Large-N Summation of Chiral Logs for Generalized Parton Distributions

Sep, 2008
19 pages
Published in:
  • Phys.Rev.D 79 (2009) 014028
e-Print:

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Abstract: (arXiv)
We demonstrate that in the region of Bjorken x ~m_\pi^2/(4\pi F_\pi)^2 and/or x ~|t|/(4\pi F_\pi)^2 the standard ChPT for the pion GPDs fails and one must perform all order resummation of ChPT. 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 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 behaviour q(x)~1/x^\omega, the leading large impact parameter (bb_\perp\to\infty) asymptotics of the quark distribution in the transverse plane has the form (mπ=0m_\pi=0) q(x,b)1/xω lnω(b2)/b2(1+ω)q(x,b_\perp)\sim 1/x^\omega\ \ln^{\omega}(b_\perp^2)/b_\perp^{2{(1+\omega)}}. This result is model independent and it is controlled completely by the all order resummed ChPT developed in this paper. This asymptotic interweaves with small-xx behaviour 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.
  • 13.60.-r
  • 12.38.Cy
  • 11.15.Pg
  • perturbation theory: chiral
  • scattering amplitude: hard scattering
  • correction: chiral
  • parton: distribution function
  • pi: generalized parton distribution
  • small-x
  • expansion 1/N