Level order of quark systems: The puzzle of the Roper resonance, and related questions

TL;DR

This paper reviews the ordering of radial and orbital excitations in quark systems, highlighting the failure of current models to explain the Roper resonance's position and exploring related spectral issues.

Contribution

It demonstrates the inadequacy of existing quark models in explaining the Roper resonance and investigates spectral dependencies and bound states in simplified models.

Findings

Current quark models cannot explain the Roper resonance's low energy.

The energy levels depend on quark masses in specific ways.

Bound states are possible in simple chromoelectric models.

Abstract

The problem of ordering of radial vs.\ orbital excitations is reviewed. It is shown that the current quark models cannot explain the location of the Roper resonance which is slightly lower than the lowest negative-parity excitations. We also study some related spectral problems, such as the dependence of the energies on the quark masses, and the possibility of bound states in simple chromelectric models.