Renormalization scheme and higher loop stability in hadronic 
                $\tau$
               decay within analytic perturbation theory

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

doi:10.1007/s100520000370

Cited by 55 publications

(80 citation statements)

References 31 publications

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“…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: 54%

“…. ), on the one hand, and those of the approach of Milton, Solovtsov, Solovtsova, and Shirkov (MSSSh) [2,3,4], on the other hand, are not the same, although they must gradually merge when the loop level is increased. This is illustrated in Figs of Figs.…”

Section: Analytization Of Higher Powers Of the Coupling Parametermentioning

confidence: 99%

“…Appendix E, Eq. (E6)] cannot be reproduced with such values of Λ [4] unless large masses of u, d and s quarks are introduced (m q ≈ 0.25-0.45 GeV) [10] and the mass threshold effects become central. The above consideration motivates us to introduce low-energy modifications of the MA coupling.…”

Section: Minimal Analytic Qcd and Two Extensions Of Itmentioning

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: Minimal Analytic Qcd and Two Extensions Of Itsupporting

confidence: 54%

Section: Analytization Of Higher Powers Of the Coupling Parametermentioning

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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“…For example, within the APT the renormalization scheme (RS) dependence of results obtained, caused by the inevitable truncation of the series, is reduced drastically (see details and applications to various processes in Refs. [5][6][7][8][9][10]). Moreover, the analytic approach allows one to give a self-consistent definition of the perturbative expansion in the timelike region [11].…”

mentioning

confidence: 99%

“…In the framework of APT, where the Q 2 -analyticity is maintained, the expression for δ τ can be obtained both from the initial formula (10) and from the contour representation (11). In terms of the effective spectral function it has the form [4] In Fig.…”

mentioning

confidence: 99%

Remark on the perturbative component of inclusiveτdecay

Milton

Solovtsov²,

Solovtsova³

2002

Phys. Rev. D

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In the context of the inclusive τ -decay, we analyze various forms of perturbative expansions which have appeared as modifications of the original perturbative series. We argue that analytic perturbation theory, which combines renormalization-group invariance and Q 2 -analyticity, has significant merits favoring its use to describe the perturbative component of τ -decay.PACS Numbers: 11.10.Hi, 11.55.Fv, 12.38.Cy, 13.35.Dx A perturbative approximation in quantum chromodynamics as a rule cannot be exhaustive in the low energy region of a few GeV and a nonperturbative component has to be included. The reliability of extracting nonperturbative parameters from data is connected with uncertainties in the perturbative description of a process arising from the inevitable truncation of the perturbation theory (PT) series. The initial perturbative series that is obtained after the renormalization procedure is not the final product of the theory. This series can be modified and its properties can be improved on the basis of additional information coming from general properties of the quantity under consideration. In this note we consider various descriptions of the perturbative component in the context of an analysis of the inclusive decay of the τ lepton. We will discuss merits and drawbacks of the series expansion for the R τ -ratio in terms of powers of the parameter α s (M 2 τ ) [1], the prescription of Ref.[2] which uses a contour representation, and the approximation based on the analytic approach proposed in Ref. [3].The main object in a description of the hadronic decay of the τ -lepton and of many other physical processes is the correlator Π(q 2 ) or the corresponding Adler function D(−q 2 ) = −q 2 dΠ(q 2 )/dq 2 . The analytic properties of the D-function are contained within the relationwhere R(s) = ImΠ(s)/π. According to this equation, the D-function is an analytic function in the complex Q 2 -plane with a cut along the negative real axis. After renormalization, the perturbative expansion of the D-function has the form of a power series in the expansion parameter a µ = α s (µ 2 )/π. In the massless case the series has the formAs is well known, this expression is unsatisfactory both from theoretical and practical viewpoints. Any partial sum of it is not renormalization-group invariant and logarithms in the coefficients lead to an ill-defined behavior in both infrared and ultraviolet regions. The modification of the initial representation (2) based on renormalization-group invariance readswhereā(Q 2 ) is the running coupling. This commonly used modification removes some of the undesirable features of the expansion (2). A partial sum of the series (3) is now µ-independent. The log-terms in the coefficients of Eq, (2) have been summed into the running coupling and the series (3) can now be used in the ultraviolet region. However, the correct analytic properties of the partial sum of Eq. (2), the principal merit of this expansion, are no longer valid due to unphysical singularities of the perturbative running coup...

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

Solovtsov¹

2003

Particle Physics in the New Millennium

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Renormalization scheme and higher loop stability in hadronic $\tau$ decay within analytic perturbation theory

Cited by 55 publications

References 31 publications

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

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

Remark on the perturbative component of inclusiveτdecay

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

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