Pade-Improved Estimate of Perturbative Contributions to Inclusive Semileptonic $b\to u$ Decays

Pade-approximant methods are used to estimate the three-loop perturbative contributions to the inclusive semileptonic $b \to u$ decay rate. These improved estimates of the decay rate reduce the theoretical uncertainty in the extraction of the CKM matrix element $|V_{ub}|$ from the measured inclusive semileptonic branching ratio.