TY - JOUR

T1 - Two-dimensional SU(N) gauge theory on the light cone

AU - Sugihara, Takanori

AU - Matsuzaki, Masayuki

AU - Yahiro, Masanobu

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevD.50.5274

DO - 10.1103/PhysRevD.50.5274

M3 - Article

AN - SCOPUS:0008980740

VL - 50

SP - 5274

EP - 5288

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 8

ER -