Two-dimensional SU(N) gauge theory is accurately analyzed with the light-front Tamm-Dancoff approximation, both numerically and analytically. The light-front Einstein-Schrödinger equation for the mesonic mass is reduced to the 't Hooft equation in the large N limit with g2N fixed, where g is the coupling constant. Two mesonic and one baryonic bound states are obtained numerically in the region of g2Nm2 for small N, where m is the bare quark (q) mass. The lightest meson and the baryon consist predominantly of valence quarks. The second mesonic state is highly relativistic in the sense that it has a large four-body (qqq̄ q̄) component in addition to the valence (qq̄) one. Our results are consistent with results of the lattice calculation for SU(2) and also with the prediction of bosonization for ratios of the two mesonic masses to the baryonic one in the strong coupling limit. Analytic solutions to the lightest hadronic masses are obtained, with a reasonable approximation, as 2Cm (1-1/N2)1/4 for the meson and CmN(N-1) (1-1/N2)1/4 for the baryon, where C=(g2Nπ/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.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy (miscellaneous)