A mass formula for baryon resonances

TL;DR

This paper proposes a new mass formula for light-baryon resonances based on their intrinsic angular momenta, successfully explaining observed mass patterns and degeneracies within the non-relativistic quark model.

Contribution

It introduces a novel baryon mass formula that accounts for mass degeneracies and regular spacings, aligning well with experimental data.

Findings

Resonances with even and odd parity lie on the same Regge trajectory.

Mass shifts depend on the antisymmetric component of the wave function.

Sequential resonances are evenly spaced in squared mass.

Abstract

Light-baryon resonances with u,d, and s quarks only can be classified using the non-relativistic quark model. When we assign to baryon resonances with total angular momenta J intrinsic orbital angular momenta L and spin S we make the following observations: plotting the squared masses of the light-baryon resonances against these intrinsic orbital angular momenta L, Delta's with even and odd parity can be described by the same Regge trajectory. For a given L, nucleon resonances with spin S=3/2 are approximately degenerate in mass with Delta resonances of same total orbital momentum L. To which total angular momentum L and S couple has no significant impact on the baryon mass. Nucleons with spin 1/2 are shifted in mass; the shift is - in units of squared masses - proportional to the component in the wave function which is antisymmetric in spin and flavor. Sequential resonances in the same partial wave are separated in mass square by the same spacing as observed in orbital angular momentum excitations. Based on these observations, a new baryon mass formula is proposed which reproduces nearly all known baryon masses.