Evaluations of Low-Energy Physical Quantities in QCD with IR Freezing of the Coupling

Cvetič, Gorazd

doi:10.1007/s00601-013-0797-8

Cited by 5 publications

(4 citation statements)

References 64 publications

(42 reference statements)

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“…[145,146]. It turns out that in the series (A5b), the LB parts can be resummed [147][148][149] d (LB) (Q 2 ) = a(κQ 2 ) + ∞ n=1 c n,n (κ) β n 0 a n+1 (κQ 2 )…”

Section: Discussionmentioning

confidence: 99%

“…If LB resummation were not used, we could use the power expansion (A5a) for the Adler function [i.e., CIPT for rτ (A4)] since the considered holomorphic coupling a(Q 2 ) is perturbative. On the other hand, if the considered holomorphic coupling (and beta function) were nonpertubative [a(Q 2 ) → A(Q 2 )], the use of the expansion (A5b) in logarithmic derivatives ( an →) An of A (and its possible resummations) for the Adler function would be obligatory because otherwise the series goes out of control due to incorrect treatment of nonperturbative contributions[148,149].…”

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confidence: 99%

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Perturbative QCD in acceptable schemes with holomorphic coupling

Contreras

Cvetič

Kögerler

et al. 2015

Int. J. Mod. Phys. A

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Perturbative QCD in mass independent schemes leads in general to running coupling $a(Q^2)$ which is nonanalytic (nonholomorphic) in the regime of low spacelike momenta $|Q^2| \lesssim 1 \ {\rm GeV}^2$. Such (Landau) singularities are inconvenient in the following sense: evaluations of spacelike physical quantities ${\cal D}(Q^2)$ with such a running coupling $a(\kappa Q^2)$ ($\kappa \sim 1$) give us expressions with the same kind of singularities, while the general principles of local quantum field theory require that the mentioned physical quantities have no such singularities. In a previous work, certain classes of perturbative mass independent beta functions were found such that the resulting coupling was holomorphic. However, the resulting perturbation series showed explosive increase of coefficients already at ${\rm N}^4{\rm LO}$ order, as a consequence of the requirement that the theory reproduce the correct value of the $\tau$ lepton semihadronic strangeless decay ratio $r_{\tau}$. In this work we successfully extend the construction to specific classes of perturbative beta functions such that the perturbation series do not show explosive increase of coefficients, the perturbative coupling is holomorphic, and the correct value of $r_{\tau}$ is reproduced. In addition, we extract, with Borel sum rule analysis of the V+A channel of the semihadronic strangeless decays of $\tau$ lepton, reasonable values of the corresponding D=4 and D=6 condensates.Comment: v3: 27 pages; 12 figures; includes new Sec.V - sum rule analysis for semihadronic decays of tau lepton in a proposed QCD scheme; new Refs.: [114,115,118-132]; to appear in Int.J.Mod.Phys.

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“…[145,146]. It turns out that in the series (A5b), the LB parts can be resummed [147][148][149] d (LB) (Q 2 ) = a(κQ 2 ) + ∞ n=1 c n,n (κ) β n 0 a n+1 (κQ 2 )…”

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

Perturbative QCD in acceptable schemes with holomorphic coupling

Contreras

Cvetič

Kögerler

et al. 2015

Int. J. Mod. Phys. A

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“…In a mathematical sense, the QCD effective charges belong to the same class of holomorphic couplings. Moreover, as pointed out by Cvetič [51], evaluation of renormalization scale-invariant quantities at low Q 2 , in terms of infrared finite couplings, can be effectively done as a series in derivatives of the coupling with respect to the logarithm of Q 2 . This truncated series exhibit significantly better convergence properties.…”

Section: The Qcd Effective Chargementioning

confidence: 99%

“…That is, α s has a nonholomorphic behavior at low q 2 [49]. This problem has been worked out by using analytic versions of QCD whose coupling α s (q 2 ) is holomorphic in the entire complex plane except the timelike axis (q 2 < 0) [50], with many applications in hadronic physics [51,52]. In a mathematical sense, the QCD effective charges belong to the same class of holomorphic couplings.…”

Section: The Qcd Effective Chargementioning

confidence: 99%

QCD effective charges and the structure function F2 at small-x: Higher twist effects

2020

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We consider the effect of higher twist operators of the Wilson operator product expansion in the structure function F2(x, Q 2 ) at small-x, taking into account QCD effective charges whose infrared behavior is constrained by a dynamical mass scale. The higher twist corrections are obtained from the renormalon formalism. Our analysis is performed within the conventional framework of next-to-leading order, with the factorization and renormalization scales chosen to be Q 2 . The infrared properties of QCD are treated in the context of the generalized double-asymptotic-scaling approximation. We show that the corrections to F2 associated with twist-four and twist-six are both necessary and sufficient for a good description of the deep infrared experimental data. * dimiter@if.ufrgs.br †

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anQCD: A Mathematica package for calculations in general analytic QCD models

Ayala

Cvetič

2015

Computer Physics Communications

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We provide a Mathematica package that evaluates the QCD analytic couplings (in the complex domain) A ν (Q 2 ), which are analytic analogs of the powers a(Q 2 ) ν of the underlying perturbative QCD (pQCD) coupling a(Q 2 ) ≡ α s (Q 2 )/π, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2δanQCD), and Massive Perturbation Theory (MPT). The analytic (holomorphic) running couplings A ν (Q 2 ), in contrast to the corresponding pQCD expressions a(Q 2 ) ν , reflect correctly the analytic properties of the spacelike observables D(Q 2 ) in the complex Q 2 plane as dictated by the general principles of quantum field theory. They are thus more suited for evaluations of such physical quantities, especially at low momenta |Q 2 | ∼ 1 GeV 2 . Program Summary Title of program: anQCDThe main program ( anQCD.m) and supplementary modules ( Li nu.m and s0r.m), and the zipped file containing all three files ( anQCD Mathematica.zip), available from the web page:No. of bytes in distributed program including test data etc.: 63 kB (main module anQCD.m), 2 kB (supplementary module Li nu.m), 18 kB (supplementary module s0r.m);Nature of the physical problem: Evaluation of the values for analytic couplings A ν (Q 2 ; N f ) in analytic QCD [the analytic analog of the power (α s (Q 2 ; N f )/π) ν ] based on the dispersion relation; A ν represents a physical (holomorphic) function in the plane of complex squared momenta −q 2 ≡ Q 2 . In anQCD.m we collect the formulas for three different analytic models depending on the energy scale, Q 2 , number of flavors N f , the QCD scale Λ N f , and the (nonpower) index ν. The considered models are: Analytic Perturbation theory (APT), Two-delta analytic QCD (2δanQCD) and Massive Perturbation Theory (MPT). Method of solution:anQCD uses Mathematica functions to perform numerical integration of spectral function for each analytic model, in order to obtain the corresponding analytic images A ν (Q 2 ) via dispersion relation.Restrictions on the complexity of the problem: It could be that for an unphysical choice of the input parameters the results are meaningless. Typical running time: For all operations the running time does not exceed a few seconds.

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Evaluations of Low-Energy Physical Quantities in QCD with IR Freezing of the Coupling

Cited by 5 publications

References 64 publications

Perturbative QCD in acceptable schemes with holomorphic coupling

Perturbative QCD in acceptable schemes with holomorphic coupling

QCD effective charges and the structure function F2 at small-x: Higher twist effects

anQCD: A Mathematica package for calculations in general analytic QCD models

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