Semileptonic decays of heavy $\Omega$ baryons in a quark model

The semileptonic decays of ${\Omega }_c$ and ${\Omega }_b$ 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 ${\Omega }_b$ to ${\Omega }_c$ 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 ${\Lambda }_c^{+}\to \Lambda e^{+}\nu$ rate, with wave functions expanded in both harmonic oscillator and Sturmian bases. Decay rates of ${\Omega }_b$ to pairs of ground and excited ${\Omega }_c$ 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 ${\Omega }_Q$ vary minimally within the models we use. We obtain an average value of ($84\pm 2$%) for the fraction of ${\Omega }_c\to {\Xi }^{(*)}$ decays to ground states and 91% for the fraction of ${\Omega }_c\to {\Omega }^{(*)}$ decays to the ground state Ω. The elastic fraction of ${\Omega }_b\to {\Omega }_c$ ranges from about 50% calculated with the two harmonic-oscillator models to about 67% calculated with the two Sturmian models.

Figure 1

Form factors for ${\Omega }_b\to {\Omega }_c(1/2^{+})$ obtained using harmonic oscillator wave functions (left panel: HOSR and HONR models) and Sturmian wave functions (right panel: STSR and STSR models). In each panel, the solid curves arise from the semirelativistic version of the model, while the dashed curves arise from the nonrelativistic version.

Figure 2

The differential decay rates for selected ${\Omega }_b\to {\Omega }_c^{(*)}$ transitions, in the various models that we use. The panels on the left arise from the two versions of the harmonic oscillator model, while those on the right are from the Sturmian models. The upper panels are for ${\Omega }_b\to {\Omega }_c^{(*)}\ell {\overline{\nu }}_{\ell }$, where $\ell$ is $e^{-}$ or ${\mu }^{-}$. The lower panels are for ${\Omega }_b\to {\Omega }_c^{(*)}\tau {\overline{\nu }}_{\tau }$. The curves are for final states with $J^P=3/2^{+}$, $1/2^{+}$, $3/2^{-}$, and $5/2^{-}$. In each panel, the solid curves arise from the semirelativistic version of the model, while the dashed curves arise from the nonrelativistic version.

Figure 3

The differential decay rates for selected ${\Omega }_c\to {\Xi }^{(*)}$ transitions, in the various models that we use. The panel on the left arises from the harmonic oscillator models, while the one on the right arises from the Sturmian models. They key to the curves is as in Fig. 2.