B-QuarkProductionatHadronColliders
S.Riemersma
DepartmentofPhysics,SouthernMethodistUniversity,FondrenScienceBuilding,Dallas,TX75275-0175,USA
and
RuibinMeng
HighEnergyPhysicsDivision,ArgonneNationalLaboratory,
Argonne,IL60439
Abstract
Resultsforb-quarkproductionathadroncolliders,bothcurrentandpro-posed,arepresented.DistributionsinptarepresentedfortheTeVatronand
SSC.ConfirmationofagreementbetweentheO(α3
dataispresented,andthediscrepancybetweentheS)calculationsandUA1
O(α3
S)calculationsandtheCDFresultsisupdatedwiththemostrecentdata.
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1Introduction
StudyingB-physicsathadronacceleratorsrequiresagoodunderstandingofthetotalanddifferentialcrosssectionsforb-quarkproduction.Thisknowl-¯mixing,rareBdecays,andthosetryingtoedgegivesthoseinvolvedinBB
determinetheCKManglesα,β,andγanideaofhowmanyeventstheycanexpect,giventheluminosityandthebranchingratios.ItisparticularlyimportantforthosestudyingrareBdecaysastheysetlimitsonwherewecanhopetoseenewphysics.Forthesereasonsandothers,thecomplete
3O(αS)correctionstoheavy-quarkproductionathadronacceleratorswerecalculatedin[1]and[2].Alsothreegroups[3],[4],[5]haveattemptedtocal-culateheavy-quarkproductionusingresummationtechniquesinthesmall-xkinematicregion.Thesetechniquesarenecessary√sincetheb-quarkmassmbissmallrelativetothecenter-of-massenergies
s≈mb≈pt,
√
b-production,oneneedstomultiplytheseresultsbyafactoroftwo.
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Table1.CrossSectionsforProposedFixed-TargetExperiments.
√
Born
4317nb1240.58µb2001.6µbThesecrosssectionsweregeneratedusingprogramscreatedby[2]withthe
followinginputs:mbwaschosentobe4.75GeV/c2,themassfactorizationscaleM2waschosentobem2b,andthepartondistributionsetusedwasCTEQ1M[6].Wewouldalsoliketomentionherethatsimilarresultshavebeenobtainedearlierinin[7]usingasimilarpartondistributionsetandournumbersinTable1.aswellasinTable2.belowagreewiththeirs.FromTable√1.,weseethatthecorrectionsevenattheselowenergiesaresizeable.For
S(TeV)
17µb92µb170µb
3O(αS)
presentintheO(α3
S)correctionsareabsentintheBornapproximationcalcu-lation.Abetterindicationoftheconvergenceshouldbefoundincomparing
theO(α4S)resultswiththeO(α3
S)corrections.Wewerealsopresentedwithalistofcutsfromvariousexperimentalgroups,andwhatwassettleduponwasthefollowing:forCDF,wewereaskedforpseudorapidities|η|<1andpt>4GeV/cinthecentralregion.TheD0cutswere|η|<3.4andpt>5GeV/cinthecentralregion.IntheforwardregionattheTeVatron,therequestwasfor2.5<|η|<5.5andpt>1.5GeV/c.AttheSSC,thecentralregionwasdeterminedtobe|η|<2.5andpt>10GeV/c,andtheforwardregiongivenwas1.5<|η|<5.5andpt>1.5GeV/c.Thecalculationsaredonewithcutsinrapiditynotpseudorapidity,butthedifferenceshouldbesmall.Table3.showstheresultsforthesecuts.
Table3.CrossSectionswithCutsImplemented.CDFTeVatronSSCCentral
Forward
Forward
13µb
62µb
approximationresultsbyafairlyuniformamountacrosstheentirept-range.Figure2.showsadramaticfall-offintheforwardregionasptincreases,againwithmostofthecrosssectioninthelow-ptregion.Inthelow-ptrange,thecrosssectionisreducedbyafactorofthreetofivecomparedtothecentralregion.dependingonthecutmade.TurningtotheSSC,Figure3.showsthatbyimposingapt-cutof10GeV/c,mostofthecrosssectionislostinthecentralregion.Atlargept,wefindthatthecontributionisstillappreciable.Finally,intheforwardregion,Figure4.revealsthelarge-ptregionisagainstillsignificant,butagainthemajorityofthecrosssectioncomesfromthelow-ptregion.ThelossofcrosssectionasptincreasesisnotsodramaticasitisintheforwardregionattheTeVatron.
