Gell-Mann-Okubo formula

A perturbative formula for the mass spectrum of strongly interacting particles, baryons and mesons. In 1961, M. Gell-Mann and Y. Ne'eman classified baryons and mesons and grouped them into multiplets, labeled by irreducible representations of the Lie algebra , with each particle in a multiplet being represented by a normalized weight vector (the number of particles in the multiplet equals the dimension of the representation) and with weights giving values of observable quantities: the isotopic spin and the hypercharge [a1]. To explain the variation of masses of particles belonging to the same multiplet, a mass formula was suggested by Gell-Mann and S. Okubo [a2]: , where is the normalized weight vector representing a particle and

Here, , and are empirical constants related to a given multiplet, and are the representatives of the two elements from the universal enveloping algebra of that are expressed in terms of the Gell-Mann matrices as and , respectively.

References

[a1]	M. Gell-Mann, Y. Ne'eman, "The eightfold way" , Benjamin (1964)
[a2]	S. Okubo, "Note on unitary symmetry in strong interactions" Progress Theor. Phys. , 27 (1962) pp. 949–969