Large-N Summation of Chiral Logs for Generalized Parton Distributions
Sep, 2008
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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 () asymptotics of the quark distribution in the transverse plane has the form () . 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- 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
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