Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments II: Renormalon Norm and Application in ${\alpha }_s$ Determinations

Abstract

In a previous article, we have shown that the discrepancy between the fixed-order (FOPT) and contour-improved (CIPT) perturbative expansions for $\tau$ hadronic spectral function moments, which had affected the precision of ${\alpha }_s$ determinations for many years, may be reconciled by employing a renormalon-free (RF) scheme for the gluon condensate (GC) matrix element. In addition, the perturbative convergence of spectral function moments with a sizeable GC correction can be improved. The RF GC scheme depends on an IR factorization scale $R$ and the normalization $N_g$ of the GC renormalon. In the present work, we use three different methods to determine $N_g$, yielding a result with an uncertainty of $40\%$. Following two recent state-of-the-art strong coupling determination analyses at $\mathcal{O}({\alpha }_s^5)$, we show that using the renormalon-free GC scheme successfully reconciles the results for ${\alpha }_s(m_{\tau }^2)$ based on CIPT and FOPT. The uncertainties due to variations of $R$ and the uncertainty of $N_g$ only lead to a small or moderate increase of the final uncertainty of ${\alpha }_s(m_{\tau }^2)$, and affect mainly the CIPT expansion method. The FOPT and CIPT results obtained in the RF GC scheme may be consistently averaged. The RF GC scheme thus constitutes a powerful new ingredient for future analyses of $\tau$ hadronic spectral function moments.

43 pages, 5 figures; presentation in section 3.2 improved, results unchanged; version published in the Journal of High Energy Physics

References in corpus (13)

• alpha_s and the tau hadronic width: fixed-order, contour-improved and higher-order perturbation theory
• The Determination of alpha_s from Tau Decays Revisited
• The strong coupling from the revised ALEPH data for hadronic $\tau$ decays
• Unraveling duality violations in hadronic tau decays
• ${\alpha }_s$ from $\tau$ decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion
• What is the Top Quark Mass?
• The strong coupling from an improved $\tau$ vector isovector spectral function
• The strong coupling from hadronic $\tau$ decays: a critical appraisal
• Higher-order perturbative coefficients in QCD from series acceleration by conformal mappings
• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments II: Renormalon Norm and Application in ${\alpha }_s$ Determinations
• Renormalon Subtraction from the Average Plaquette and the Gluon Condensate
• Higher-order behaviour of two-point current correlators
• Using improved Operator Product Expansion in Borel-Laplace Sum Rules with ALEPH $\tau$ decay data, and determination of pQCD coupling

Cited by in corpus (1)

• Reconciling the Contour-Improved and Fixed-Order Approaches for $\tau$ Hadronic Spectral Moments II: Renormalon Norm and Application in ${\alpha }_s$ Determinations