Quantum Groups as Flavor Symmetries: Account of Nonpolynomial SU(3)-Breaking Effects in Baryon Masses

The use, for flavor symmetries, of the quantum (or q-) analogs of unitary groups SU(n_f) yields new, very accurate, baryon mass sum rules. We show, in the 3-flavor case, that such approach accounts for nonpolynomial SU(3)-breaking effects in the octet and decuplet baryon masses. A version of this approach with manifestly q-covariant mass operator is given. The obtained new version of the q-deformed mass relation is simpler than those derived before, but, for its empirical validity, the parameter q is to be fixed by fitting. As shown, the well-known Gell-Mann--Okubo octet mass sum rule results, besides usual SU(3), also from an exotic "symmetry" encoded in the singular case q=-1 of the q-algebra U_q(su_3).