebeenruledout,therearestillviablemodelsworthyofinvestigationinlightofthecapabilitiesofthecurrentgenerationofexperiments.Weaddressherethetheoryoftopcolorassistedtechnicolor(TC2)[7],specificallytypeI[8].Thismodelisstillconsistentwithexperiment[9].WefirstoutlinethemodelinSec.II,discussthephenomenologyofthemodelinSec.III,andthenpresentconclusionsandtheoutlookforupcomingexperiments.DetailsofsomeoftheanalyticalcalculationsarepresentedintheAppendices.

1

II.THETOPCOLORASSISTEDTECHNICOLORMODEL

Dynamicaltheoriesoffermionmassgeneration,themostviableofwhichisextendedtechnicolor(ETC),typicallyhavedifficultyaccommodatingthelargetopquarkmass.TC2wasproposedtoassuagethisproblem,byhavingtwoseparatestronglyinteractingsectors.One(topcolor,orTC)providesforthelargetopquarkmassbuthascomparativelylittlecontributiontoEWSB,whiletheother(ETC)isresponsibleforthebulkofEWSBbutcontributesalmostnothingtomt.DetailsofTC2maybefoundinRef.[7].Here,webrieflyreviewthecharacteristicsmostrelevantfordiscussionofitsphenomenology.

TopcolorgaugeinteractionscausetopquarkpaircondensationatsomescaleΛviaastrongfour-fermioninteraction

g2

2

0

󰀂

,(2)

wherefπisthevacuumexpectationvalue(vev)ofthetopquarkpaircondensate,and󰀴τarethePaulimatrices.NotethatthehyperchargeofΦis−1.TypeItopcolorcontainsanextraU(1)whichtiltsthefermioninteractiontodisallowcondensationofab¯bcondensateaswell.Asimilarcondensation¯LTR>oftechnifermionsoccursintheETCsector,withitsownvevvT,andonemaywritetheSU(2)doubletΦETCinthesameform.

ThePagels-Stokarformula[10]givesthevalueofthevevfπintermsofthenumberoftopcolors,thetopquarkmass,andthescaleatwhichthecondensationoccurs:

2fπ≃

Nc

m2t

󰀂

+K,

󰀄

(3)

whereKisaconstantoforder1.ForcondensationaroundtheEWSBscaleof1TeV,fπ≃60GeV,

butitshouldbeunderstoodthatthisisonlyaroughguide,andfπmayinfactbesomewhatlowerorhigher,sayintherange40−80GeV.Allowingfπtovaryoverthisrangedoesnotqualitativelychangeourconclusionsandhasonlyminimalimpactonourquantitativeresults.Therefore,weusethevaluefπ=60Gevthroughoutouranalysisasaconvenientbaseline.

Welinearizethetheoryandrearrangethepionsintwoorthogonallinearcombinationstoformthelongitudinaldegreesoffreedomoftheweakgaugebosonsandatripletof“top-pions”,Π0,±,whichbecomephysicaldegreesoffreedom.(SeeAppendixAfordetails.)Thetop-pionsareanalogoustotheneutralCP-oddandchargedHiggsscalarsofatwo-Higgsdoubletmodel(2HDM),ofwhichtheMSSMHiggssectorisasubset.Contributionstothetopquarkmasscancomefrombothsectors,butthemodelassumesthatthedominantcontributionisfromTC.ThetopquarkYukawatermintheLagrangian,ignoringmixingbetweenthetwoHiggsmodes,iswrittenas

2

LYuk,t

1¯t=−Ytfπ+ǫtvTt2󰀁󰀂1¯t−YtHTC+ǫtHETCt2󰀁󰀂i¯γ5t.YtvT−ǫtfπΠ0t−2

󰀁󰀂

(4)

whereYtistheTCYukawacoupling,andǫtisasmallETCcontribution.Oncefπisfixed,vTis

22

uniquelydeterminedbytheEWSBrequirementthatfπ+vT=v2≃(246GeV)2.Forfπ=60GeV,wemusthavevT=239GeV.ThemeasuredtopmassthenfixesYttobeoforder3-4forsmallǫt.ThemaximalvalueofYtisYt,max=4.1occurswhenǫt=0.Weneglecttheeffectsofflavor-changing

¯c.Ithasbeenneutralcurrents(FCNCs),inparticularthoseinducedbyLagrangiantermslikeUtcΠ0t

arguedpreviously[7,11]thatthesetermscouldbelargeandleadtoasignificantbranchingratioforΠ0→tc.WewilladdressthisagaininSec.III.

