Charge specific baryon mass relations with deformed SU_q(3) flavor symmetry

Abstract

The quantum group $SU_q(3)=U_q(su(3))$ is taken as a baryon flavor symmetry. Accounting for electromagnetic contributions to baryons masses to zeroth order, new charge specific $q$-deformed octet and decuplet baryon mass formulas are obtained. These new mass relations have errors of only 0.02\% and 0.08\% respectively; a factor of 20 reduction compared to the standard Gell-Mann-Okubo mass formulas. A new relation between the octet and decuplet baryon masses that is accurate to 1.2\% is derived. An explicit formula for the Cabibbo angle, taken to be $\frac{\pi}{14}$, in terms of the deformation parameter $q$ and spin parity $J^P$ of the baryons is obtained.