Ratios of heavy hadron semileptonic decay rates

Ratios of charmed meson and baryon semileptonic decay rates appear to be satisfactorily described by considering only the lowest-lying (S-wave) hadronic final states and assuming the kinematic factor describing phase space suppression is the same as that for free quarks. For example, the rate for $D_s$ semileptonic decay is known to be $(17.0 \pm 5.3)%$ lower than those for $D^0$ or $D^+$, and the model accounts for this difference. When applied to hadrons containing $b$ quarks, this method implies that the $B_s$ semileptonic decay rate is about 1% higher than that of the nonstrange $B$ mesons. This small difference thus suggests surprisingly good local quark-hadron duality for $B$ semileptonic decays, complementing the expectation based on inclusive quark-hadron duality that these differences in rates should not exceed a few tenths of a percent. For $\Lambda_b$ semileptonic decay, however, the inclusive rate is predicted to be about 13% greater than that of the nonstrange $B$ mesons. This value, representing a considerable departure from a calculation using a heavy quark expansion, is close to the corresponding experimental ratio $\Gamma(\Lambda_b)/ \bar \Gamma(B) = 1.13 \pm 0.03$ of total decay rates.