ThetwoCP-evenHiggsmodesinthiseffective2HDM,labeledHTCandHETC,areknownasthe“top-Higgs”andthe“techni-Higgs”,respectively.TheirmassescanbeestimatedintheNambu–Jona–Lasinio(NJL)modelinthelarge-Ncapproximation.Forthetop-HiggsthisisfoundtobeontheorderofMH≃2mt;forthetechni-Higgsitismuchhigher.However,thereisnoreasontoexpecttheNJLmodeltobecorrect,itonlyservesasaroughguide;themassesofthetop-andtechni-Higgsmodesmayinfactbeverylight.Thetop-pionsontheotherhandhavemassesproportionaltoǫtandthemassofthecoloroctetofTCgaugebosons,MB.Inthefermionbubbleapproximationthisis

2MΠ

=

2

Ncǫtm2tMB

8π2

∼6.6kGeV.(6)

Togetalimitonk,weuseabottomquarkpolemassofmb≈4.8GeV,sothattheentirebquark

masswouldcomefromcontributionduetotopcolorinstantonsfork∼0.73.SinceEq.6isonlyaroughestimatewewillusek=0.8asthemaximumpossiblevalueinouranalysis.TheremainingmBcontributionisassumedtocomefromETC,viaaYukawacouplingǫb.TheLagrangiantermsfortheETCbottomYukawaandinstantonsectorsare

ǫbvT¯+LYuk,b=−m∗bbb

2󰀁√󰀂i−vT−ǫbfπΠ0¯bγ5b.

fπ2

󰀁

󰀂

(7)

Forfixedfπ,thiscouplingdependsonlyonk(ǫbisrelatedtokbymb),andhasazeroatk=0.043.

Suchasmallnon-zerovalueseemsextraordinarilyfine-tunedsowedonotconsideritasaspecial

3

casefurther.AmoreinterestingspecialcaseiswhereETChasflavoruniversalYukawacouplings,

>4(recalli.e.ǫb=ǫt.ThiscanoccuronlyforverylargevaluesofthetopcolorYukawacoupling,Yt∼

forourfixedvalueoffπ,Yt,max∼4.1).Atthelowerlimitofthisbound,k=0andthereisnotopcolorinstanton-inducedbquarkmass.

III.PHENOMENOLOGYOFTHEMODEL

OneimmediatelycanseefromEq.4thatthecouplingsofboththetop-Higgsmodeandthetop-piontotopquarksareenhancedbyafactorofseveral(YtTC/YtSM≃3−5forthetop-Higgsand(YtTCvT−ǫtfπ)/vYtSM≃3−4forthetop-pion)relativetotheSM.Asaresult,thesestateshaveagreatlyenhancedtopquarkloop-inducedcouplingtogluons.Inclusiveproduction,gg→Π0,thusoccursatamuchgreaterratethanintheSM.Thislatterfeaturehasbeenaddressedpreviouslyintheliterature,brieflyinRef.[13]andinmoredetailinRef.[11],andwedonotdiscussithere.Furthermore,wewillnotdiscusseitherthetop-Higgsorthetechni-Higgsinthispaper,leavingthemforfutureanalysis[14].Instead,weconcentrateourinvestigationtheneutraltop-pion,whichhasnotbeenexaminedverycloselyinpreviousstudies.

