2011/01/26 by Anatoly Radyushkin, A. V. Radyushkin · 1 citation
Mathematics · Physics and Astronomy · #Ansatz #Distribution function #Gravitational singularity #Hadron #High-Energy Particle Collisions Research #Mathematical analysis #Mathematical physics #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Parton #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Singularity #hep-ph
paper · pdf · doi:10.1103/physrevd.83.076006
published as Phys.Rev.D83:076006,2011 · 19 pages, 13 figures; references added, typos corrected
arxiv created 2011/01/26 · openalex publication_date 2011/04/12 · arxiv updated 2015/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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(\ensuremathβ)/\ensuremathβ rather than with the usual parton density f(\ensuremathβ). This results in a nonintegrable singularity at \ensuremathβ=0 exaggerated by the fact that f(\ensuremathβ)'s, on their own, have a singular \ensuremathβ^\ensuremath-a Regge behavior for small \ensuremathβ. 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,\ensuremathξ) that are finite and continuous at the ``border point'' x=\ensuremathξ. 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 \ensuremathβ=0 singularities is proposed that is based on the separation of the initial single DD f(\ensuremathβ,\ensuremathα) into the ``plus'' part [f(\ensuremathβ,\ensuremathα)]+ 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(\ensuremathα).