Generalized parton distributions and their singularities

A. V. Radyushkin
Phys. Rev. D 83, 076006 – Published 12 April 2011

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(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 βa 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).

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  • Received 26 January 2011

DOI:https://doi.org/10.1103/PhysRevD.83.076006

© 2011 American Physical Society

Authors & Affiliations

A. V. Radyushkin

  • Physics Department, Old Dominion University, Norfolk, Virginia 23529, USA
  • Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
  • Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Russian Federation

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Issue

Vol. 83, Iss. 7 — 1 April 2011

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