AstheΠ0isaCP-oddstate,itdoesnotcoupletoweakbosonsattreelevel.Thislimitstheproductionmodesatahadroncollider,aswellasthepossibledecaymodes.Wethereforefocuson

¯-associatedproduction,andcomparetheTC2ratestocorrespondingratesinbothsingle-top-andtt

0

theSMandallowedregionsoftheMSSM.WealsoconfineourfocustothemassregionMΠ<2mt.Formassesabovethetopquarkpairthreshold,decaystotopquarksdominate,resultinginaratherlargefourtopquarkcrosssectionthatmaybeexperimentallyobservable,asdiscussedinRef.[15].Allourcalculationsareperformedwithparton-levelMonteCarlousingCTEQ4Lpartondistribu-tionfunctions[16]andαs(MZ)=0.1185.Boththefactorizationandrenormalizationscalesarechosenasµf,r=mt+1

Figure1.Totalwidth(left)anddominantbranchingratios(right)oftheneutraltop-pion,asafunctionofkforfixedYt=4.0.Shownarethecurvesforkis0.8(solid),0.4(dashed)and0(dot-dashed).TheSMHiggstotalwidthisshownbythedottedlineintheleftpanel.Intherightpanel,BR(b¯b)areinblue(downwardsloping),andBR(gg)areingreen(upwardsloping).TheΠ0–quarkinteractionsareassumedtobeflavordiagonal(seetext).

quicklybecomesnegligible.Ifinsteadk=kmax∼0.8,evenatMΠ0=100GeVthebranchingratiotogluonsisabout5%,thesmallestitevergets.Forlargertop-pionmassesormoremoderatevaluesofk,thereistypicallyaratherlargebranchingratiotogluons.Wewilllaterplaceroughlimitsonwhatweexpectσ·BRtobeforeachdecaymodeasafunctionofYtandk.

ForMΠ0>2mt,thetop-piontotalwidthexceedstheSMHiggstotalwidthbyafactor3-5,dependingonthechoiceofYt.Inthisregion,decaystotopquarkpairsdominatethewidthtosuchadegreethattheirbranchingratioiseffectivelyunity;allotherdecaymodesmaybeignored.Singletopassociatedproduction

Diagrams by MadGraph

u d W+ Π0 Π− u d W t t Π0 graph 2

b graph 1

t b Figure2.t-channelWsingletopassociatedΠ0production.AsintheMSSMthereisastrongcancellationbetweenthetwodiagrams,leadingtosmall,almostcertainlyunobservablerates.

5

√

ThelargestsingletopproductioncrosssectionattheTevatron(

s=14TeV).

OnemayeasilyestimatethatateithertheTevatronorLHC,evenifs-channelsingletopassociatedproductionofaneutraltop-pionisenhancedrelativetotheSMHiggsrateby∼32,anorderofmagnitude,thisisnotenoughtobeobserved[18].t-channelproductionisadifferentstory.InthiscasethereisastrongcancellationintheSMbetweenthegraphswheretheHiggsisradiatedoffthet-channelWbosonoroffthefinalstatetopquark,whichpreservesunitarityathighenergies[18].Combinedwiththeratherlargebackgroundrates,thisrendersSMHiggssingletopassociatedproductionunobservableatboththeTevatronandLHC.EvenintheMSSMitisdifficulttoachieveasignificantenoughenhancementtohopeformuchimprovedprospects.ButinTC2,theneutraltop-pioncannotbeemittedfromthet-channelW,soonewouldna¨ıvelyexpectcancellationstobeabsentandtheratetobeconsiderablylarger.Unfortunately,thereisaW+Π−Π0vertex,asshowninFig.2,whichleadstoasimilarstrongcancellationbetweenthediagrams,againasrequiredbyunitarity(seeAppendixBfordetails).SinceattheLHCthetop-pionproductioncrosssectionisnevermorethanafactortwolargerthanfortheSMHiggs,webelievethischannelisnotusefulanddonotconsideritfurther.Topquarkpairassociatedproduction

¯Π0v.StandardModeltt¯HcrosssectionsattheTevatron(left)andLHC(right).TC2Figure3.Totaltt

modelinputisfπ=60GeVandYt=3.0(solid),3.5(dashed),and4.0(dotdahsed).TheSMcrosssectionsareshownbythedottedcurves.

