Analytic perturbation theory and inclusive τ decay

Milton, Kimball A.; Solovtsov, I. L.; Solovtsova, O. P.

doi:10.1016/s0370-2693(97)01207-0

Cited by 106 publications

(256 citation statements)

References 19 publications

Supporting

Mentioning

248

Contrasting

Order By: Relevance

“…By introducing and using a specific evaluation method within the MA QCD, the authors of Refs. [2,3,4] reproduced the measured values of the higher energy QCD observables (|q 2 | > 10 GeV 2 ) when the scale parameter Λ had the value Λ (n f =5) ≈ 0.26 GeV (where n f is the number of active quark flavors). This corresponds to Λ (n f =3) ≈ 0.4 GeV.…”

Section: Minimal Analytic Qcd and Two Extensions Of Itsupporting

confidence: 60%

“…The singularity sector 0 < Q 2 ≤ Λ 2 in a(Q 2 ), Eqs. (2) and (4), is therefore nonphysical. The most straightforward rectification of this problem is to eliminate that sector from the dispersion relation (4) while keeping the pQCD discontinuity function ρ (pt) (σ; β 2 , .…”

Section: Minimal Analytic Qcd and Two Extensions Of Itmentioning

confidence: 99%

“…There exists a practical iterative solution [16,17] to RGE (1) based on the Lambert function [19]. This solution is an expansion of a different form than (2). When the number of terms in the Lambert-based expansion and in expansion (2) increases, the two solutions for A (MA) 1 converge to the exact numerical solution rapidly for all Q 2 , but the Lambert-based expansion converges faster.…”

Section: Minimal Analytic Qcd and Two Extensions Of Itmentioning

confidence: 99%

“…The subscript (∞) in Eq. (31) means that this is the quantity obtained by not truncating RGE beta-function (1), i.e., for j max = ∞ and keeping the same value of Λ in expansion (2) as in the case of the truncated beta-function (i.e., j max = n max + 1). The second identity in Eq.…”

Section: Analytization Of Higher Powers Of the Coupling Parametermentioning

confidence: 99%

“…We investigate the RScl-and RSch-dependence of the numerical curves, and in the MA-case we compare the results of d b (Q 2 ) obtained by our skeleton-motivated evaluation approach with those of the APT approach of Refs. [2,3,4]. Numerical calculations were performed using Mathematica [13].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Cvetič

Valenzuela

2006

Phys. Rev. D

View full text Add to dashboard Cite

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.

show abstract

Section: Minimal Analytic Qcd and Two Extensions Of Itsupporting

confidence: 60%

Section: Minimal Analytic Qcd and Two Extensions Of Itmentioning

confidence: 99%

Section: Minimal Analytic Qcd and Two Extensions Of Itmentioning

confidence: 99%

Section: Analytization Of Higher Powers Of the Coupling Parametermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Cvetič

Valenzuela

2006

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

Ghost-Free APT Analysis of Perturbative QCD Observables

Shirkov

2003

Particle Physics in the New Millennium

View full text Add to dashboard Cite

We establish direct connection between ghost-free formulations of RG-invariant perturbation theory in the both Euclidean and Minkowskian regions.By combining the trick of resummation of the π 2 -terms for the invariant QCD coupling and observables in the time-like region with fresh results on the "analyticized" coupling α an (Q 2 ) and observables in the space-like domain we formulate a self-consistent scheme, free of ghost troubles. The basic point of this joint construction is the "dipole spectral relation" (1) emerging from axioms of local QFT.Then we consider the issue of the heavy quark thresholds and devise a global scheme for the data analysis in the whole accessible space-like and time-like domain with various numbers of active quarks. Observables in both the regions are presented in a form of non-power perturbation series with improved convergence properties.Preliminary estimates indicate that this global scheme produces results a bit different -on a few per cent level forᾱ s -from the usual one, thus influencing the total picture of the QCD parameters correlation.

show abstract

Target Mass Effects and the Jost-Lehmann-Dyson Representation for Structure Functions

Solovtsov¹

2003

Particle Physics in the New Millennium

View full text Add to dashboard Cite

Analytic perturbation theory and inclusive τ decay

Cited by 106 publications

References 19 publications

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

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

Ghost-Free APT Analysis of Perturbative QCD Observables

Target Mass Effects and the Jost-Lehmann-Dyson Representation for Structure Functions

Contact Info

Product

Resources

About