Semileptonic decays of heavy Ω baryons in a quark model

The semileptonic decays of Ω_c and Ω_b are treated in the framework of a constituent quark model developed in a previous article on the semileptonic decays of heavy Λ baryons. Analytic results for the form factors for the decays to ground states and a number of excited states are evaluated. For Ω_b to Ω_c the form factors obtained are shown to satisfy the relations predicted at leading order in the heavy-quark effective theory at the nonrecoil point. A modified fit of nonrelativistic and semirelativistic Hamiltonians generates configuration-mixed baryon wave functions from the known masses and the measured Λ_c⁺→Λe⁺ν rate, with wave functions expanded in both harmonic oscillator and Sturmian bases. Decay rates of Ω_b to pairs of ground and excited Ω_c states related by heavy-quark symmetry calculated using these configuration-mixed wave functions are in the ratios expected from heavy-quark effective theory to a good approximation. Our predictions for the semileptonic elastic branching fraction of Ω_Q vary minimally within the models we use. We obtain an average value of (84±2%) for the fraction of Ω_c→Ξ^(*) decays to ground states and 91% for the fraction of Ω_c→Ω^(*) decays to the ground state Ω. The elastic fraction of Ω_b→Ω_c ranges from about 50% calculated with the two harmonic-oscillator models to about 67% calculated with the two Sturmian models.