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Asymmetric Gluon Distributions and Hard Diffractive Electroproduction

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: $r = ζp$, and it is convenient to parameterize the matrix element <p-r|G...G|p> by an asymmetric distribution function ${\cal F}_ζ^g (X)$ depending on the total fractions $X \equiv x+y ζ$ and $X-ζ= x- (1-y) ζ$ of the initial hadron momentum p carried by the gluons.I formulate evolution equations for ${\cal F}_ζ^g (X)$, study some of their general properties and discuss the relationship between ${\cal F}_ζ^g (X)$, F_g(x,y) and f_g(x).