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

References in corpus (26)

• Gauge-Invariant Decomposition of Nucleon Spin and Its Spin-Off
• Wave Functions, Evolution Equations and Evolution Kernels from Light-Ray Operators of QCD
• Generalized Parton Distributions
• Deeply Virtual Compton Scattering
• Unraveling hadron structure with generalized parton distributions
• Hard Exclusive Reactions and the Structure of Hadrons
• Factorization for hard exclusive electroproduction of mesons in QCD
• Impact Parameter Dependent Parton Distributions and Off-Forward Parton Distributions for $\zeta \to 0$
• Scaling Limit of Deeply Virtual Compton Scattering
• Probing partonic structure in gamma* gamma -> pi pi near threshold
• Hard exclusive electroproduction of two pions and their resonances
• Chiral Corrections to Matrix Elements of Twist-2 Operators
• Is the Sullivan Process Compatible with QCD Chiral Dynamics?
• Chiral Perturbation Theory and the first moments of the Generalized Parton Distriputions in a Nucleon
• Constructing Parton Convolution in Effective Field Theory
• Tomography for amplitudes of hard exclusive processes
• Generalized parton distributions for the pion in chiral perturbation theory
• Leading Chiral Corrections to the Nucleon Generalized Parton Distributions
• Chiral perturbation theory for nucleon generalized parton distributions
• Generalized parton distributions for the nucleon in chiral perturbation theory
• Chiral dynamics and the growth of the nucleon's gluonic transverse size at small x
• On "dual" parametrizations of generalized parton distributions
• Dual parameterization and Abel transform tomography for twist-3 DVCS
• Taming Deeply Virtual Compton Scattering
• Generalised parton distributions of the pion in partially-quenched chiral perturbation theory
• Breakdown of chiral expansion for parton distributions

Cited by in corpus (8)

• Chiral dynamics and partonic structure at large transverse distances
• Chiral dynamics and peripheral transverse densities
• Quantifying the nucleon's pion cloud with transverse charge densities
• Leading Infrared Logarithms from Unitarity, Analyticity and Crossing
• The energy-momentum tensor and D-term of Q-clouds
• On chiral corrections to nucleon GPD
• Generalized parton distributions of sea quarks in the proton from nonlocal chiral effective theory
• Exact summation of leading infrared logarithms in 2D effective field theories