$\alpha_s$ from $\tau$ decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion

TL;DR

This paper introduces a new QCD perturbation expansion using conformal mapping to improve the determination of alpha_s from tau decays, reducing discrepancies between contour-improved and fixed-order methods.

Contribution

It develops a novel perturbation expansion incorporating Borel plane analytic continuation, enhancing the accuracy of alpha_s extraction from tau decay data.

Findings

New expansion functions improve convergence with increasing perturbative order.

Discrepancy between CI and FO methods is significantly reduced.

Predicted alpha_s(m_tau^2) aligns with standard FOPT results with better theoretical justification.

Abstract

We consider the determination of $\alpha_s$ from $\tau$ hadronic decays, by investigating the contour-improved (CI) and the fixed-order (FO) renormalization group summations in the frame of a new perturbation expansion of QCD, which incorporates in a systematic way the available information about the divergent character of the series. The new expansion functions, which replace the powers of the coupling, are defined by the analytic continuation in the Borel complex plane, achieved through an optimal conformal mapping. Using a physical model recently discussed by Beneke and Jamin, we show that the new CIPT approaches the true results with great precision when the perturbative order is increased, while the new FOPT gives a less accurate description in the regions where the imaginary logarithms present in the expansion of the running coupling are large. With the new expansions, the discrepancy of 0.024 in $\alpha_s(m_\tau^2)$ between the standard CI and FO summations is reduced to only 0.009. From the new CIPT we predict $\alpha_s(m_\tau^2)= 0.320 ^{+0.011}_{-0.009}$, which practically coincides with the result of the standard FOPT, but has a more solid theoretical basis.