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

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 $Λ$-like baryons from $Σ$-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.

14 pages, 7 tables, 6 figures [29 subfigures]. Figure 1 and 4 have been redesigned. Added a new figure [Fig. 3]; The condition for Eq. (31b) to hold is now explicit [Eq. (32]; Eq. (46) now has the proper sign. Some arguments reworded and clarified; Some values in Tables I, II, and VI fixed; Typographical fixes. Results and conclusions are unchanged