The Gell-Mann-Okubo and Colemann-Glashow relations for octet and decuplet baryons in the $S{U}_q(3)$ quantum algebra

Abstract

The q-deformed Clebsch-Gordan coefficients corresponding to the $\text{lrpy}3\times \text{lrpy}21$ reduction of the $S{U}_q(3)$ quantum algebra are computed. From these results and using the quantum Clebsch-Gordan coefficients for the $\text{lrpy}21\times \text{lrpy}21$ reduction found by Zhong Qi Ma, the q-deformed Gell-Mann-Okubo mass relations for octet and decuplet baryons are determined by generalizing the procedure used for the SU(3) algebra. We also determine the Coleman-Glashow relations for octet and decuplet baryons in the $S{U}_q(3)$ algebra. Finally, by using the experimental particle masses of the octet and decuplet baryons, two values of the $q$-parameter are found and adjusted for the predicted masses expressions (one for the Gell-Mann-Okubo mass relations and the other for the Coleman-Glashow relations) and a possible physical interpretation is given.

Comments: 19 pages, 4 figures. Corrected typos