3Conclusions
Whatcanweconcludefromtheseresults?First,thefixed-targetresultsareprobablysolid,sincewecanseefromFigure5.theresultsfromUA1[10]
3
areingoodagreementwiththeO(αS)results,andtheenergiesforthefixed-targetexperimentsarelowerthanthatofUA1.LookingatFigure6.,we
3
comparetheO(αS)calculationsof1,2withthe1988-89and1992-93resultsofCDF[11].Someofthesedataarestillpreliminary,ofcourse,butitappearsthatthedatadonotfitthecalculation.Fromthefigurecaptionweseethatweareoffbyaaboutafactorof2.6.Butwehavesomeconsolationbecausetheshapeisapproximatelycorrect,althoughaslightlysteeperdistributionasdiscussedin[12]wouldfitbetter.Thisfactorof2.6willonlybemagnifiedwhenwelookattheresultsfortheSSC.Clearly,wehaveaproblem.
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Whatarethepossiblesolutions?CalculatetheO(αS)correctionsandseewhatdifferencethatmakes.Thatisanenormousendeavorandwouldtakeyears.Trytomakefurtherheadwayonthesmall-xfront.Thisispossiblebutlargeuncertaintiesremain.Asanexample,oneinterestingmechanismtoaccomodatetheCDFdatashowninFigure6.istoaltertheformofthegluondistributioninthesmall-xregion[12].Butfora’ballparkestimate’thatprobablyisnottoobad,whynotdothefollowing:try
σexp=σ0e(K−1),
(3.1)
whereσ0istheBorncrosssection,Kistheappropriate’K-factor,’andσexpistheexpectedcrosssection.InthecaseoftheTeVatron,σ0=17
5
microbarnsandK=2.2.Wewouldgetσexp=56microbarns.FortheSSC,σ0=170microbarnsandK=3.2.Hereσexp=1.5millibarns.Thedistributionswouldalsohavethefactore(K−1)multiplyingthelowest-orderdistributions.Thisisofcourseratheradhoc,buttheresultslookreasonable.Moretheoreticallyvalidcalculationsarestillwelloffinthedistance,andthenumbersareneedednow.
Finally,inthecourseofmanydiscussions[13],itwasdecidedthatap-proximatecrosssectionfiguresforeachofthecolliders,currentandproposed,shouldbeprovidedsothatanestimateofB-physicseventratescouldbemade.Towardthatend,wepresentTable4.,acompilationofcrosssectionfiguresthatshouldbecorrectwithinafactoroftwo.
Table4.CrossSectionFiguresforReference.
√σ
43GeV
0.5µb
200GeV
100µb
15.4TeV
1mb
Thenumbersforthelowerenergieswerearrivedatessentiallybyrounding
3
theresultsoftheO(αS)calculation.The1.8TeVresultwasderivedinthefollowingway:wetookthefactthatthecurvethatfitsthedataofCDFis
3
2.6timestheO(αS)result.Multiplyingthe37microbarnsbythefactorof2.6,wegetaconvenientnumberof100microbarnsfortheTeVatronwithnocuts.ThenumbersfortheLHCandtheSSCwerebaseduponvariousestiamtesobtainedusingvariouspartondistributionsets.Theywerealsoagreeduponin[13]andfurtherdetaileddiscussionsabouttheuncertaintiescanbefoundin[7],[13].
Acknowledgements.TheauthorswouldliketothankJackSmithforhiscarefulreadingofthemanuscript.ThisworkwassupportedbytheLightnerSamsFoundation,Inc.andtheU.S.DepartmentofEnergy,DivisionofHighEnergyPhysics,ContractW-31-109-ENG-38.
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Fig.1.dσ/dptvs.ptforthekinematiccutsimposedfortheCDFcollabo-ration(solidline)andtheD0collaboration(dashedline)inthecentralregion.Fig.2.dσ/dptvs.ptforthekinematiccutsimposedintheforwardregion
attheTeVatron.Fig.3.dσ/dptvs.ptforthekinematiccutsimposedinthecentralregion
attheSSC.Fig.4.dσ/dptvs.ptforthekinematiccutsimposedintheforwardregion
attheSSC.
√min
Fig.5.σvs.ptfor
S=1.8TeVwith|y|<1.Thehighsolidcurvewas
runwithmb=4.5GeV/c2,andM=mb/2.Themiddlesolidcurvewasrunwithmb=4.75GeV/c2,andM=mb.Thelowsolidcurvewasrunwithmb=5.0GeV/c2,andM=2mb.CTEQ1Mdistributionfunctionswereused.Thedatawiththethickerrorbarsaretakenfromthe88-89andthethinerrorbarsfromthe92-93runsofCDF[11].Thedashedcurveisthemiddlesolidcurvemultipliedbyafactorof2.6.
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