Exclusive/inclusive ratio of semileptonicΛbdecays

We present theoretical evidence that the exclusive/inclusive ratio of semileptonic ${\Lambda }_b$ decays exceeds that of semileptonic B decays where the experimental exclusive/inclusive ratio amounts to about 66%. We start from the observation that the spectator quark model provides a lower bound on the leading order Isgur-Wise function of the ${\Lambda }_b\to {\Lambda }_c$ transition in terms of the corresponding $\overrightarrow{B}{D,D}^{*}$ mesonic Isgur-Wise function. Using experimental data for the $\overrightarrow{B}{D,D}^{*}$ mesonic Isgur-Wise functions this bound is established. Applying a Bethe-Salpeter model including spectator quark interactions and a QCD sum rule estimate of the ${\Lambda }_b\to {\Lambda }_c$ transition form factor which satisfy the spectator quark model bound we predict the exclusive/inclusive ratio of semileptonic ${\Lambda }_b$ decay rates to lie in a range between 0.81 and 0.92. We also provide an upper bound on the baryonic Isgur-Wise function which is determined from the requirement that the exclusive rate should not exceed the inclusive rate.