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

TL;DR

This paper develops a quantum-mechanical approach to solve the three-quark Hamiltonian for baryons on the light front, providing exact solutions for masses and wave functions of specific symmetric baryons.

Contribution

It introduces an exact solution method for the three-quark light-front Hamiltonian using harmonic oscillator and triangular cup bases, advancing baryon structure modeling.

Findings

Calculated masses of symmetric baryons like $bbb$, $ccc$, $sss$, $uuu$.

Derived light front wave functions for these baryons.

Provided exact solutions in a novel basis framework.

Abstract

This work is a continuation in our series of papers, that addresses quark models of hadronic structure on the light front. The chief focus of this paper is the quantum-mechanical solution of the three-quark model Hamiltonian, describing baryons. In Jacobi coordinates, we use a harmonic oscillator basis for the transverse directions. For the longitudinal momentum fractions $x_i$, the pertinent basis follows from quantum mechanics in a "triangular cup" potential, which we solve exactly. We calculate the masses and light front wave functions for the flavor symmetric $\frac 32^+$ baryons $bbb,ccc,sss,uuu$.