Effective hamiltonians for 1/N expansion in two-dimensional QCD

TL;DR

This paper develops effective Hamiltonians for systematic 1/N expansion in two-dimensional QCD using light-cone quantization, providing explicit expressions and analyzing corrections to meson properties.

Contribution

It introduces a formalism for effective Hamiltonians in 2D QCD with explicit vertex functions and demonstrates the validity of 1/N as a small expansion parameter.

Findings

1/N corrections to meson mass are small.

Explicit vertex functions derived from 't Hooft equation.

Formalism applicable to meson decay form factors.

Abstract

We discuss the general structure of effective hamiltonians for systematic 1/N expansion in QCD using the light-cone quantization. These are second-quantized hamiltonians acting on the Fock space of mesons and glueballs defined by the solution of the $N=\infty$ problem. In the two-dimensional case we find only cubic and quartic interaction terms, and give explicit expressions for the vertex functions as integrals of solutions of 't Hooft equation. As examples of possible applications of our formalism, we study 1/N corrections to meson mass and form factors for decays of $Q\bar{q}$ states, recently discussed by Grinstein and Mende in the large-N limit. We find that 1/N is a good small expansion parameter.