¯Π0productionastherearenocancellationsbetweendiagrams.Thesituationisverydifferentfortt

¯HThecrosssectionattheTevatron,shownintheleftpanelofFig.3,iscomparabletothatforSMtt

<150GeV,varyingwithinafactorofseveralsmallertofewlarger.AtlargerproductionforMΠ0∼

>150GeV,theTCrateisalwayslarger,althoughthetotalrateisnotenoughtoΠ0masses,MΠ0∼

yieldenoughevents[19].Thattherateisonlycomparableratherthansignificantlylarger,asonewouldguessfromtherelativemagnitudeofthequark-quark-scalarcouplings,isduetoadifferentsort

¯Π0vertexcontainsaγ5,duetotheCP-oddnatureofthescalar,thereisofcancellation:sincethett

destructiveinterferencebetweenthepin·poutandm2ttermsintheDiracstructureoftheamplitude.TheTevatronrunsatapartoniccenterofmassenergywherethetermsareofcomparablesize,sothe

6

overallcouplingenhancementof≈32isunfortunatelycountered;iftheγ5werenotpresent,thecrosssectionattheTevatronwouldbelargerbyanorderofmagnitude[14].

¯HSMeventsattheTevatronwereinitiallybelievedtobegoodforProspectsforobservationoftt

<135GeV[19],butrecentNLOcalculationsofpp¯HSMrevealedanunexpectedsuppressionMH∼¯→tt

ratherthanenhancement[20],whichmakethesearchmuchmoredifficult.1ItisnotyetknownwhattheNLOresultisforpseudoscalarproductioninassociationwithtopquarkpairsathadroncolliders2,sowecannotmakedefinitivecommentsonthepotentialobservabilityofthischannel.Theslightly

¯Π0productionislikelytobemissedattheTevatron,lowercrosssectionsforlowΠ0masssuggestthattt

atleastforsmalltomoderateYt,butthisshouldbeviewedasachallengetothemachineanddetectorgroups.ObservingorrulingoutTC2basedonitsneutralpseudoscalarcontentwillattheveryleastbeextremelydifficultattheTevatronunlessthemachineperformsexceedinglywell.

AcompletelydifferentparadigmwillreignattheLHC.Fromrecentstudieswithdetectorsimula-¯H→ℓνjjb¯tion[22],itisknownthataSMHiggsofmassMH=120GeVcanbediscoveredinthettbb¯b

channel.Thestudiesfoundthatthebackgroundscanbereducedtothelevelofthesignal,S/B∼1/1,yieldingastatisticalsignificanceofabout12σatCMSandabout10σatATLAS,for100fb−1ofdata.Bothstudiesusedthesampleconsistingofonetopquarkdecayinghadronicallyandtheother

¯Heventsample.leptonically,≈1/3ofthetotaltt

¯Π0;Π0→b¯WepredictthatanyttbratethatismorethanhalftheSMrateforthesameMφ

willbeobservableatgreaterthan5σ.ExaminingtheleftpanelofFig.4,forMΠ0=120GeVthiscorrespondstoYt=3.0andverysmallk,closeto0(ignoringtheexactzeroatk≈0.05).ForlargerYt,thetop-pionsignalonlybecomesstronger,astheproductioncrosssectionincreasesfasterthanBR(b¯b)fallsoff.(ThisbehaviorholdsgenerallyforallΠ0masses.)Itismanifestthatanyregionof

>300fbislikewiseaccessible.Infactthesituationismuchbetter,parameterspacewithσ·BR(b¯b)∼

¯b¯sincethettbbackgroundfallsoffveryquicklywithincreasingmb¯b.However,wecannotmatchthe

levelofsophisticationpresentedinRef.[22],andaparton-levelMonteCarlocalculationwouldbeamisleadingcomparison,soweleavethedetailsofreachinthischanneltofutureworkbydetectorcollaborations.Wedonote,however,thatfortheobviouslyverylargeregionofparameterspacewherestatisticalsignificancewouldbe≫5σ,themethodsofRef.[5]shouldalsoallowforconfirmationofthepseudoscalarnatureoftheresonance.

