Asymmetric gluon distributions and hard diffractive electroproduction

Due to the momentum transfer r = p - p' from the initial proton to the final, the ''asymmetric'' matrix element [p'\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 lowest-twist pQCD formalism based on the concept of double distribution F-g(x,y), which specifies the fractions xp, yr, (1-y) r of the (lightlike) initial momentum p and the momentum transfer r, resp., carried by the gluons. I discuss one-loop evolution equation for the double distribution F-g(x,y; mu) and obtain the solution of this equation in a simplified situation when the quark-gluon mixing effects are ignored. For r(2) = 0, the momentum transfer 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 F-zeta(g)(X) depending on the total fractions X = x + y zeta and X - zeta = x - (1 - y)zeta of the initial proton momentum p carried by the gluons. I formulate evolution equations for F-zeta(g)(X), study some of their general properties and discuss the relationship between F-zeta(g)(X), F-g(x,y) and f(g)(x).