The semileptonic decays of ${\Lambda }_c$ and ${\Lambda }_b$ are treated in the framework of a constituent quark model. Both nonrelativistic and semirelativistic Hamiltonians are used to obtain the baryon wave functions from a fit to the spectra, and the wave functions are expanded in both the harmonic-oscillator and the Sturmian bases. The latter basis leads to form factors in which the kinematic dependence on $q^2$ is in the form of multipoles, and the resulting form factors fall faster as a function of $q^2$ in the available kinematic ranges. As a result, decay rates obtained in the two models with the Sturmian basis are significantly smaller than those obtained with the harmonic-oscillator basis. In the case of the ${\Lambda }_c$, decay rates calculated with the Sturmian basis are closer to the experimentally reported rates. However, we find a semileptonic branching fraction for the ${\Lambda }_c$ to decay to excited ${\Lambda }^{*}$ states of 11 to 19%, in contradiction to what is assumed in available experimental analyses. Our prediction for the ${\Lambda }_b$ semileptonic decays is that decays to the ground state ${\Lambda }_c$ provide a little less than 70% of the total semileptonic decay rate. For the decays ${\Lambda }_b\to {\Lambda }_c$, the analytic form factors we obtain satisfy the relations expected from heavy-quark effective theory at the nonrecoil point, at leading and next-to-leading orders in the heavy-quark expansion. In addition, some features of the heavy-quark limit are shown to naturally persist as the mass of the heavy quark in the daughter baryon is decreased.

• Received 10 March 2005

DOI:https://doi.org/10.1103/PhysRevC.72.035201