Solving bound-state equations in $\text{QCD}_2$ with bosonic and fermionic quarks

TL;DR

This paper derives and numerically solves bound-state equations for exotic hadrons in two-dimensional QCD, revealing how their wave functions evolve under boosting and connecting different quantization frameworks.

Contribution

It introduces the first BSEs for a baryon in the extended 't Hooft model in FMF and confirms known results for tetraquarks using diagrammatic methods.

Findings

Numerical solutions yield mass spectra for tetraquark and baryon states.

Wave functions approach light-cone form when boosted, backward components diminish.

BSEs are derived in both light-front and equal-time quantizations, confirming consistency.

Abstract

We investigate the bound-state equations (BSEs) in two-dimensional QCD in the $N_c\to \infty$ limit, viewed from both the infinite momentum frame (IMF) and the finite momentum frame (FMF). The BSE of a meson in the original 't Hooft model, viz., spinor $\text{QCD}_2$ containing only fermionc quarks, has been extensively studied in literature. In this work, we focus on the BSEs pertaining to two types of "exotic" hadrons, a "tetraquark" which is composed of a bosonic quark and bosonic antiquark, and a "baryon" which is composed of a bosonic antiquark and a fermionic quark. Utilizing the Hamiltonian approach, we derive the corresponding BSEs for both types of "exotic" hadrons, from the perspectives of the light-front and equal-time quantization, and confirm the known results. The recently available BSEs for "tetraquark" in FMF has also been recovered with the aid of the diagrammatic approach. For the first time we also present the BSEs of a "baryon" in FMF in the extended 't Hooft model. By solving various BSEs numerically, we obtain the mass spectra pertaining to "tetraquark" and "baryon" and the corresponding bound-state wave functions of the lowest-lying states. It is numerically demonstrated that, when a "tetraquark" or "baryon" is continuously boosted, the forward-moving component of the bound-state wave function approaches the corresponding light-cone wave function, while the backward-moving component fades away.