Quantum Chromodynamics(QCD)is a fundamental theory that describes the strong interaction between quarks and gluons.As the non-perturbative properties of QCD in four-dimensional spacetime pose many challenging problems,some lower-dimensional solvable models can provide us theoretical assistance in further understanding micro-scopic particle structures.In this paper,we study the bound-state equations of QCD in two-dimensional spacetime with the number of colors N_C approaching infinity.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 Hamiltonian operator approach,we derive the corre-sponding bound-state equations for both types of hadrons from the perspectives of the light-front quantization and equal-time quantization,and confirm the known results.We also investigate other non-perturbative properties of the exotic”mesons”and”baryons”in two-dimensional QCD,such as the parton distribution function(PDF)and the quasi-parton distribution function(quasi-PDF).In addition,we develop two renormalization schemes to deal with the ultraviolet divergences arising from the self-energy correction of the bosonic quark.Furthermore,we numerically solve the bound-state equations,the parton distribution function,and the quasi-parton distribution function to obtain the lowest energy spectra of the hadrons,the bound-state wave functions,and the parton distribution functions and quasi-parton distribution functions.The numerical results verify an important inference of the large momentum effective theory:as the quasi-parton distribution function of the hadron is pushed to the infinite momentum frame,its shape gradually approaches the corresponding light-cone parton distribution function.Our study provides a comprehensive analysis of the bound-state properties and non-perturbative properties of the exotic”mesons”and”baryons”in two-dimensional QCD,which contributes to a deeper understanding of the strong interaction between quarks and gluons. |