Small-x behavior of the structure function F_2 and its slope partial ln(F_2)/partial ln(1/x) for "frozen" and analytic strong-coupling constants

Cvetic, G.; Illarionov, A. Yu.; Kniehl, B. A.; Kotikov, A. V.

doi:10.48550/arxiv.0906.1925

Cited by 8 publications

(15 citation statements)

References 29 publications

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“…The solution of the problem (a) has been known for some time, and it consists of two parts: (a1) replacing the pQCD coupling a(κQ 2 ) by a coupling A(κQ 2 ) which has no Landau singularities, i.e., it is holomorphic (analytic) in the complex Q 2 -plane with the exception of (a part of) the negative semiaxis, thus reflecting qualitatively the correct holomorphic properties of the spacelike observables D(Q 2 ) in the Q 2 -complex plane; (a2) reorganizing the perturbation series D(Q 2 ) = d n (κ)a(κQ 2 ) n+1 into a series D(Q 2 ) = d n (κ) a n+1 (κQ 2 ) with logarithmic derivatives a n+1 [Eqs. (2), (13)], and replacing these pQCD logarithmic derivatives by the corresponding logarithmic derivatives A n+1 of A [cf. Eqs.…”

Section: Discussionmentioning

confidence: 99%

“…(B11) and (B14)] and, as always, κ ≡ µ 2 /Q 2 is the (arbitrary) dimensionless renormalization scale parameter (0 < κ ∼ 1). The terms in the series (73) do not suffer from Landau singularities at low positive Q 2 (0 ≤ Q 2 1 GeV 2 ), in contrast to the terms in the pQCD series (13). However, the series (73) are asymptotically divergent, as are also the pQCD series (13).…”

Section: B Construction Of the Characteristic Distribution Function G...mentioning

confidence: 97%

“…[22,23]). Several versions of QCD holomorphic couplings have been applied in evaluations of various QCD quantities [24][25][26][27]. [37] Two recently constructed QCD variants with holomorphic couplings A(Q 2 ), the aforementioned 2δ AQCD [17] and 3δ AQCD [16], fulfill several phenomenological constraints of the low-Q 2 QCD (|Q 2 | 1 GeV 2 ) as mentioned earlier.…”

Section: Numerical Evaluationmentioning

confidence: 99%

“…The terms in the series (73) do not suffer from Landau singularities at low positive Q 2 (0 ≤ Q 2 1 GeV 2 ), in contrast to the terms in the pQCD series (13). However, the series (73) are asymptotically divergent, as are also the pQCD series (13). The corresponding resummation of the series D AQCD (Q 2 ), with the characteristic functions G D (t) and G (SL) D (t), turns out to be completely similar to the resummation (68) in pQCD, with the simple substitution a → A…”

Section: B Construction Of the Characteristic Distribution Function G...mentioning

confidence: 99%

“…, 3). 13 Nonetheless, the SL term proportional to α was included in the Borel transform ansätze ( 51) and ( 58) because of the knowledge of the exact value of the parameter ĉ(4) 1 , Eq. ( 50), which makes it possible to extract the value of α [cf.…”

Section: Evaluation Of the Semihadronic τ Decay Ratio Rτmentioning

confidence: 99%

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Renormalon-motivated evaluation of QCD observables

Cvetič

2019

Phys. Rev. D

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Section: Discussionmentioning

confidence: 99%

Section: B Construction Of the Characteristic Distribution Function G...mentioning

confidence: 97%

Section: Numerical Evaluationmentioning

confidence: 99%

Section: B Construction Of the Characteristic Distribution Function G...mentioning

confidence: 99%

Section: Evaluation Of the Semihadronic τ Decay Ratio Rτmentioning

confidence: 99%

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Renormalon-motivated evaluation of QCD observables

Cvetič

2019

Phys. Rev. D

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FAPT: A Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory

