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

Ayala, César; Cvetič, Gorazd

doi:10.1016/j.cpc.2014.12.024

Cited by 38 publications

(50 citation statements)

References 108 publications

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“…In this work we fit the theoretical OPE expressions to the experimental BSR results in pQCD, in (F)APT, and two additional extensions of QCD to low Q 2 , namely the 2δ [22,23] and 3δ [24,25] AQCD. The latter two extensions have the coupling A(Q 2 ) [the analog of the pQCD coupling a(Q 2 )] which is free of Landau singularities and physically motivated in the entire relevant regime of Q 2 in the complex plane, Q 2 ∈ C\(−∞, −M 2 thr ], where M 2 thr 1 GeV 2 is a positive threshold scale.…”

Section: Introductionmentioning

confidence: 99%

Bjorken polarized sum rule and infrared-safe QCD couplings

et al. 2018

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Experimental data obtained for the polarized Bjorken sum rule (BSR) Γ p−n 1 (Q 2 ) are fitted by using predictions derived within a truncated operator product expansion (OPE) approach to QCD. Four QCD versions are considered: perturbative QCD (pQCD) in the MS scheme, Analytic Perturbation Theory (APT), and 2δ and 3δ analytic QCD versions. In contrast to pQCD, these QCD variants do not have Landau singularities at low positive Q 2 , which facilitates the fitting procedure significantly. The fitting procedure is applied first to the experimental data of the inelastic part of BSR, and the known elastic contributions are added after the fitting. In general, when 2δ and 3δ QCD coupling is used the fitted curves give the best results, within the Q 2 -range of the fit as well as in extended Q 2intervals. When the fitting procedure is applied to the total BSR, i.e., to the sum of the experimental data and the elastic contribution, the quality of the results deteriorates significantly.

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Section: Introductionmentioning

confidence: 99%

Bjorken polarized sum rule and infrared-safe QCD couplings

et al. 2018

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“…All the relations of this section have been mostly paraphrased from Refs. [12,13] and we are inevitable to express them to clarify the discussed subject for readers.…”

Section: An Overview On Different Aspects Of Analytic Perturbatiomentioning

confidence: 99%

“…We then imply this formalism with the help of the main module Mathematica package that is called anQCD.m as introduced in [13]. (1) for pQCD: ∆m (1,2) pQCD and for anQCD in 2δanQCD: ∆m (1,2) anQCD .…”

Section: Extracting the Polarized Structure Function Using 2δanqmentioning

confidence: 99%

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Nonsinglet polarized nucleon structure function in infrared-safe QCD

2019

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Deep inelastic scattering is investigated here as a tool to probe the polarized nucleon structure function in nonsinglet case. During the solution of evolution equations in moment space we will encounter with non-integer power of coupling constant. Therefore it is possible to use the approach of fractional analytical perturbation theory (FAPT). Using this approach, the singularity of renormalized coupling constant is removed at Q = Λ scale as Landau pole and an opportunity would be performed to employ the perturbative calculations at small values of energy scales even less than Λ sclae. To modify the analytical perturbation theory, a newer approach is introduced, called 2δanQCD in which the analytical coupling constant at low energy region is controlling by two delta functions. This model give us more reliable results for the concerned QCD observable and ends up with safe infrared result. We intend to calculate the nonsinglet part of polarized nucleon structure function, using 2δanQCD model and compare it with the result from conventional perturbative QCD (pQCD). For this purposes we employ anQCD package in Mathematica environment to establish the analytic coupling constant. The results at some energy scales are also compared with the available experimental data which involves good consistency with them. Investigating the results indicates that the nucleon structure function at small energy scales contain smoother behaviour, using 2δanQCD model than the conventional pQCD. It is due to the more converging consequence of pertutbative series in the analytic perturbation theory. We also consider the Q 2 dependence of Bjorken sum rule (BSR), using 2δanQCD model. There is good agreement between the available experimental data for BSR and the result from utilized model, specially at low energy scales.

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“…The mathematical tool for numerical calculations of A ν for any ν up to four-loop order is given in Refs. [11,12]. It should be stressed that values of the QCD scale parameter Λ are different in the PT and APT approaches.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

The polarized nonsinglet $\Delta q_3$ and nonsinglet fragmentation function $D^{\pi^{+}}_{u_v}$ in the analytic approach to QCD

Solovtsova¹,

Sidorov²

2015

Proceedings of XXII International Baldin Seminar on High Energy Physics Problems — PoS(Baldin ISHEPP XXII)

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We discuss the application of an analytic approach called the analytic perturbation theory (APT) to the QCD analysis of DIS data. In particular, the results of the QCD analysis of a set of 'fake' data on the polarized nonsinglet ∆q 3 and the nonsinglet fragmentation function D π + u v by using the Q 2 -evolution within the APT are considered. The 'fake' data are constructed based on parametrization of the polarized PDF and nonsinglet combination of the pion fragmentation functions. We confirm that APT can be successfully applied to QCD analysis of ∆q 3 (x, Q 2 ) and D π + u v (z, Q 2 ) and that the inequality Λ APT > Λ PT obtained previously for the xF 3 (x) structure function takes place.

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

Cited by 38 publications

References 108 publications

Bjorken polarized sum rule and infrared-safe QCD couplings

Bjorken polarized sum rule and infrared-safe QCD couplings

Nonsinglet polarized nucleon structure function in infrared-safe QCD

The polarized nonsinglet $\Delta q_3$ and nonsinglet fragmentation function $D^{\pi^{+}}_{u_v}$ in the analytic approach to QCD

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