Baryon wave function in large-Nc QCD: Universality, nonlinear evolution equation and asymptotic limit

TL;DR

This paper develops a universal large-Nc QCD framework for baryon wave functions, deriving a nonlinear evolution equation, solving it asymptotically, and calculating anomalous dimensions analytically up to next-to-leading order.

Contribution

It introduces a universal 1/Nc expansion for baryon wave functions, deriving a nonlinear Hamilton-Jacobi type evolution equation and providing analytical solutions and anomalous dimensions.

Findings

Universal form of baryon wave function in large-Nc limit

Analytical solution of the nonlinear evolution equation

Calculation of anomalous dimensions up to next-to-leading order

Abstract

The 1/Nc expansion is formulated for the baryon wave function in terms of a specially constructed generating functional. The leading order of this 1/Nc expansion is universal for all low-lying baryons [including the O(1/Nc) and O(Nc^0) excited resonances] and for baryon-meson scattering states. A nonlinear evolution equation of Hamilton-Jacobi type is derived for the generating functional describing the baryon distribution amplitude in the large-Nc limit. In the asymptotic regime this nonlinear equation is solved analytically. The anomalous dimensions of the leading-twist baryon operators diagonalizing the evolution are computed analytically up to the next-to-leading order of the 1/Nc expansion.