A Transverse Lattice QCD Model for Mesons

TL;DR

This paper develops an analytical transverse lattice QCD model for mesons, extending the 't Hooft equation to include spin, and provides a framework for calculating meson properties relevant to QCD observables.

Contribution

It introduces a solvable transverse lattice QCD model that generalizes the 't Hooft equation by incorporating spin, enabling analytical and numerical analysis of meson spectra and wavefunctions.

Findings

Derived an integral equation for mesons including spin.

Provided numerical methods for spectrum and wavefunction calculation.

Suggested applications to QCD observables like deep inelastic scattering.

Abstract

QCD is analysed with two light-front continuum dimensions and two transverse lattice dimensions. In the limit of large number of colours and strong transverse gauge coupling, the contributions of light-front and transverse directions factorise in the dynamics, and the theory can be analytically solved in a closed form. An integral equation is obtained, describing the properties of mesons, which generalises the 't Hooft equation by including spin degrees of freedom. The meson spectrum, light-front wavefunctions and form factors can be obtained by solving this equation numerically. These results would be a good starting point to model QCD observables which only weakly depend on transverse directions, e.g. deep inelastic scattering structure functions.