Meson structure on the light-front III : The Hamiltonian, heavy quarkonia, spin and orbit mixing

TL;DR

This paper develops a light front Hamiltonian from first principles to study meson structure, including heavy quarkonia, spin effects, and chiral symmetry breaking, connecting wavefunctions to observable quantities.

Contribution

It introduces a first-principles derived light front Hamiltonian that models meson spectra, spin interactions, and chiral symmetry effects, extending the t'Hooft interaction to the light front.

Findings

Reproduces Regge trajectories with harmonic modes

Matches heavy quarkonia spectra with Schrödinger equation results

Provides wavefunctions for deriving parton distributions and constants

Abstract

This is the third paper on hadronic light front wave functions (LFWFs). We derive a light front Hamiltonian from first principles using the key features of the QCD vacuum at low resolution. In the first approximation, it gives transverse oscillator and longitudinal harmonic modes and yields the correct Regge trajectories. For heavy quarkonia, we compare its spectrum to that obtained from the usual Schroedinger equation in the rest frame. We use the same approach for light quarks, and investigate the role of confinement and chiral symmetry breaking in the quark-antiquark sector. We then study spin-spin and spin-orbit mixing, resulting in e.g. quadrupole moments of vector mesons. For the light mesons, we show how to extend the famed t$^\prime$Hooft interaction to the light front, which solves the U(1) problem and helps produce a light pion. We use the ensuing light front wavefunctions, to derive the pertinent parton distribution functions, parton amplitudes and low energy constants.