Asymmetric gluon distributions and hard diffractive electroproduction

Due to the momentum transfer r{equivalent_to} p{minus}p{prime} from the initial proton to the final, the asymmetric matrix element {l_angle}p{prime}{vert_bar}G...G{vert_bar}p{r_angle} that appears in the pQCD description of hard diffractive electroproduction does not coincide with that defining the gluon distribution function f{sub g}(x). The author outlines a pQCD formalism based on a concept of the double distribution F{sub g}(x,y), which specifies the fractions xp, yr, (1{minus}y)r of the initial proton momentum p and the momentum transfer r, resp., carried by the gluons. He discusses the one-loop evolution equation for the double distribution F{sub g}(x,y,{mu}) and obtains the solution of tis equation in simplified situation when the quark-gluon mixing effects are neglected. For r{sup 2}=0, the momentum transfer r is proportional to p: r = {zeta}p, and it is convenient to parameterize the matrix element {l_angle}p{minus}r{vert_bar}G...G{vert_bar}p{r_angle} by an asymmetric distribution function F{sub {zeta}}{sup g}(X) depending on the total fractions X {equivalent_to} x+y{zeta} and X{minus}{zeta} = x{minus}(1{minus}y){zeta} of the initial hadron momentum p carried by the gluons. He formulates evolution equations for F{sub {zeta}}{sup g}(X), studies some of their general properties and discusses the relationship between F{sub {zeta}}{sup g}(X), F{sub g}(x,y) and f{sub g}(x)