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 $$f(\beta)/\beta$$ rather than with the usual parton density $$f(\beta)$$. This results in a non-integrable singularity at $$\beta=0$$ exaggerated by the fact that $$f(\beta)$$'s, on their own, have a singular $$\beta^{-a}$$ Regge behavior for small $$\beta$$. 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 $$H(x,\xi)$$ that are finite and continuous at the "border point'' $$x=\xi$$. Using a simple input forward distribution, we illustrate the implementation of the new approach for explicit construction of model GPDs. As a further development, a more general method of regulating the $$\beta=0$$ singularities is proposed that is based on the separation of the initial single DD $$f(\beta, \alpha)$$ into the "plus'' part $$[f(\beta,\alpha)]_{+}$$ and the $$D$$-term. It is demonstrated that the "DD+D'' separation method allows 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 $$D(\alpha)$$.
- Research Organization:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- AC05-06OR23177
- OSTI ID:
- 1013040
- Report Number(s):
- JLAB-THY-11-06; DOE/OR/23177-1383; arXiv:1101.2165; PRVDAQ; TRN: US201110%%424
- Journal Information:
- Phys. Rev. D, Vol. 83, Issue 07; ISSN 1550-7998
- Country of Publication:
- United States
- Language:
- English
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