The Determination of alpha_s from Tau Decays Revisited

TL;DR

This work refines the extraction of the strong coupling from hadronic tau decays by incorporating the recently computed four-loop coefficient $K_4$, improved BABAR $e^+e^-$ data for vector/axial-vector separation, and updated strange-decay measurements. It rigorously compares fixed-order and contour-improved perturbation theories, finding CIPT to be more stable and reliable, and confirms that nonperturbative effects are small within the experimental precision. A combined fit to the tau width and spectral moments yields $\alpha_S(m_\tau^2)=0.344(5)(7)$, which evolves to $\alpha_S(M_Z^2)=0.1212(5)(8)(5)$, providing one of the most precise tests of QCD running and achieving the most precise tau-based determination of $\alpha_S(M_Z^2)$. The results are consistent with NNLO electroweak fits and demonstrate that tau decays offer a highly competitive determination of the strong coupling with controlled theoretical uncertainties.

Abstract

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 obtain 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.

Figures (7)

• Figure 1: The mass-squared distribution for $\tau\to \nu_\tau\xspace K \overline{ K}{}\xspace \pi$ decay modes from ALEPH and the predictions for the vector component obtained by CVC using DM1, DM2 and BABAR $e^+e^-$ data.
• Figure 2: Vector ($V$), axial-vector ($A$), $V+A$ and $V-A$$\tau$ hadronic spectral functions measured by ALEPH, and updated using the new $V,A$ separation in the $K \overline{ K}{}\xspace\xspace \pi$ channels discussed in the text. The shaded areas indicate the main contributing exclusive $\tau$ decay channels. The curves show the predictions from the parton model (dotted) and from massless perturbative QCD using $\alpha_{ S}\xspace(M_Z\xspace^2)\xspace=0.120$ (solid).
• Figure 3: Real part of $\alpha_{ S}\xspace(s)$ computed along the $|s|=s_0$ contour for $\xi=1$, using respectively ${\rm FOPT}^{++}$ (solid line, see text), FOPT and ${\rm FOPT}^{+}$ (dashed, see text) and CIPT (dashed-dotted).
• Figure 4: Real part of $(4\pi^2 D(s) - 1)$ (left) and of the integrand in Eqs. (\ref{['eq:an']}) and (\ref{['eq:knan']}) (right), computed along the integration contour for $\xi=1$, using respectively ${\rm FOPT}^{++}$ (solid line), FOPT (dashed), CIPT (dashed-dotted) and ${\rm FOPT}^{+}$ (dotted, not shown on the right hand plot because it is almost indistinguishable from CIPT).
• Figure 5: Scale dependence of $\delta^{(0)}$ in $R_\tau$ computed at the third to the estimated sixth order with FOPT (left) and CIPT (right).