Large-N Summation of Chiral Logs for Generalized Parton Distributions

Understand

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 ($m_\pi=0$) $q(x,b_\perp)\sim 1/x^\omega\ \ln^{\omega}(b_\perp^2)/b_\perp^{2{(1+\omega)}}$.