ForlargermassesMΠ0,itmaybepossibletoobservethedecaymodeΠ0→ggoversomeregionofTC2parameterspace.Weknowofnoothermodelwherethisispossible.Toillustrateourclaim

¯+jjweexamineafewpointsinparameterspaceinTableI.HerewecalculatethesignalandQCDtt

backgrounds[23]atpartonlevelwithfullmatrixelements,includingthedecayΠ0→gg.Weconsiderthefinalstatewhereonetopquarkdecayshadronicallyandtheotherdecaysleptonically,providingahardleptonfortriggering.Wedonotattempttoincludedetectoreffects,butwedoincludesomemajordetectorefficienciessuchasbjettagging(60%each)andleptonID(85%),whichreducesthecapturedratesconsiderably.Wealsoapplytheratherseverekinematiccutsneededtosatisfythe

Figure4.Weshowthetop-pionproductioncrosssectionsforYt=3.0,multipliedbythebranchingratiostob¯b(left)andgg(right),forvariousvaluesofk:0.8(solid),0.2(dashed),0(dotdashed).TheSMHiggsratesareshownbythedottedlines.

experimentalcriteriaforhighluminosityrunning:

pT(j)>30GeV,pT(b)>30GeV,pT(l)>15GeV,p/T>50GeV,

|η(j)|<4.5,

|η(b)|<2.5,|η(l)|<2.5,△Rij>0.4.

(8)

Inaddition,werequireanadditionalcutpT>40(50)GeVonthejetsfromdecayoftheΠ0forMΠ0=200(300)GeV.AstheΠ0isanarrowstateevenatthehighermass,weexaminesignalv.backgroundina±20GeVbinaroundthecentralvalue.Duetothelackofdetaileddetectorsimulation,thiscomparisonshouldbetakenonlyasaroughguideforthereachavailableinthischannel.OurgoalistoshowthepotentialdistinctivecharacteristicsoftheTC2model.

TableIrevealsthattheΠ0→ggdecaymodeisprobablyobservableonlyforlargeYtorverysmallk.Whilethenumberofbackgroundeventsisverylarge,S/BandtotalnumberofsignalandbackgroundeventsarequitesimilartotheSMgg→H→γγsearchattheLHC,whichhasbeenshowntobeaccessible[2].Ourestimatealsomakesnoattempttoutilizethecomplexnatureofthesefinalstates,whichhaselsewherebeenshowntoyieldsignificantimprovementsbeyondoursimpleapproach[22].TheTablesuggeststhatthismodemaybeabletoprovidediscoverycoverageoverregionsofparameterspacewheretheΠ0→b¯bmodeisnotaccessible.

IfwenowdeviatefromourassumptionthattheΠ0–quarkinteractionsareflavordiagonal,forthe

¯ccanoccurwithsubstantial,evendominant¯,tΠ0massrangemt+mcbranchingratio,dependingonthemagnitudeofUtc.Wearenotconcernedwiththishere,becausein¯Π0eventsitwouldleadtoaspectacularsignatureofthreetopquarksandanadditionalcharmjet.tt

ThereisnoSMprocessthatcangivethis,andtherateforpp→tttbattheLHCislessthan0.2fb;theb→cmistaggingprobabilitywouldreducethisevenfurther.Wewilladdresstheflavor-changingpossibilitiesseparately[14]anddonotdiscussthemfurtherhere.

