Solving the Bars-Green equation for moving mesons in two-dimensional QCD

Abstract

The two-dimensional QCD in the large $N$ limit, generally referred to as the 't Hooft model, is numerically investigated in the axial gauge in a comprehensive manner. The corresponding Bethe-Salpeter equation for a bound $q\bar{q}$ pair, originally derived by Bars and Green in 1978, was first numerically tackled by Li and collaborators in late 1980s, yet only for the {\it stationary} mesons. In this paper, we make further progress by numerically solving the Bars-Green equation for {\it moving} mesons, ranging from the chiral pion to charmonium. By choosing several different quark masses, we computed the corresponding quark condensates, meson spectra and their decay constants for a variety of meson momenta, and found satisfactory agreement with their counterparts obtained using light-cone gauge, thus numerically verified the gauge and Poincaré invariance of the 't Hooft model. Moreover, we have explicitly confirmed that, as the meson gets more and more boosted, the large component of the Bars-Green wave function indeed approaches the corresponding 't Hooft light-cone wave function, while the small component of the wave function rapidly fades away.

v2, 25 pages, 12 figures, and 1 table; Some figures updated, references added, typo corrrected; to appear in JHEP

References in corpus (10)

• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Parton Physics on Euclidean Lattice
• Explicit Quark-hadron Duality in Heavy-light Meson Weak Decays in the 't Hooft Model
• Two-dimensional QCD in the Coulomb gauge
• Trivial Vacua, High Orders in Perturbation Theory and Nontrivial Condensates
• Off-Forward Parton Distributions in 1+1 Dimensional QCD
• How Chiral Symmetry Breaking Affects the Spectrum of the Light-Heavy Mesons in the 't Hooft Model
• A Study of the 't Hooft Model with the Overlap Dirac Operator
• The Strongly Coupled 't Hooft Model on the Lattice
• Strongly coupled 't Hooft model on the lattice

Cited by in corpus (28)

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• First direct lattice-QCD calculation of the $x$-dependence of the pion parton distribution function
• Nucleon Tomography and Generalized Parton Distribution at Physical Pion Mass from Lattice QCD
• Pion and Kaon Distribution Amplitudes in the Continuum Limit
• Matching Quasi Generalized Parton Distributions in the RI/MOM scheme
• Complete Matching for Quasi-distribution Functions in Large Momentum Effective Theory
• Partonic quasidistributions in two-dimensional QCD
• Matching the Quasi Meson Distribution Amplitude in RI/MOM scheme
• Master Integrals for two-loop QCD corrections to Quasi PDFs
• One-Loop Hybrid Renormalization Matching Kernels for Quasi-Parton Distributions
• Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions
• Renormalon Effects in Quasi Parton Distributions
• Matching the B-meson quasidistribution amplitude in the RI/MOM scheme
• Chiral Perturbation for Large Momentum Effective Field Theory
• Quantum Entanglement and the Thermal Hadron
• 1+1D Hadrons Minimize their Biparton Renyi Free Energy
• Mapping Parton Distributions of Hadrons with Lattice QCD
• Quark-hadron duality for heavy meson mixings in the 't Hooft model
• Light-front dynamic analysis of the longitudinal charge density using the solvable scalar field model in (1+1) dimensions
• Revisiting quark-hadron duality for heavy meson non-leptonic decays in two-dimensional QCD
• Parton physics of the large-$N_c$ mesons
• Gauge-invariant decomposition of meson energy in two-dimensional QCD
• Effective mesonic theory for the 't Hooft model on the lattice
• The Continuum and Leading Twist Limits of Parton Distribution Functions in Lattice QCD
• One-loop Matching Factors for Singlet Quasi-Parton Distribution Functions in the Hybrid-Ratio Scheme
• 't Hooft model in the temporal gauge
• Interpolating 't Hooft model between instant and front forms
• Meson scattering and tetraquarks in two-dimensional QCD