Bakulev¹,

Khandramai²

2013

Computer Physics Communications

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We provide here all the procedures in Mathematica which are needed for the computation of the analytic images of the strong coupling constant powers in Minkowski (Ā ν (s; n f ) and A glob ν (s)) and Euclidean (Ā ν (Q 2 ; n f ) and A glob ν (Q 2 )) domains at arbitrary energy scales (s and Q 2 , correspondingly) for both schemes -with fixed number of active flavours n f = 3, 4, 5, 6 and the global one with taking into account all heavy-quark thresholds. These singularity-free couplings are inevitable elements of Analytic Perturbation Theory (APT) in QCD [1-3], and its generalization -Fractional APT [4][5][6], needed to apply the APT imperative for renormalization-group improved hadronic observables.Computer for which the program is designed and others on which it is operable: Any work-station or PC where Mathematica is running.Operating system or monitor under which the program has been tested: Windows XP, Mathematica (versions 5 and 7).No. of bytes in distributed program including test data etc.: 47 kB (main module FAPT.m) and 4 kB (interpolation module FAPT Interp.m); 21 kB (notebook FAPT Interp.nb showing how to use the interpolation module); 10 888 kB (interpolation data files: AcalGlob i.dat and UcalGlob i.dat with = 1, 2, 3, 3P, and 4) 1 Distribution format: ASCIINature of physical problem: The values of analytic imagesĀ ν (Q 2 ) andĀ ν (s) of the QCD running coupling powers α ν s (Q 2 ) in Euclidean and Minkowski regions, correspondingly, are determined through the spectral representation in the QCD Analytic Perturbation Theory (APT). In the program FAPT we collect all relevant formulas and various procedures which allow for a convenient evaluation ofĀ ν (Q 2 ) andĀ ν (s) using numerical integrations of the relevant spectral densities. Method of solution:FAPT uses Mathematica functions to calculate different spectral densities and then performs numerical integration of these spectral integrals to obtain analytic images of different objects.Restrictions on the complexity of the problem: It could be that for an unphysical choice of the input parameters the results are out of any meaning.Typical running time: For all operations the running time does not exceed a few seconds. Usually numerical integration is not fast, so that we advice to use arrays of precalculated data and apply then the routine Interpolate (as shown in supplied example of the program usage, namely in the notebook FAPT Interp.nb).

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Average gluon and quark jet multiplicities at higher orders

Bolzoni¹,

Kniehl²,

Kotikov³

2013

Nuclear Physics B

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We develop a new formalism for computing and including both the perturbative and nonperturbative QCD contributions to the scale evolution of average gluon and quark jet multiplicities. The new method is motivated by recent progress in timelike small-x resummation obtained in the MS-bar factorization scheme. We obtain next-to-next-to-leading-logarithmic (NNLL) resummed expressions, which represent generalizations of previous analytic results. Our expressions depend on two nonperturbative parameters with clear and simple physical interpretations. A global fit of these two quantities to all available experimental data sets that are compatible with regard to the jet algorithms demonstrates by its goodness how our results solve a longstandig problem of QCD. We show that the statistical and theoretical uncertainties both do not exceed 5% for scales above 10 GeV. We finally propose to use the jet multiplicity data as a new way to extract the strong-coupling constant. Including all the available theoretical input within our approach, we obtain alpha_s^(5)(M_Z)=0.1199 +- 0.0026 in the MS-bar scheme in an approximation equivalent to next-to-next-to-leading order enhanced by the resummations of ln(x) terms through the NNLL level and of ln(Q^2) terms by the renormalization group, in excellent agreement with the present world average.Comment: 33 pages, 11 figures; two more experimental data sets included; accepted for publication in Nucl. Phys.

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Small-x behavior of the structure function F_2 and its slope partial ln(F_2)/partial ln(1/x) for "frozen" and analytic strong-coupling constants

Cited by 8 publications

References 29 publications

Renormalon-motivated evaluation of QCD observables

Renormalon-motivated evaluation of QCD observables

FAPT: A Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory

Average gluon and quark jet multiplicities at higher orders

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