Evolution and models for skewed parton distributions

We discuss the structure of the “forward visible” (FV) parts of double and skewed distributions related to the usual distributions through reduction relations. We use factorized models for double distributions (DD’s) $\tilde{f}(x,\alpha )$ in which one factor coincides with the usual (forward) parton distribution and another specifies the profile characterizing the spread of the longitudinal momentum transfer. The model DD’s are used to construct skewed parton distributions (SPD’s). For small skewedness, the FV parts of SPD’s $H(\tilde{x},\xi )$ can be obtained by averaging forward parton densities $f\left(\tilde{x}-\xi \alpha \right)$ with the weight $\rho \left(\alpha \right)$ coinciding with the profile function of the double distribution $\tilde{f}(x,\alpha )$ at small x. We show that if the $x^n$ moments $f_n\left(\alpha \right)$ of DD’s have the asymptotic $(1\mathrm{}-{\alpha }^2{)}^{n+1\mathrm{}}$ profile, then the $\alpha$ profile of $\tilde{f}(x,\alpha )$ for small x is completely determined by the small-$x$ behavior of the usual parton distribution. We demonstrate that, for small $\xi ,$ the model with asymptotic profiles for $f_n\left(\alpha \right)$ is equivalent to that proposed recently by Shuvaev et al., in which the Gegenbauer moments of SPD’s do not depend on $\xi .$ We perform a numerical investigation of the evolution patterns of SPD’s and give an interpretation of the results of these studies within the formalism of double distributions.