Generalized isospin, generalized mass groups, and generalized Gell-Mann--Okubo formalism

TL;DR

This paper extends the concepts of isospin, mass groups, and the Gell-Mann--Okubo formalism to baryons with any quark flavor, enabling better classification and mass predictions across a wide range of baryon multiplets.

Contribution

It introduces a generalized framework for isospin and GMO formalism applicable to baryons with arbitrary quark flavors, enhancing classification and predictive capabilities.

Findings

Provides new quantum numbers to distinguish baryon types.

Quantifies flavor symmetry quality in baryon multiplets.

Predicts baryon masses with ~50 MeV accuracy across various mass scales.

Abstract

The current concepts of isospin and baryon mass groups are only well-adapted to deal with baryon multiplets involving both the u and d quarks, and some other quark k. In this paper, we generalize isospin and mass groups to accommodate baryon multiplets involving quarks of any flavor, and the Gell-Mann--Okubo (GMO) formalism is generalized accordingly. Generalized isospin proves to be a simple and valuable framework when working in non-udk baryon multiplets, and provides new quantum numbers that allows us to distinguish $\Lambda$-like baryons from $\Sigma$-like baryons in the non-udk multiplets. The generalized GMO formalism allows us to quantify the quality of flavor symmetries seen in baryon multiplets, and also allows us to predict the masses of all observable $J^P = \frac{1}{2}^+$ and $\frac{3}{2}^+$ baryons with an estimated accuracy on the order of 50 MeV in the worst cases, on mass scales that span anywhere from 1000 MeV to 15000 MeV.