Abstract
We extend our method of analytic ERBL evolution for the case of distribution amplitudes that have jumps at some points x = ζi inside the support region 0 < x < 1. As an application of the method, we use it for evolution of the two-photon generalized distribution amplitude. Our approach has advantages over the standard method of expansion in Gegenbauer polynomials, which requires infinite number of terms in order to accuretly reproduce functions in the vicinity of singular points, and over the method of straightforward iteration of initial distribution with evolution kernel which produces logarithmically divergent terms at each iteration. In our method, the logarithmic singularities are summed from the start, which immediately produces a continuous curve, with only one or two iterations needed afterwards in order to get precise results.
Highlights
Construction of theoretical models for Generalized Parton Distributions (GPDs) [1, 2, 3, 4] is an inherent part of their studies
Analysis of simple one-loop diagrams is the basis of the factorized DD Ansatz [8] (FDDA) that is a standard element of codes generating models for GPDs
The strategy is to take the expression for some one-loop diagram as the starting function for evolution, and use evolved patterns for modeling GPDs
Summary
Construction of theoretical models for Generalized Parton Distributions (GPDs) [1, 2, 3, 4] is an inherent part of their studies. These models should satisfy several nontrivial requirements that follow from most general principles of quantum field theory. In this context, one could mention polynomiality, positivity, hermiticity, time reversal invariance, etc. Unlike GPDs, GDAs evolve according to the same ζ-independent ERBL kernels as usual DAs, which allows us to concentrate on studying implications due to the non-analytic structure of the initial distribution. In the QCD lowest order, it is proportional to the V V → V V ERBL evolution kernel, but the evolution of its ln Q2 derivative, in the leading logarithm approximation, is governed by the qq → qq ERBL kernel, just as in examples considered in Ref. [9]
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