Mathematical aspects of the asymptotic expansion in contour improved perturbation theory for hadronic tau decays

Néstor G. Gracia; André H. Hoang; Vicent Mateu

doi:0.48550/arXiv.2305.10288

Mathematical aspects of the asymptotic expansion in contour improved perturbation theory for hadronic tau decays

Néstor G. Gracia
, André H. Hoang
, Vicent Mateu

Particle Physics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

In a previous work by one of the authors, it was demonstrated that the discrepancy between the fixed-order and contour-improved (CIPT) perturbative expansions for τ-lepton decay hadronic spectral function moments, which had been affecting the precision of αs determinations for many years, is related to the CIPT expansion being inconsistent with the standard formulation of the operator product expansion. Even though the problem can be alleviated phenomenologically for the most part by employing a renormalon-free scheme for the gluon-condensate matrix element, the principal inconsistency of CIPT remains. The CIPT expansion is special because it is not a power expansion, but represents an asymptotic expansion in a sequence of functions of the strong coupling. In this article we provide a closer look at the mathematical aspects of the asymptotic sequence of the functions the CIPT method is based on, and we expose the origin of the CIPT inconsistency as well as the reasons for its apparent good convergence at low orders. Our results are of general interest, and may in particular provide a useful tool to check for the consistency of expansion methods that are similar to CIPT.

Original language	English
Article number	034013
Number of pages	21
Journal	Physical Review D
Volume	108
Issue number	3
DOIs	https://doi.org/0.48550/arXiv.2305.10288 https://doi.org/10.1103/PhysRevD.108.034013
Publication status	Published - 1 Aug 2023

Funding

This work has been supported by the MECD Grant No. PID2019–105439GB-C22, the EU STRONG-2020 project under Program No. H2020-INFRAIA-2018-1, Grant Agreement No. 824093 and the COST Action No. CA16201 PARTICLEFACE. N. G. G. has been supported by a JCyL scholarship funded by the regional government of Castilla y León and European Social Fund, 2017 call, and thanks the Particle Physics Group at the University of Vienna for hospitality while parts of this work were completed. We thank M. Jamin and D. Boito for carefully reading the manuscript and for their useful comments.

Austrian Fields of Science 2012

103012 High energy physics

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10.1103/PhysRevD.108.034013Licence: CC BY 4.0

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title = "Mathematical aspects of the asymptotic expansion in contour improved perturbation theory for hadronic tau decays",

abstract = "In a previous work by one of the authors, it was demonstrated that the discrepancy between the fixed-order and contour-improved (CIPT) perturbative expansions for τ-lepton decay hadronic spectral function moments, which had been affecting the precision of αs determinations for many years, is related to the CIPT expansion being inconsistent with the standard formulation of the operator product expansion. Even though the problem can be alleviated phenomenologically for the most part by employing a renormalon-free scheme for the gluon-condensate matrix element, the principal inconsistency of CIPT remains. The CIPT expansion is special because it is not a power expansion, but represents an asymptotic expansion in a sequence of functions of the strong coupling. In this article we provide a closer look at the mathematical aspects of the asymptotic sequence of the functions the CIPT method is based on, and we expose the origin of the CIPT inconsistency as well as the reasons for its apparent good convergence at low orders. Our results are of general interest, and may in particular provide a useful tool to check for the consistency of expansion methods that are similar to CIPT.",

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N2 - In a previous work by one of the authors, it was demonstrated that the discrepancy between the fixed-order and contour-improved (CIPT) perturbative expansions for τ-lepton decay hadronic spectral function moments, which had been affecting the precision of αs determinations for many years, is related to the CIPT expansion being inconsistent with the standard formulation of the operator product expansion. Even though the problem can be alleviated phenomenologically for the most part by employing a renormalon-free scheme for the gluon-condensate matrix element, the principal inconsistency of CIPT remains. The CIPT expansion is special because it is not a power expansion, but represents an asymptotic expansion in a sequence of functions of the strong coupling. In this article we provide a closer look at the mathematical aspects of the asymptotic sequence of the functions the CIPT method is based on, and we expose the origin of the CIPT inconsistency as well as the reasons for its apparent good convergence at low orders. Our results are of general interest, and may in particular provide a useful tool to check for the consistency of expansion methods that are similar to CIPT.

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Mathematical aspects of the asymptotic expansion in contour improved perturbation theory for hadronic tau decays

Abstract

Funding

Austrian Fields of Science 2012

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