8

MΠ0(GeV)200200200200300300300300σB(fb)680680680680290290290290NB62,40062,40062,40062,40026,60026,60026,60026,600

√NS/0.64.21.05.11.34.23.68.1

¯Π0→b¯TABLEI.Crosssectionsforthetopcolorassistedtechnicolorsignalpp→ttblνjjgg(1leptonic

√

¯jj→→b¯and1hadronicdecayofthetopquarks)andbackgroundpp→ttblνjjjjattheLHC,

determinableatahadroncollider.Butbyalsoobservinganotherproductionmodeinthesamedecaychannel,suchasgg→Π0→b¯b,onecangetaroundhavingtoknoweitherkorǫb.Whilethenumberofunknownsisreducedtofour,thenumberofmeasurementsisstilleffectivelythree.Thisleavesthesystemunderdetermined,sothatadditionalmeasurementswouldbenecessary,suchastherateofHTCproductiontimesBR(b¯b,gg)rateineithergluonfusionortopquarkassociatedproduction.

ACKNOWLEDGMENTS

WewanttothankChrisHillforhelpingustounderstandtopcolorassistedtechnicolorandGustavoBurdmanforusefuldiscussions.FermilabisoperatedbyURAunderDOEcontractNo.DE-AC02-76CH03000.

APPENDIXA:THETC2LAGRANGIAN

WebeginbywritingtheeffectiveTC2Lagrangianinlinearizedform.Thekinetictermis

Lkin=

󰀁

DµΦTC

󰀂†󰀁

DµΦTC+DµΦETC

󰀂󰀁󰀂†󰀁

DµΦETC,

󰀂

(A1)

wheretheSU(2)doubletsΦhavetheform

ΦTC=

󰀁

(fπ+HTC+

0iπTC)/

√

2

󰀂

−iπETC

,(A2b)

andthecovariantderivativeis

Dµ=∂µ+i

gY

2

i

τiWµ.

(A3)

ThehyperchargeofthedoubletsisY=−1,andgisgweak.Wemakethefollowingredefinitionof

fields:

112

(Wµ∓iWµ),2

3Wµ=Zµcosθ+Aµsinθ,Bµ=−Zµsinθ+Aµcosθ.

±Wµ=

(A4)(A5)

(A6)

Afterreplacementofthephysicalvectorbosonfields,theDµΦitermforeachdoubletwillbeoftheform

DµΦi=

󰀁

1

(∂µHi2

0

+i∂µπi)−i∂µπi

󰀂

+

igZ

󰀁

√

√i

2

wheregZ=g/cosθWande=gsinθW.AfterexpandingthetermsinEq.A1,weformorthogonal

0,±

linearcombinationsofthefieldsπi,

w0,±=

0,±0,±

fππT+vπTCETC

v

(physicaltop−pions),(A9)

22

wherev2=fπ+vT=(246GeV)2.

AfterrearrangementtheFeynmanrulescansimplybereadoff.Atthispointwereversetheflowofallbosonsfromincomingtooutgoing,tomatchthetreatmentusedinMadgraph/HELAS.ThecoefficientofeachtermistheHELAScoupling.TableIIliststhe3-pointgaugecouplingsforallphysicalfields;theGoldstonebosonand4-pointcouplingsarenotlistedforbrevity.

11

H0−iv(pµ−pµ)

+gZ(1−2sin2θW)(p−µ−pµ)

+−iv(pHµ−pµ)++iv(pHµ−pµ)

−1

11

ZµHETCΠ0AµΠ−Π+

W+µΠ−HTCW+µΠ−HETC

2

gZ

fπ

−1

g2g

2

vTfπ

TABLEII.Madgraph/HELAS3-pointTC2gaugecouplingsforthephysicalfields;Goldstonebosonand4-pointcouplingsarenotlisted.Allbosons(chargeandmomentum)flowoutintheHELASconvention.

UsingthesamescalarSU(2)doubletsinEq.A2,theYukawatermintheLagrangianiswrittenas

†¯LΦTCtR+t¯LΦETCtR+t¯RΦ†¯LY=−YtΨΨ−ǫΨΦLtRTCETCΨL,

󰀁󰀂󰀁󰀂

(A10)

whereΨListheSU(2)Ltop-bottomquarkdoubletasusual.Rearrangementofthepionfieldsresultsin

theFeynmanrulesforthequarkYukawainteractionswiththetop-Higgs,techni-Higgsandtop-pions,showninTableIII.

