Meson 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 (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 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.

Hadronic structure on the light-front IV: Heavy and light Baryons

“…There are no sudden changes, as one go from heavy to light quarks. Quark masses enter the H LF in a very uniform way and (as we have shown in the previous papers of the series [1][2][3]), one can consistently derive the mesonic properties from bb to light qq by the same tools. Indeed, in the first approximation, the transverse oscillator Hamiltonian generates near-linear Regge dependences of M 2 , on the principal quantum number n and angular momentum m. Dynamical issues also get less severe.…”

“…↑↑↑ and the global quantum number to be 3 2 + . We will focus to the sector with zero orbital momentum, thereby avoiding the inclusion of spin-orbit mixing (on which we focused in the previous paper [3]).…”

“…Since this is the fourth paper of the series [1][2][3], it does not need an extensive introduction. Let us just state that its main goal is to bridge the gaps between subfields of hadronic physics, with our general direction being from (I) the vacuum structure in its Euclidean formulation (instantons and lattice), to (ii) the hadronic structure and quark-quark interactions and resulting spectroscopy, to (iii) the hadronic structure on the light front with its novel Hamiltonians and wave functions.…”

Longitudinal dynamics for mesons on the light cone

“…x + r 2 y + r z ) is still not rotationally invariant. Shuryak and Zahed proposed an alternative confining interaction that generalizes the 't Hooft model to 3+1D while combining the light-front holographic interaction [22,23].…”

“…are considered. Recently, attention has focused on the role of longitudinal dynamics [14][15][16][17][18][19][20][21][22][23][24]. The longitudinal dynamics is important for incorporating finite quark masses, chiral dynamics and longitudinal excitations as well as for identifying the physical states in the excitation spectrum [25].…”