Bilocal expansion of the Borel amplitude and the hadronic tau decay width

Cvetič, Gorazd; Lee, Taekoon

doi:10.1103/physrevd.64.014030

Cited by 56 publications

(110 citation statements)

References 79 publications

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“…At this point, we will turn to the question of the RSch-dependence of the (truncated) perturbation series (62). The RSch independence of the series (40) implies specific transformation rules of the expansion coefficients d j under the change of β j 's (j ≥ 2) [29] …”

Section: Skeleton-motivated Expansionmentioning

confidence: 99%

“…In this Appendix, we present explicit formulas for the coefficients t (j) i appearing in the skeleton-motivated expansion (67), which is a slightly reorganized form of expansion (62). We consider the case when, in MS RSch (β k = b k = b kj β j 0 , k ≥ 2) and at RScl µ 2 = Q 2 , the first three coefficients in expansion (40) are explicitly known (d j , j = 1, 2, 3), and all the leading-β 0 parts c (1) nn β 0 n of coefficients d n (n ≥ 1) in expansion (42) are known (we note that c (1) n,−1 = 0 in MS).…”

Section: Appendix A: Relevant Coefficients Of the Skeleton-motivated mentioning

confidence: 99%

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Various versions of analytic QCD and skeleton-motivated evaluation of observables

Cvetič

Valenzuela

2006

Phys. Rev. D

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We present skeleton-motivated evaluation of QCD observables. The approach can be applied in analytic versions of QCD in certain classes of renormalization schemes. We present two versions of analytic QCD which can be regarded as low-energy modifications of the "minimal" analytic QCD and which reproduce the measured value of the semihadronic τ decay ratio rτ . Further, we describe an approach of calculating the higher order analytic couplings A k (k = 2, 3, . . .) on the basis of logarithmic derivatives of the analytic coupling A1(Q 2 ). This approach can be applied in any version of analytic QCD. We adjust the free parameters of the afore-mentioned two analytic models in such a way that the skeleton-motivated evaluation reproduces the correct known values of rτ and of the Bjorken polarized sum rule (BjPSR) d b (Q 2 ) at a given point (e.g., at Q 2 = 2 GeV 2 ). We then evaluate the low-energy behavior of the Adler function dv(Q 2 ) and the BjPSR d b (Q 2 ) in the afore-mentioned evaluation approach, in the three analytic versions of QCD. We compare with the results obtained in the "minimal" analytic QCD and with the evaluation approach of Milton et al. and Shirkov. Changes in v3: the values of parameters of analytic QCD models M1 and M2 were refined and the numerical results modified accordingly; the penultimate paragraph of Sec. II and the ultimate paragraph of Sec. III are new; discussion of Figs. 4 was extended; new references were added.

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Section: Skeleton-motivated Expansionmentioning

confidence: 99%

Section: Appendix A: Relevant Coefficients Of the Skeleton-motivated mentioning

confidence: 99%

Various versions of analytic QCD and skeleton-motivated evaluation of observables

Cvetič

Valenzuela

2006

Phys. Rev. D

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“…In a previous paper [22], two of us addressed the second problem, by employing in the resummation a (ordinary) Borel transform D(b) that includes the leading IR renormalon via the ansatz D(b) = R(b)/(1 − b/2) 1+ν , and by introducing in addition conformal transformations b = b(w) in order to map sufficiently far away from the origin the singularities of the UV (and the remaining IR) renormalons. However, the integrand in the (ordinary) Borel integral is RScl-and RSch-dependent.…”

Section: Modified Borel Transformsmentioning

confidence: 99%

“…Another interesting feature is that they represent integral transformations of a significantly different form than the ordinary Borel transformation, and have therefore a different singularity structure. Therefore, their application to the hadronic tau decay width ratio and the subsequent extraction of the prediction for α s (M 2 z ) could represent a powerful cross-check of the results of previous work [22] based on ordinary Borel transformations.…”

Section: Introductionmentioning

confidence: 99%

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Resummation of the hadronic tau decay width with the modified Borel transform method

et al. 2001

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A modified Borel transform of the Adler function is used to resum the hadronic tau decay width ratio. In contrast with the ordinary Borel transform, the integrand of the Borel integral is renormalization-scale invariant. We use an ansatz which explicitly accounts for the structure of the leading infrared renormalon. Further, we use judiciously chosen conformal transformations for the Borel variable, in order to map sufficiently away from the origin the other ultraviolet and infrared renormalon singularities. In addition, we apply Padé approximants for the corresponding truncated perturbation series of the modified Borel transform, in order to further accelerate the convergence. Comparing the results with the presently available experimental data on the tau hadronic decay width ratio, we obtain α s (M 2 z ) = 0.1192± 0.0007 exp. ± 0.0010 EW+CKM ± 0.0009 th. ± 0.0003 evol. . These predictions virtually agree with those of our previous resummations where we used ordinary Borel transforms instead. PACS number(s): 13.35. Dx, 11.15.Tk

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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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Bilocal expansion of the Borel amplitude and the hadronic tau decay width

Cited by 56 publications

References 79 publications

Various versions of analytic QCD and skeleton-motivated evaluation of observables

Various versions of analytic QCD and skeleton-motivated evaluation of observables

Resummation of the hadronic tau decay width with the modified Borel transform method

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

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