Asymmetric Gluon Distributions and Hard Diffractive Electroproduction

Abstract

The ``asymmetric'' matrix element <p-r|G...G|p> that appears in the pQCD description of hard diffractive electroproduction does not coincide with that defining the gluon distribution function f_g(x). I outline a pQCD formalism based on a concept of the double distribution F_g(x,y), which specifies the fractions xp, yr, (1-y)r of the initial proton momentum p and the momentum transfer r, resp., carried by the gluons. For $t\equiv r^2=0$, r is proportional to p: $r=\zeta p$, and it is convenient to parameterize the matrix element <p-r|G...G|p> by an asymmetric distribution function ${\mathcal{F}}_{\zeta }^g(X)$ depending on the total fractions $X\equiv x+y\zeta$ and $X-\zeta =x-(1-y)\zeta$ of the initial hadron momentum p carried by the gluons.I formulate evolution equations for ${\mathcal{F}}_{\zeta }^g(X)$, study some of their general properties and discuss the relationship between ${\mathcal{F}}_{\zeta }^g(X)$, F_g(x,y) and f_g(x).

Comments: Definition of asymmetric gluon distribution is corrected to conform with the reduction formulas