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1、NORDITA-96/3Phep-ph/9601333January25,1996CharmoniumProductionviaFragmentationatHigherOrdersinαsP.Ernstr¨om,P.Hoyer,andM.V¨anttinenNORDITABlegdamsvej17,DK-2100CopenhagenØAbstractQuarkoniumproductionatagivenlargepTisdominatedbypartonfragmentation:aparton
2、whichisproducedwithtransversemomen-tumpT/zfragmentsintoaquarkoniumstatewhichcarriesafractionzofthepartonmomentum.SincepartonproductioncrosssectionsfallsteeplywithpT,highzfragmentationisfavored.However,quan-tumnumberconstraintsmayrequiretheemissionofglu
3、onsinthearXiv:hep-ph/9601333v125Jan1996fragmentationprocess,andthissoftensthezdependenceofthefrag-mentationfunction.Wediscussthepossibilitythathigher-orderpro-cessesmayenhancethelargezpartoffragmentationfunctionsandthuscontributesignificantlytothequarko
4、niumcrosssection.Anex-plicitcalculationoflightquarkfragmentationintoηcshowsthatthehigher-orderprocessq→qηcinfactdominatesthelowest-orderpro-cessq→qgηc.1.IntroductionHeavyquarkproductionisahardQCDprocess,andtheperturbativeex-pansionofproductionamplitude
5、sinαsisexpectedtoapply.However,theperturbationseriesisnotalwaysdominatedbyitslowest-orderterm.Forexample,whenthetransversemomentumpTofacollinearheavyquarkpairismuchlargerthanitsinvariantmassM,lightpartonfragmentationdom-inatesthelowest-orderproductionp
6、rocessesbyapowerofp2/M2[1].TheTdataoncharmoniumproductionindeedshowsa1/p4behaviorofthecrossTsection[2,3],compatiblewiththepredictionforafragmentationprocess.QCDcalculationsbasedonthecolorsingletmodel[4]neverthelessdis-agreewithdataontherelativeproducti
7、onratesofSandPwavequarkoniaandontheabsolutenormalizationofthecrosssectionsatbothlow[5,6]andhigh[2,3,7]valuesofpT.Order-of-magnitudediscrepancieshavebeenobservedforbothcharmoniumandbottomonium.InQCD,thefragmentationofavirtualgluonintoa3Squarkoniumstate1
8、(J/ψ,Υ)requirestheemissionofatleasttwoextragluons,g∗→3S+gg,1whereasfragmentationintoa3PstatecanproceedwiththeemissionofaJsinglegluon,g∗→3P+g.TheemissionoftheextragluonsuppressestheJcalculated3Scrosssectionconsiderablycomparedtothe3Pcros
