Large-N Summation of Chiral Logs for Generalized Parton Distributions

Abstract

We demonstrate that in the region of Bjorken x ~m_π^2/(4πF_π)^2 and/or x ~|t|/(4πF_π)^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^ω, the leading large impact parameter ($b_{\perp }\to \infty$) asymptotics of the quark distribution in the transverse plane has the form ($m_{\pi }=0$) $q(x,b_{\perp })\sim 1/x^{\omega }{\ln }^{\omega }(b_{\perp }^2)/b_{\perp }^{2(1+\omega )}$. 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-$x$ 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.

19 pages, 4 figures

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