Reducing the theoretical uncertainty in extracting ∣V[sub ub]∣ from the inclusive B→X[sub u]l[sup −]ν̄[sub l] decay rate

Abstract

Utilizing asymptotic Padé-approximant methods, we estimate the three-loop order MS¯ coefficients of αs3[log(μ2/mb2(μ))]k terms [k={0,1,2,3}] within the b→ul−ν̄l 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 Padé-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 Padé-approximant estimate of the RG-inaccessible k=0 term. By a judicious choice in the renormalization scale parameter, we are able to extract |Vub| from the inclusive decay rate to within ±7% theoretical uncertainty.