Hard Exclusive Electroproduction of Pions(8)

We investigate the exclusive electroproduction of pi^+ mesons from nucleons. To leading twist, leading order alpha_s accuracy the corresponding production amplitude can be decomposed into pseudovector and pseudoscalar parts. Both can be expressed in terms

maximumvalueofBjorken-xisdeterminedbythecondition|t|≥|tmin|.FormodelAthepseudovectorcontributiondecreasesslowlywithdecreasingxBjanddominatesthecrosssectionatxBj<～0.1.AtxBj～xmaxthetotalpionproductioncrosssectionisabouthalfaslargeasobtainedfromthepioncloudcontributionaloneduetostronginterferencee ects.Ontheotherhand,inmodelBthexBj-dependenceofthepseudovectorcontributionissimilartotheonefromthepioncloud.Also,contrarytothepreviouscase,atxBj～xmaxtheproductioncrosssectionisabout20%largerthanobtainedfromthepioncloudalone.FinallywecompareinFig.3totheleadingtwistproductioncrosssectionforπ0mesonswhichhasbeeninvestigatedin[4].Att=tminthepseudovectorcontributiontoπ+productionisaboutafactor5–10largerascomparedtotheπ0case.AtxBj～0.3largecontributionsfromthepioncloud,whichareabsentinπ0production,addfurthertothecrosssectionratio.

Itshouldbeemphasizedthatthedominanceofthehardgluonexchangeprocessesconsideredinthispapercanonlybeensuredforsu cientlylargevaluesofQ2.Justlikeinthecaseofthepionformfactor,competingcontributionsareprovidedbysoftmechanismswhich,inthiscase,correspondtothenonperturbativeoverlapofthreehadronicwavefunctions.TheinterplayofsoftandhardinteractionmechanismshasbeenstudiedrecentlyforthepionformfactorinaQCDsumrulerelatedmodel[26].GuidedbytheresultsofthisinvestigationweexpectthedominanceofhardgluonexchangeforvaluesofQ2above10GeV2.

6Summary

Wehavediscussedthehardexclusiveelectroproductionofπ+mesonsfromnucleons.Forlongitudinallypolarizedphotonsonecanexpressthecorrespondingphotoproductionam-plitudetoleadingtwist,leadingorderαsaccuracyintermsofquarkdoubledistributionfunctionsofthenucleon.We ndthattheamplitudereceivescontributionsfrompseu-dovectorandpseudoscalarpieces.Thepseudovectorcontributionisdeterminedbyquarkdoubledistributionswithwellknownpropertiesintheforwardlimit,asgivenbyordinarypolarizedquarkdistributionfunctions.However,forthepseudoscalarpartsuchinforma-tionisnotavailable.Inthisworkithasbeenmodeledintermsofaninteractionofthevirtualphotonwiththenucleonpioncloud.Asaconsequence,therelateddoubledistri-butionisdeterminedbythepiondistributionamplitude.Thecorrespondingcontributiontothepionproductionamplitudeturnsouttobeproportionaltothepionformfactor.Wehavefoundthatboth,pseudovectorandpseudoscalartermsshouldbeincludedifoneconsidersthewhole0<xBj<1range.Inparticular,wehaveobservedthatthepseudovectorpartdominatesatsmallxBj<0.1.Ontheotherhand,thepioncloudcontributioncontrolstheπ+productionatsmallt～tminand0.1<xBj<0.4.Atlargervaluesof|t|～0.4GeV2therelativeweightofpseudoscalarandpseudovectorcontributionshasbeenfoundtobesensitivetodetailsoftherelevantdoubledistributionfunctions.Furtherinvestigationsofdoubledistributionfunctions,aswellasexperimentaldataonexclusivemesonproductionarecertainlyneeded.