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

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.Comment: 44 page

Renormalized Path Integral for the Two-Dimensional Delta-Function Interaction

A path-integral approach for delta-function potentials is presented. Particular attention is paid to the two-dimensional case, which illustrates the realization of a quantum anomaly for a scale invariant problem in quantum mechanics. Our treatment is based on an infinite summation of perturbation theory that captures the nonperturbative nature of the delta-function bound state. The well-known singular character of the two-dimensional delta-function potential is dealt with by considering the renormalized path integral resulting from a variety of schemes: dimensional, momentum-cutoff, and real-space regularization. Moreover, compatibility of the bound-state and scattering sectors is shown.Comment: 26 pages. The paper was significantly expanded and numerous equations were added for the sake of clarity; the main results and conclusions are unchange