The determination of αS from τ decays revisited

We revisit the determination of α S ( m τ 2 ) using a fit to inclusive τ hadronic spectral moments in light of (1) the recent calculation of the fourth-order perturbative coefficient K 4 in the expansion of the Adler function, (2) new precision measurements from BABAR of e + e − annihilation cross sections, which decrease the uncertainty in the separation of vector and axial-vector spectral functions, and (3) improved results from BABAR and Belle on τ branching fractions involving kaons. We estimate that the fourth-order perturbative prediction reduces the theoretical uncertainty, introduced by the truncation of the series, by 20% with respect to earlier determinations. We discuss to some detail the perturbative prediction of two different methods: fixed-order perturbation theory (FOPT) and contour-improved perturbative theory (CIPT). The corresponding theoretical uncertainties are studied at the τ and Z mass scales. The CIPT method is found to be more stable with respect to the missing higher order contributions and to renormalization scale variations. It is also shown that FOPT suffers from convergence problems along the complex integration contour. Nonperturbative contributions extracted from the most inclusive fit are small, in agreement with earlier determinations. Systematic effects from quark-hadron duality violation are estimated with simple models and found to be within the quoted systematic errors. The fit based on CIPT gives α S ( m τ 2 )=0.344±0.005±0.007, where the first error is experimental and the second theoretical. After evolution to M Z we obtain α S ( M Z 2 )=0.1212±0.0005±0.0008±0.0005, where the errors are respectively experimental, theoretical and due to the evolution. The result is in agreement with the corresponding N 3 LO value derived from essentially the Z width in the global electroweak fit. The α S ( M Z 2 ) determination from τ decays is the most precise one to date.