2008/09/11 by N. Kivel, Maxim V. Polyakov, M. V. Polyakov +2
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph #nucl-th
paper · pdf · doi:10.1103/physrevd.79.014028
19 pages, 4 figures
arxiv created 2008/09/11 · openalex publication_date 2009/01/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We demonstrate that in the region of Bjorken xBj\ensuremath∼m_\ensuremathπ2/(4\ensuremathπF_\ensuremathπ)2 and/or xBj\ensuremath∼|t|/(4\ensuremathπF_\ensuremathπ)2 the standard \ensuremathχPT for the pion generalized parton distributions (GPDs) fails and one must perform all order resummation of \ensuremathχPT. We perform such resummation in the large-N limit of the O(N+1) extension of the chiral theory. Explicit resummation allows us to reveal novel phenomena---the form of the leading chiral correction to pion parton distribution functions (PDFs) and GPDs depends on the small x asymptotic of the pion PDFs. In particular, if the pion PDF in the chiral limit has the Regge-like small x behavior q(x)\ensuremath∼1/x^\ensuremathω, the leading large impact parameter (b_\ensuremath⊥\ensuremath→\ensuremath∞) asymptotics of the quark distribution in the transverse plane has the form (m_\ensuremathπ=0) q(x,b_\ensuremath⊥)\ensuremath∼1/x^\ensuremathωln^\ensuremathω(b_\ensuremath⊥2)/b_\ensuremath⊥^2(1+\ensuremathω). This result is model independent and it is controlled completely by the all order resummed \ensuremathχPT developed in this paper. This asymptotic interweaves with small-x behavior of usual PDFs, hence it depends on the scale, at which the corresponding PDF is defined. This is a new and interesting result in which the chiral expansion meets the QCD evolution.