Reconciling the FOPT and CIPT Predictions for the Hadronic Tau Decay Rate

Benitez-Rathgeb, Miguel A.; Boito, Diogo; Hoang, André H.; Jamin, Matthias

doi:10.48550/arxiv.2111.09614

Cited by 5 publications

(7 citation statements)

References 35 publications

(66 reference statements)

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“…Some of the elements of our renormalon-free GC scheme have recently been briefly outlined in the large-β 0 approximation in ref. [36]. In the current paper we discuss the case of full QCD which is more involved, provide many more details and discuss numerous conceptual and practical aspects.…”

Section: Jhep07(2022)016mentioning

confidence: 99%

Reconciling the contour-improved and fixed-order approaches for τ hadronic spectral moments. Part I. Renormalon-free gluon condensate scheme

Benitez-Rathgeb

Boito

Hoang

et al. 2022

J. High Energ. Phys.

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We propose a simple and easy-to-implement scheme for a renormalon-free gluon condensate (GC) matrix element, which is analogous to implementations of short-distance heavy-quark mass renormalization schemes existing in the literature already for a long time. Because the scheme is based on a perturbative subtraction at the level of the matrix element, with a freely adaptable infrared factorization scale, it can be implemented with little effort for any observable where the GC is relevant. The scheme depends on the renormalon norm of the GC which has to be supplemented independently. We apply the scheme to the fixed-order (FOPT) and contour-improved (CIPT) perturbative expansions of τ hadronic spectral function moments. These expansions exhibit a long-standing discrepancy for moments used in high-precision determinations of the strong coupling in the commonly used GC scheme that is not renormalon-free. We show that the scheme is capable of resolving the FOPT-CIPT discrepancy problem. At the same time, the perturbative behaviour of the moments that previously showed bad convergence properties and for which the non-perturbative corrections from the GC are sizeable, is substantially improved. The new GC scheme may provide a powerful theoretical tool for future phenomenological applications.

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Section: Jhep07(2022)016mentioning

confidence: 99%

Reconciling the contour-improved and fixed-order approaches for τ hadronic spectral moments. Part I. Renormalon-free gluon condensate scheme

Benitez-Rathgeb

Boito

Hoang

et al. 2022

J. High Energ. Phys.

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“…Using the estimate of eq. (2.15), which corresponds to the MS coefficient c5,1 = 280 [58], the O(α ) . The uncertainties at order 5 come from varying c5,1 within the uncertainty estimate given in eq.…”

Section: Conformal Mapping Approachmentioning

confidence: 99%

Reconciling the contour-improved and fixed-order approaches for τ hadronic spectral moments. Part II. Renormalon norm and application in αs determinations

Benitez-Rathgeb

Boito

Hoang

et al. 2022

J. High Energ. Phys.

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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 $$ \mathcal{O} $$ O ($$ {\alpha}_s^5 $$ α s 5 ), we show that using the renormalon-free GC scheme successfully reconciles the results for αs($$ {m}_{\tau}^2 $$ m τ 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($$ {m}_{\tau}^2 $$ m τ 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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“…A construction of Borel transforms of CI sum rules was proposed and investigated in[52] (cf. also[53]).…”

mentioning

confidence: 98%

Using improved Operator Product Expansion in Borel-Laplace Sum Rules with ALEPH $τ$ decay data, and determination of pQCD coupling

Ayala,

Cvetic,

Teca

2021

Preprint

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We use improved truncated Operator Product Expansion (OPE) for the Adler function, involving two types of terms with dimension D = 6, in the double-pinched Borel-Laplace Sum Rules and Finite Energy Sum Rules for the V+A channel strangeless semihadronic τ decays. The generation of the higher order perturbative QCD terms of the D = 0 part of the Adler function is carried out using a renormalon-motivated ansatz incorporating the leading UV renormalon and the first two leading IR renormalons. The trunacted D = 0 part of the Sum Rules is evaluated by two variants of the fixed-order perturbation theory (FO), by Principal Value of the Borel resummation (PV), and by contour-improved perturbation theory (CI). For the experimental V+A channel spectral function we use the ALEPH τ -decay data. We point out that the truncated FO and PV evaluation methods account correctly for the renormalon structure of the Sum Rules, while this is not the case for the truncated CI evaluation. We extract the value of the MS coupling αs(m 2 τ ) = 0.3198 +0.0149 −0.0143[αs(M 2 Z ) = 0.1187 ± 0.0018] for the average of the two FO methods and the PV method, which we consider as our main result. If we included in the average also CI extraction, the value would be αs(m 2 τ ) = 0.3270 +0.0244 −0.0241 [αs(M 2 Z ) = 0.1195 ± 0.0030]. This work is an extension and improvement of our previous work [1] where we used for the truncated OPE a more naive (and widely used) form and where the extracted values for αs(M 2 Z ) were somewhat lower.

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Reconciling the FOPT and CIPT Predictions for the Hadronic Tau Decay Rate

Cited by 5 publications

References 35 publications

Reconciling the contour-improved and fixed-order approaches for τ hadronic spectral moments. Part I. Renormalon-free gluon condensate scheme

Reconciling the contour-improved and fixed-order approaches for τ hadronic spectral moments. Part I. Renormalon-free gluon condensate scheme

Reconciling the contour-improved and fixed-order approaches for τ hadronic spectral moments. Part II. Renormalon norm and application in αs determinations

Using improved Operator Product Expansion in Borel-Laplace Sum Rules with ALEPH $τ$ decay data, and determination of pQCD coupling

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