Single top production at HERA in the Standard Mode

arXiv:hep-ph/0606073v217Oct2007DESY06-041ISSN0418-9833MPP-2006-57hep-ph/0606073June2006SingletopproductionatHERAintheStandardModelanditsminimalsupersymmetricextensionW.Hollika,A.H¨uttmannb∗,B.A.KniehlbaMax-Planck-Institutf¨urPhysik(Werner-Heisenberg-Institut),F¨ohringerRing6,80805Munich,GermanybII.Institutf¨urTheoretischePhysik,Universit¨atHamburg,LuruperChaussee149,22761Hamburg,GermanyReveived7June2006AbstractTheH1CollaborationattheDESYelectron-protoncolliderHERAhasobserved,inphotoproductionandneutral-currentdeep-inelasticscattering,anunexpectedexcessofeventswithisolatedleptonsandmissingtransversemomentum,especiallyatlargevaluesofhadronictransversemomentum—asignaturetypicalforsingletop-quarkproduction.ThisobservationisbeingsubstantiatedintheHERAIIrun.Motivatedbythis,weevaluatethecrosssectionofsingletop-quarkphoto-andelectroproductionbothinthestandardmodelanditsminimalsupersymmetricextension,consideringbothminimalandnon-minimalflavour-violationscenariosinthelattercase.PACSnumbers:12.60.Jv,13.60.Hb,13.85.Ni,14.65.Ha∗Presentaddress:DeutschesElektronen-Synchrotron(DESY),Notkestr.85,22607Hamburg,Ger-many.1IntroductionSearchesforsingletop-quarkproductionviatheneutralcurrent(NC),e±p→e±t+X,(1)havebeenperformedbytheH1Collaboration[1]andtheZEUSCollaboration[2]attheDESYelectron-protoncolliderHERA.TheH1Collaborationfoundseveralevents,leadingtoacrosssectionofσ=0.29+0.15−0.14pb.Alternatively,assumingthattheobservedeventsareduetoastatisticalfluctuation,upperlimitsof0.55pbonσandof0.27ontheanomaloustuγcouplingκtuγwereestablishedatthe95%confidencelevel(CL).Ontheotherhand,theZEUSCollaborationfoundnoevidencefortop-quarkproductionandwasabletoplaceupperboundsof0.225pbonσandof0.174onκtuγat95%CL.Singletop-quarkproductionviathechargedcurrent(CC)ispossibleatthetreelevel,butitscrosssectionislessthan1fb[3].Furthermore,sucheventscanbeseparatedexperimentallyduetotheabsenceofascatteredelectronorpositroninthefinalstate.Inthiswork,wecalculatethecrosssectionofprocess(1)inthestandardmodel(SM)anditsminimalsupersymmetric(SUSY)extension(MSSM),consideringbothscenarioswithminimalflavourviolation(MFV)andnon-minimalflavourviolation(NMFV).Thebulkofthecrosssectionisduetophotoproductionandelectromagneticdeep-inelasticscattering(DIS),whilethecontributionduetotheexchangeofavirtualZbosonisgreatlysuppressedbyitsmass.Sincephotonicinteractionscannotchangeflavourandthetopquarkdoesnotappearasapartonintheproton,wearedealingherewithaloop-inducedprocess.IntheSMandtheMFVMSSM,itscrosssectionisfurthersup-pressedbythesmallnessofthecontributingelementsoftheCabibbo-Kobayashi-Maskawa(CKM)matrix.InmoregeneralMSSMscenarios,misalignmentbetweenthequarkandsquarksectorscanappear,andtheCKMmatrixisnolongertheonlysourceofflavourviolation.Thus,theflavour-changing(FC)couplingsarenotCabibbosuppressed,andsizeablecontributionstoFCNCprocessescanoccur.Ontheotherhand,therearestrongexperimentalboundsonsquarkmixinginvolvingthefirstgeneration,comingfromdataonK0–K0andD0–D0mixing[4].Ifthesquarkmixinginvolvingthefirstgenerationisneglectedcompletely,therearenonewverticesforincomingup-quarkscomparedtotheMFVMSSM.Thus,everynewcontributioninthisscenarioissuppressedbythepartondistributionfunction(PDF)ofthecharmquarkintheproton.BecausetheSMcrosssectionforNCsingletop-quarkproductionishighlysuppressed,everydetectedeventisanindicationofphysicsbeyondtheSM.Thispaperisorganisedasfollows.InSection2,wedescribetheanalyticalcalculationoftheSMcrosssection.InSection3,weoutlinethetheoreticalframeworkofFCinter-actionsintheMSSM.ThenumericalanalysisispresentedinSection4.OurconclusionsaresummarisedinSection5.2SMcrosssectionInthissection,theanalyticalcalculationoftheSMcrosssectionisdescribed.AsindicatedinFig.1,wedenotethefour-momentaoftheincomingproton,parton(uporcharmquark),andelectronbyP,p,andk,respectively,andthoseoftheoutgoingtopquarkandelectronbyp′andk′,respectively.Asforthecentre-of-mass(CM)energyandthetop-quarkmass,2wehaveS=(P+k)2andm2t=(p′)2.Weneglectthemassesoftheproton,theincomingquarks,andtheelectron,sothatP2=p2=k2=k′2=0.Thefour-momentumoftheexchangedphotonisgivenbyq=k−k′,and,asusual,weintroducethevirtualityvariableQ2=−q20.Thevariabley=(q·P)/(k·P)measurestherelativeelectronenergylossintheprotonrestframe.2.1ElectroproductionSingletop-quarkproductioninNCDISoccursviathepartonicsubprocesse±q→e±t,(2)whereq=u,c.TheFeynmandiagramscontributingintheSMtoprocess(2)withq=uaredepictedinFig.2.Theonesforq=caresimilar.TheamplitudeofthisprocesseswasalsocalculatedinRef.[5].Thereappearsatleastoneoff-diagonalelementoftheCKMmatrixineachterm.Ifthecontributionsoftheinner-quarkflavourstoasingleFeynmandiagramareaddedupandtheirmassesareneglected,theamplitudeofthisFeynmandiagramvanishesduetotheunitarityoftheCKMmatrix.Thus,wecannotneglecttheinner-quarkmasseshere.Althoughourchoicemc=0mdappearsunphysicalatfirstsight,itisinconsequentialinpractice.Infact,weverifiedthattheuseofarealisticvalueofmcaffectsournumericalresultsonlyinsignificantly.Adetailedproofofhard-scatteringfactorisationwiththeinclusionofheavy-quarkmassesmaybefoundinRef.[6].Ourcalculatio