Hard Exclusive Electroproduction of Pions(3)

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

exchangedominatesatintermediatevaluesofBjorken-x,perturbativequarkexchangeisrelevantmainlyatsmallxBj.

Thepaperisorganizedasfollows:inSec.2wepresenttheamplitudesforchargedpionelectroproduction.Pseudovectorandpseudoscalarpartsoftherelevantdoubledis-tributionfunctionsareassociatedinSec.3and4withtheperturbativeandpionpolecontribution,respectively.ResultsarepresentedinSec.5.Finallywesummarize.2Amplitudes

ThecalculationofmesonelectroproductionamplitudesisbasedonPQCDfactorization[1].Itappliestoincidentlongitudinallypolarizedphotonswithlargespace-likemomenta,<2Q2= q2 Λ2QCD,andmoderatemomentumtransfertothenucleontarget,|t|～Λingthetechniquesoutlinedinrefs.[1,2,4,11]givesthefollowingresultfortheπ+virtualphotoproductionamplitudeinleadingtwist,leadingorderαsaccuracy:Aπ+=i

g2CF

Q¯(P′,S′)γ5nN N(P,S)

ττ¯

ω¯

d[x,y]x+2y xω¯ i ¯du)×(ed Fdu eu F

ig2CF

Q¯(P′,S′)γ5N(P,S)N

ττ¯

1d[x,y]

x+2y xω¯ i ¯du)×(ed Kdu eu K

.(1)

¯Herethenotationd[x,y]...=01dx0xdy...,withx¯=1 xisused.N(P,S)and¯(P′,S′)aretheDiracspinorsoftheinitialandscatterednucleon,respectively,withtheN

correspondingfour-momentaP,P′andspinsS,S′.Mstandsforthenucleonmass.The¯=(P+P′)/2,andthemomentumtransferaveragenucleonmomentumisdenotedbyP

isr=P P′witht=r2.Theproducedmesoncarriesthefour-momentumq′and¯/( qq¯=(q+q′)/2.Furthermore,wehaveintroducedthevariableω¯=2¯q·P¯2).Finally,nisalight-likevectorwithn·a=a+=a0+a3foranyvectora,andn =γµnµ.

Thelongdistancedynamicsofthepioninthe nalstateiscontainedinthedecayconstantfπ=133MeVandthedistributionamplitudeΦπ(τ)[18,19]:

¯u(x)γ5n π(q)|ψ ψd(y)|0 = ifπ(q′·n)+′ 1

0τy)Φπ(τ)eiq·(τx+¯dτ,′(2)

wherequark eldsψwithproper avorquantumnumbersenter.

Thenucleonpartoftheamplitude(1)isdeterminedbydoubledistributionfunctions Fduand Kduwhicharenondiagonalin avor.Theyarede nedasmatrixelementsof