Hard Exclusive Electroproduction of Pions(7)

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

where

εL=i

2fπ

2Ncu 2(15)

istheleadingQCDcontributiontotheπ+electromagneticformfactoratlargeQ2[18,19].2Totwist-2accuracy,i.e.neglectingtermsofordert/Q2andm2π/Q,theamplitude

(13)isexplicitlygaugeinvariant.ThisisguaranteedbythefactorεL·(q′+r)whicharisesfromthehardphoton-quarkinteraction.Intheonepionexchangeapproximation¯dudecouplesfromtheconsideredproductionprocess.Finally,thedi erence Kdu K

notethatinthecaseofπ0productionat-channelexchangecontributionsimilarto(12)appearsintheproductionamplitudewithazerocoe cientfromthedi erenceoftwoequalquarkcharges.

Tothisendsomecommentsregardingonepiont-channelexchange,asusedabove,areinorder.Ingeneraloneexpectsthatatlargecenter-of-massenergiesanyt-channelexchangeofanhadronicstateshouldbereplacedbythecorrespondingReggetrajectory.Therefore,atsmallvaluesofBjorken-xadditionalcontributionstothepseudoscalarpartoftheproductionamplitudeAπ+couldoccur.Oncethepionpolecontributionisreplacedbyreggeizedpion(andrho)exchange[24]therelationtothepionelectromagneticformfactorseemstobelost(see,however,ref.[25]foranattempttointerpretpionelectroproductiondataintheframeworkofaReggeexchangemodel).Werestrictourselvesinthisworktothesimplestmodelforthepseudoscalarpartoftheproductionamplitudeinthehopethatitcontainsthedominantcontributionatsmallmomentumtransfers,i.e.closetothepionpole.

5Results

InFigs.1and2wepresentresultsforthecrosssectionofexclusiveπ+productioninthescatteringoflongitudinallypolarizedphotonsfromnucleonsatQ2=10GeV2.Uptologarithmiccorrectionsthecrosssectionisproportionalto1/Q6asonecaninferfromeq.(1).

InFig.1weshowthedi erentialproductioncrosssectionfortheminimalkinematically

2allowedvalueoft=tmin= x2BjM/(1 xBj).We ndthatthepseudovectorcontribution

(6)dominatesatsmallvaluesoftheBjorkenvariablexBj.ItsxBj-dependencere ectsthebehavioroftherelevantforwardpartondistributions(7).Atx～0.3thecrosssectionisgovernedbythepseudoscalarpioncloudcontribution(11).

WhilemodelsAandBgivequalitativelysimilarcrosssectionsatsmallmomentumtransfers,theystarttodi erforincreasing|t|.ThisisillustratedinFig.2wherewepresentresultsforthedi erentialproductioncrosssectiontakenatt= 0.4GeV2.The