The Determination of $\alpha_s$ from Tau Decays Revisited

We revisit the determination of alpha_s(m_tau) using a fit to inclusive tau 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 tau 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 and show that the effect of the incomplete knowledge of the series is reduced by using the so-called contour-improved calculation, as opposed to fixed-order perturbation theory which manifests convergence problems. The corresponding theoretical uncertainties are studied at the tau and Z mass scales. 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 gives alpha_s(m_tau) = 0.344 +- 0.005 +- 0.007, where the first error is experimental and the second theoretical. After evolution to M_Z we obtai n alpha_s(M_Z) = 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 NNNLO value derived from essentially the Z width in the global electroweak fit. The alpha_s(M_Z) determination from tau decays is the most precise one to date.