Hadronic structure on the light front. III. The Hamiltonian, heavy quarkonia, spin, and orbit mixing

Abstract

This is the third paper on hadronic light-front wave functions. 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 Schr\"odinger 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 Hooft interaction to the light front, which solves the U(1) problem and helps produce a light pion. We use the ensuing light front wave functions to derive the pertinent parton distribution functions, parton amplitudes, and low energy constants.