We develop a perturbative QCD factorization theorem for the semileptonic heavy baryon decay Lambda b -->Lambda(c)l<(nu)over bar>, whose form factors are expressed as the convolutions of hard b quark decay amplitudes with universal Lambda(b) and Lambda(c) baryon wave functions. Large logarithmic corrections are organized to all orders by Sudakov resummation, which renders perturbative expansions more reliable. It is observed that perturbative QCD is applicable to Lambda(b)-->Lambda(c), decays for velocity transfer greater than 1.2. Under the requirement of heavy quark symmetry, we predict the branching ratio B(Lambda(b)-->Lambda(c)(.)l<(nu)over bar>)similar to 2%, and determine the Lambda(b) and Lambda(c) baryon wave functions.
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