Hard Exclusive Electroproduction of Pions(6)

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

moredi cult.Nevertheless,someintuitionabouttheirmagnitudehasbeenobtainedfrommodelcalculations[23].Still,contributions

oftheso-calledK-termstohardexclu-sivemesonproductionhavebeenneglectedsofar.Inthepresentcaseofπ+productionthesituationisdi erent.Aswewillshow,thepseudoscalarpieceoftheamplitudeAπ+canbeassociatedwiththevirtualphotoproductionofpionsfromthenucleonpioncloud.Duetothesmallpionmassthismechanismisexpectedtobeimportant,especiallyatsmallmomentumtransferst.

Weareinterestedinevaluatingthecontributiontothenucleonmatrixelement(3)arisingfromasituationwhenaquark-antiquarkpairwithlowinvariantmasspropagatesinthet-channel,suchthatitbecomesclosetoaπ+boundstate.Toconstructthecorre-spondingdoubledistributionfunctionweintroduceane ectiveLagrangiandescribingapseudovectorpion-nucleoninteraction[22]:

LπNN=gπNN

× ¯(P′,S′)γ5N(P,S)2gπNNN

¯d(0)γ5nd4xe ir·x 0|T[ψ [0,z]ψu(z)φ+(x)]|0 z2=0,(10)

where +=1

2( 1+i 2)isthepion eldassociatedwiththeπ+meson.Theleading-twist

contributiontothematrixelement(10)arisesfromtheregionofphasespacewherethequark eldsarelocalizednearthelight-cone,z+～0.Insertingafullsetofintermediatepionstatesbetweenthepion eldandthenon-localquarkoperatorgives:

¯d(0)γ5n n(P′,S′)|ψ [0,z]ψu(z)|p(P,S) z2=0√ i+¯d(0)γ5n 0|ψ [0,z]ψ(z)|π(r) z2=0.=N(P′,S′)γ5N(P,S)um2 tπ(11)

Usingthepiondistributionamplitude(2)andcomparingwiththede nitionofthepseu-doscalardoubledistributionfunctionsineq.(3)yields:

√ 2¯du(x,y,t≈0)= δ(x)Φπ(y).(12) Kdu+ K2mπ t

Asthiscontributioncanbeexpressedentirelyintermsof Kthereisnodangerofdoublecountingifweaddthistermtothecontributionarisingfromamodelfor F,asdiscussedintheprevioussection.

Onecanexpressthet-channelonepionexchangecontributionalsointheform:

Aπ+√= m2π t

εL·(q′+r)Fπ+(Q2),(13)