Abstract

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 $f(\ensuremath{\beta})/\ensuremath{\beta}$ rather than with the usual parton density $f(\ensuremath{\beta})$. This results in a nonintegrable singularity at $\ensuremath{\beta}=0$ exaggerated by the fact that $f(\ensuremath{\beta})$'s, on their own, have a singular ${\ensuremath{\beta}}^{\ensuremath{-}a}$ Regge behavior for small $\ensuremath{\beta}$. 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 $H(x,\ensuremath{\xi})$ that are finite and continuous at the ``border point'' $x=\ensuremath{\xi}$. 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 $\ensuremath{\beta}=0$ singularities is proposed that is based on the separation of the initial single DD $f(\ensuremath{\beta},\ensuremath{\alpha})$ into the ``plus'' part $[f(\ensuremath{\beta},\ensuremath{\alpha}){]}_{+}$ 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 $D(\ensuremath{\alpha})$.

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