Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-02-16
Phys.Rev. D50 (1994) 5274-5288
Physics
High Energy Physics
High Energy Physics - Theory
34 pages, plain TeX, figures not included, available via conventional mail
Scientific paper
10.1103/PhysRevD.50.5274
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.
Matsuzaki Masayuki
Sugihara Takanori
Yahiro Masanobu
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