Abstract
In a previous article, we have shown that the discrepancy between the fixed-order (FOPT) and contour-improved (CIPT) perturbative expansions for τ hadronic spectral function moments, which had affected the precision of αs 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 Ng of the GC renormalon. In the present work, we use three different methods to determine Ng, 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 αs(\( {m}_{\tau}^2 \)) based on CIPT and FOPT. The uncertainties due to variations of R and the uncertainty of Ng only lead to a small or moderate increase of the final uncertainty of αs(\( {m}_{\tau}^2 \)), 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 τ hadronic spectral function moments.
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Benitez-Rathgeb, M.A., Boito, D., Hoang, A.H. et al. Reconciling the contour-improved and fixed-order approaches for τ hadronic spectral moments. Part II. Renormalon norm and application in αs determinations. J. High Energ. Phys. 2022, 223 (2022). https://doi.org/10.1007/JHEP09(2022)223
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DOI: https://doi.org/10.1007/JHEP09(2022)223