Constituent Quark-model for BaryonsTh. Harmonic confinement and Two-body Meson-exchange Potentials

TL;DR

This paper develops a constituent quark model for baryons using harmonic confinement and meson-exchange potentials, deriving soft two-body interactions with gaussian wave-functions and applying them to baryon states and resonances.

Contribution

It introduces a parameter-free two- and three-body meson-exchange interaction model at the quark level based on ESC16 parameters, with applications to baryon spectra.

Findings

Successful description of SU(3) baryon-octet states

Two models for N-Δ splitting are proposed

Baryon sizes are approximately 1 fm

Abstract

Soft Two-body potentials between the constituent quarks of the nucleon are derived using harmonic oscillator, i.e. gaussian, quark wave-functions. The gaussian wave-functions are very suited for applications with the ESC soft-core interactions, which employ gaussian form factors. In these notes using the Fourier transformation to momentum space the local and non-local contributions of the potentials based on the ESC meson-quark-quark vertices are evaluated. Using the ESC16 parameters translated to the quark-level leads to parameter free two-body and three-body diquark and triquark meson-exchange interactions. Applications to the SU(3) baryon-octet states and the $\Delta_{33}$ resonance are performed., within the CQM using a harmonic confinement potential, leading to a satisfactory picture with relativistic constituent quarks. We present two versioins for the $N-\Delta$ splitting: (i) model A with the instanton interaction, and (ii) model B with a large color-magnetic interaction from an almost point like OGE. The size of the baryons $\approx$ 1 fm.