For an unpolarized target, the generalized parton distribution $H_q(x,0,t)$ is related to the distribution of partons in impact parameter space. The transverse distortion of this distribution for a transversely polarized target is described by $E_q(x,0,t)$

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arXiv:hep-ph/0206269v1 26 Jun 2002PositionspaceinterpretationforgeneralizedpartondistributionsMatthiasBurkardtaa DepartmentofPhysics,NewMexicoStateUniversity,LasCruces,NM88011,U.S.A.Foranunpolarizedtarget,thegeneralizedpartondistributionHq(x,0,t)isrelatedtothedistributionofpartonsinimpactparameterspace.ThetransversedistortionofthisdistributionforatransverselypolarizedtargetisdescribedbyEq(x,0,t).1.INTRODUCTIONGeneralizedpartondistributions(GPDs)[1]haveattractedsigni cantinterestsinceithasbeenrecognizedthattheycannotonlybeprobedindeeplyvirtualComptonscatteringexperimentsbutcanalsoberelatedtotheorbitalangularmomentumcarriedbyquarksinthenucleon[2].However,remarkablylittleisstillknownaboutthephysicalinterpretationofGPDs,andonemayaskthequestion:suppose,about10-15yearsfromnow,afteracombinede ortfromexperiment,simulationandtheory,weknowhowthesefunctions(i.e.GPDs)looklikeforthenucleon.Whatisit,insimplephysicalterms,thatwewillhavelearnedaboutthestructureofthenucleon?Ofcourse,wewillhavelearnedsomethingabouttheorbitalangularmomentumcarriedbythequarks[2],butisthatallthereis?Inthesenotes,IwilldiscussanotherinterestingpieceofinformationthatcanbeextractedfromGPDs,namelyhowpartonsaredistributedinthetransverseplane.Innonrelativisticquantummechanics,thephysicsofformfactorsisillucidatedby

transformingtothecenterofmassframeandbyinterpretingtheFouriertransformofformfactorsaschargedistributionsinthatframe. q(x,0⊥)]GPDs[1]aretheformfactorsofthesameoperators[lightconecorrelatorsO

whoseforwardmatrixelementsalsoyieldtheusual(forward)partondistributionfunctions(PDFs).Forexample,theunpolarizedPDFq(x)canbeexpressedintheform2

q(x,0⊥)|p,λ ,q(x)= p,λ|O

whiletheGPDsHq(x,ξ,t)andEq(x,ξ,t)arede nedas

q(x,0⊥)|p,λ = p′,λ′|O

(1)12M Eq(x,ξ,t)u(p,λ),(2)where =p′ p,2¯p=p+p′,t= 2,2¯p+ξ= +,and

q(x,b⊥)=O

2dx 2,b⊥γq+x ThisworkwassupportedbytheDOE(DE-FG03-95ER40965)Wewillsuppressthescale(i.e.Q2)dependenceofthesematrixelementsfornotationalconvenience.Intheend,the⊥‘resolution’willbelimitedby1/Q.