Leading vector coupling in baryon semileptonic decays in large-$N_c$ chiral perturbation theory revisited: Extension to decuplet baryons

The leading vector coupling defined in the semileptonic decay of a baryon is revisited in the framework of large-$N_c$ baryon chiral perturbation. Aspects of $SU(3)$ flavor symmetry breaking are taken into account in two ways: Explicitly through perturbative symmetry breaking and implicitly through the integrals occurring in the one-loop corrections. The analysis of perturbative breaking is performed by using flavor projection operators which are exceptionally helpful in understanding previously unidentified issues. The approach is extended to theoretically evaluate the leading vector coupling in the transition ${\mathrm{\Omega }}^{-}\to {{\mathrm{\Xi }}^{\ast }}^0$. A fitting procedure to data reveals that second-order symmetry breaking corrections, while small, can have a significant impact on the evaluation of the baryon vector coupling, potentially increasing its overall strength due to the involved interplay of both explicit and implicit contributions.