Large-N Summation of Chiral Logs for Generalized Parton Distributions

TL;DR

This paper develops an all-order resummation of chiral perturbation theory for pion GPDs in the large-N limit, revealing how small-x behavior influences transverse impact parameter distributions and connecting chiral expansion with QCD evolution.

Contribution

It introduces a novel all-order resummation method for chiral logs in pion GPDs using large-N techniques, uncovering new phenomena in the small-x and impact parameter regimes.

Findings

Resummation reveals dependence of chiral corrections on small-x asymptotics.

Large impact parameter behavior of quark distributions is derived and shown to be model independent.

Connects chiral expansion with QCD evolution, highlighting scale dependence.

Abstract

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 ($b_\perp\to\infty$) 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.