Two-dimensional SU(N) Gauge Theory on the Light Cone

TL;DR

This paper analyzes two-dimensional SU(N) gauge theory using light-front methods, deriving analytical and numerical results for hadronic masses, and exploring their dependence on N and quark mass with implications for relativistic bound states.

Contribution

It provides a combined analytical and numerical study of 2D SU(N) gauge theory on the light cone, deriving explicit formulas for hadronic masses and their N and mass dependence, including relativistic effects.

Findings

Lightest mesonic and baryonic states are nearly valence.

Second lightest meson has a large 4-body component.

Analytical mass formulas match numerical results.

Abstract

Two-dimensional SU($N$) gauge theory is accurately analyzed with the light-front Tamm-Dancoff approximation, both numerically and analytically. The light-front Einstein-Schr\"odinger equation for mesonic mass reduces to the 't Hooft equation in the large $N$ limit, $g^2N$ fixed, where $g$ is the coupling constant. Hadronic masses are numerically obtained in the region of $m^2 \ll g^2N$, where $m$ is the bare quark (q) mass. The lightest mesonic and baryonic states are almost in valence. The second lightest mesonic state is highly relativistic in the sense that it has a large 4-body ($ {\rm qq} \bar{\rm q} \bar{\rm q} $) component in addition to the valence (${\rm q} \bar{\rm q}$) one. In the strong coupling limit our results are consistent with the prediction of the bosonization for ratios of the lightest and second lightest mesonic masses to the lightest baryonic one. Analytic solutions to the lightest hadronic masses are obtained, with a reasonable approximation, as $\sqrt{2Cm}(1-1/N^2)^{1/4}$ in the mesonic case and $\sqrt{CmN(N-1)}(1-1/N^2)^{1/4}$ in the baryonic case, where $C=(g^2N\pi/6)^{1/2}$. The solutions well reproduce the numerical ones. The $N$- and $m$-dependences of the hadronic masses are explicitly shown by the analytical solutions.