Reducing the Theoretical Uncertainty in Extracting |V_{ub}| from the Inclusive Semileptonic b to u Decay Rate

Abstract

Utilizing asymptotic Pade-approximant methods, we estimate the three-loop order MS-bar coefficients of alpha_s^3[\log(\mu^2/m^2_b(\mu)]^k terms [k = {0,1,2,3}] within the $b\to u{\ell }^{-}{\bar{\nu }}_{\ell }$ decay rate. Except for the coefficient of the k = 0 term, all other coefficients may also be obtained via renormalization-group (RG) methods. The relative errors in asymptotic Pade-approximant estimates of the k = {1,2,3} terms are found to be 5.1% or less, thereby providing an estimate of the theoretical uncertainty in the asymptotic Pade-approximant estimate of the RG-inaccessible k = 0 term. By a judicious choice in the renormalization scale parameter, we are able to extract |V_{ub}| from the inclusive decay rate to within 7% theoretical uncertainty.

Comments: LaTeX, 9 pages, Proceedings article for MRST 2000, University of Rochester