Revisiting Hadronic Mass Relations from First Order Flavor Symmetry Breaking

TL;DR

This paper challenges the traditional distinction between linear and quadratic Gell-Mann–Okubo mass relations for baryons and mesons, showing both forms apply broadly and using them to classify and predict hadron masses.

Contribution

It demonstrates that both linear and quadratic GMO relations are applicable to baryons and mesons, supported by theoretical derivations and experimental data analysis.

Findings

Both GMO relations apply to baryons and mesons in most cases.

Mass relations help classify unassigned resonances.

Predictions for missing hadron masses are provided.

Abstract

The Gell-Mann$-$Okubo (GMO) mass relations following from $\text{SU}(3)$-flavor symmetry breaking in the strong sector have been proven to be of great success for describing hadron masses and classifying them into multiplets. Nowadays, it is widely believed that baryons being fermions have to obey GMO relations which are linear in the baryon masses, whilst mesons as bosons follow quadratic GMO relations. In this work, I challenge the distinction of GMO relations for baryons and mesons and conclude that both linear and quadratic GMO relations apply to both baryons and mesons in most instances (exceptions are the pseudoscalar meson octet and the mass relations following from heavy quark symmetry). I support this claim by presenting an in-depth analysis of the GMO relations on a theoretical and experimental level. On the theoretical side, two approaches to the derivation of the GMO relations are given and isospin symmetry breaking, electromagnetic contributions, and heavy quark symmetry are incorporated into the mass relations. Both linear and quadratic mass relations are checked against experimentally determined hadron masses. Furthermore, the mass relations are used to classify unassigned resonances like $\Lambda^+_c(2940)$ and $\Xi_c(3123)$ into multiplets and to predict the masses of missing particles in yet incomplete multiplets.