Generalized parton distributions and their singularities

A new approach to building models of generalized parton distributions (GPDs) is discussed that is based on the factorized DD (double distribution) ansatz within the single-DD formalism. The latter was not used before, because reconstructing GPDs from the forward limit one should start in this case with a very singular function f(β)/β rather than with the usual parton density f(β). This results in a nonintegrable singularity at β=0 exaggerated by the fact that f(β)'s, on their own, have a singular β-a Regge behavior for small β. It is shown that the singularity is regulated within the GPD model of Szczepaniak et al., in which the Regge behavior is implanted through a subtracted dispersion relation for the hadron-parton scattering amplitude. It is demonstrated that using proper softening of the quark-hadron vertices in the regions of large parton virtualities results in model GPDs H(x,ξ) that are finite and continuous at the 'border point' x=ξ. Using a simple input forward distribution, we illustrate implementation of the new approach for explicit construction of model GPDs. As a further development, a more general method of regulating the β=0 singularities is proposed that is based on the separation of the initial single DD f(β,α) into the 'plus' part [f(β,α)]+ and the D term. It is demonstrated that the ''DD+D'' separation method allows one to (re)derive GPD sum rules that relate the difference between the forward distribution f(x)=H(x,0) and the border function H(x,x) with the D-term function D(α).