Semileptonic Decays of Heavy Omega Baryons in a Quark Model

Abstract

The semileptonic decays of $Ω_c$ and $Ω_b$ are treated in the framework of a constituent quark model developed in a previous paper 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 non-recoil point. A modified fit of nonrelativistic and semirelativistic Hamiltonians generates configuration-mixed baryon wave functions from the known masses and the measured $\lcle$ rate, with wave functions expanded in both harmonic oscillator and Sturmian bases. Decay rates of $\ob$ to pairs of ground and excited $\omc$ 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$\pm$ 2%) for the fraction of $Ω_c\to Ξ^{(*)}$ decays to ground states, and 91% for the fraction of $Ω_c\to Ω^{(*)}$ decays to the ground state $Ω$. The elastic fraction of $\ob \to \omc$ ranges from about 50% calculated with the two harmonic-oscillator models, to about 67% calculated with the two Sturmian models.