−12Yt−12ǫt

+i2(YtvT−ǫtfπ)+i

¯LtRHTCt

¯LtRHETCt¯LtRΠ0t

−

√√v

i√

TABLEIII.Madgraph/HELASYukawaquark-quark-scalarTC2couplings.YtisthelargetopcolortopquarkYukawa,andǫtistheETCYukawagivingasmallcontributiontothetopquarkmass.Allbosons(chargeandmomentum)flowoutintheHELASconvention.

11

APPENDIXB:SINGLE-TOPASSOCIATEDΠ0PRODUCTION

ToexaminetheanalyticalbehaviorofsingletopassociatedΠ0productionathadroncolliderswewritetheamplitudesforthetwoFeynmangraphsinFig.2intheeffective-WapproximationasinRefs.[18,24]:

u¯t

󰀁

i

2

(pt−pb)2−MΠ

gg

(pb+k)2−m2t

2

v

√

γµ(1−γ5)ubǫµ.

(B2)

Thesamecouplingsappearinbothdiagrams.Usingthehighenergylimitǫµ=kµ/MW+O(MW/k0),

thefirsttermreducescompletelytothecouplingscoefficientandasimpleDiracstructure,

−

ig

(pb+k)2−m2t

u¯tp/Π(1−γ5)ub.

󰀄

(B4)

ThefirsttermofEq.B4cancelsthecontributionfromthefirstgraphinEq.B3,leavingatermthat

satisfiestheunitarityconstraintathighenergy[18,24].

12

Bibliography

[1]M.Carenaetal.,“ReportoftheTevatronHiggsworkinggroup,”hep-ph/0010338.[2]CMSTechnicalProposal,reportCERN/LHCC/94-38(1994);

ATLASCollaboration,ATLASTDR,reportCERN/LHCC/99-15(1999).

[3]D.Zeppenfeld,R.Kinnunen,A.NikitenkoandE.Richter-Was,Phys.Rev.D62,013009(2000).[4]J.G.Bransonetal.[TheCMSCollaboration],hep-ph/0110021.[5]J.F.GunionandX.G.He,Phys.Rev.Lett.76,4468(1996).[6]T.Plehn,D.RainwaterandD.Zeppenfeld,hep-ph/0105325.[7]C.T.Hill,Phys.Lett.B345,483(1995).

[8]G.Buchalla,G.Burdman,C.T.HillandD.Kominis,Phys.Rev.D53,5185(1996).[9]C.T.Hill,privatecommunication.

[10]H.PagelsandS.Stokar,Phys.Rev.D20,2947(1979).[11]G.Burdman,Phys.Rev.Lett.83,2888(1999).

[12]G.BurdmanandD.Kominis,Phys.Lett.B403,101(1997);

W.LoinazandT.Takeuchi,Phys.Rev.D60,015005(1999)[13]G.Burdman,hep-ph/9611265.

[14]A.LeibovichandD.Rainwater,inpreparation.

[15]M.SpiraandJ.D.Wells,Nucl.Phys.B523,3(1998).[16]H.L.Laietal.,Phys.Rev.D55,1280(1997).

[17]T.StelzerandW.F.Long,Comp.Phys.Comm.81,357(1994).[18]F.Maltoni,K.Paul,T.StelzerandS.Willenbrock,hep-ph/0106293.

[19]J.Goldstein,C.S.Hill,J.Incandela,S.Parke,D.RainwaterandD.Stuart,

Phys.Rev.Lett.86,1694(2001).

[20]L.ReinaandS.Dawson,hep-ph/0107101;W.Beenakkeretal.hep-ph/0107081.[21]M.Spira,Fortsch.Phys.46,203(1998).

[22]D.Green,K.Maeshima,R.VidalandW.Wu,CMS-NOTE-2001/039;

V.Drollinger,hep-ex/0105017.[23]A.Stange,privatecommunication.

[24]G.BordesandB.vanEijk,Phys.Lett.B299,315(1993).

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