An Approach towards a Constituent Quark Model on the Light Cone

TL;DR

This paper derives a light cone Hamiltonian for mesons using Wilson loops, revealing how confinement and chiral symmetry breaking influence meson properties, and solves the Schrödinger equation for different wave functions.

Contribution

It introduces a novel approach to modeling mesons on the light cone using Wilson loops and derives the Hamiltonian incorporating confinement and chiral symmetry breaking effects.

Findings

Confinement determines meson mass and wave function on the light cone.

The model reproduces the chiral symmetry breaking pattern for the pion.

Spin-dependent effects are parametrized for light mesons and charmonium.

Abstract

We use the vacuum expectation value of a Wegner-Wilson loop representing a fast moving quark-antiquark pair to derive the light cone Hamiltonian for a $q\bar q$ meson. We solve the corresponding Schr\"odinger equation for various trial wave functions. The result shows how confinement determines the meson mass and wave function for valence quarks on the light cone. We also parametrize the effect of the spin-dependent splitting for a light meson and charmonium. The correct chiral-symmetry breaking pattern for the pion mass is obtained due to the self-energy of the quark.