Solving bound state equation for scalar and hybrid QCD in two-dimensional spacetime

Abstract

Abstract We investigate the bound-state equations in two-dimensional QCD in the $N_c\to \infty$ limit. We consider two types of hadrons, an exotic ``meson" (which is composed of a bosonic quark and a bosonic anti-quark), and an exotic ``baryon" (composed of a fermionic quark and a bosonic antiquark). Using the operator approach, we derive the corresponding bound-state equations for both types of hadrons from the perspectives of light-front quantization and equal-time quantization and confirm the known results. We also present a novel diagrammatic derivation for the exotic meson bound-state equation in the equal-time quantization.Our bound-state equation for the exotic baryons in the equal-time quantization is new. We also numerically solve various bound-state equations, obtain the hadron spectrum and the bound-state wave functions of the lowest-lying states. We explicitly demonstrate the pattern that as the hadron is boosted to infinite-momentum frame, the forward-moving bound-state wave function approach the light-front wave function. 
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