Adler function for light quarks in analytic perturbation theory

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

doi:10.1103/physrevd.64.016005

Cited by 83 publications

(111 citation statements)

References 44 publications

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“…As it has been demonstrated in Ref. [20], the light D-function corresponding to the non-strange vector channel τ -data can be described by using reasonable effective quark masses with Λ MS ≃ 420 MeV.…”

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confidence: 69%

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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confidence: 69%

Remark on the perturbative component of inclusiveτdecay

Milton

Solovtsov²,

Solovtsova³

2002

Phys. Rev. D

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“…3), but fails to describe the experimental behavior of the Adler function in the low-energy domain Q 1 GeV, where the effects due to the pion mass become appreciable. Of course, in the framework of the massless APT, the infrared behavior of the Adler function can be greatly improved following the procedure introduced in [34]; this consists essentially in carrying out an appropriate resummation of threshold singularities, and introducing into (18) and (19) effects from nonperturbative light quark masses. The necessary nonperturbative information on the quark masses is furnished from the study of Schwinger-Dyson equations and quark condensates.…”

Section: Discussionmentioning

confidence: 99%

A novel integral representation for the Adler function

Нестеренко

Papavassiliou

2006

J. Phys. G: Nucl. Part. Phys.

137

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Abstract. New integral representations for the Adler D-function and the R-ratio of the electron-positron annihilation into hadrons are derived in the general framework of the analytic approach to QCD. These representations capture the nonperturbative information encoded in the dispersion relation for the D-function, the effects due to the interrelation between spacelike and timelike domains, and the effects due to the nonvanishing pion mass. The latter plays a crucial role in this analysis, forcing the Adler function to vanish in the infrared limit. Within the developed approach the D-function is calculated by employing its perturbative approximation as the only additional input. The obtained result is found to be in reasonable agreement with the experimental prediction for the Adler function in the entire range of momenta 0 ≤ Q 2 < ∞.

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“…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%

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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Adler function for light quarks in analytic perturbation theory

Cited by 83 publications

References 44 publications

Remark on the perturbative component of inclusiveτdecay

Remark on the perturbative component of inclusiveτdecay

A novel integral representation for the Adler function

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

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