2015
DOI: 10.1142/s0217751x15500827
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Perturbative QCD in acceptable schemes with holomorphic coupling

Abstract: 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 requ… Show more

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Cited by 9 publications
(23 citation statements)
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References 221 publications
(383 reference statements)
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“…The coupling is constructed in a dispersive way, resulting as a byproduct in the holomorphic behavior of A(Q 2 ) in the complex Q 2 -plane which reflects the holomorphic behavior of the spacelike QCD observables. Application of the Borel sum rules to τ -decay V + A spectral functions allows us to obtain values for the gluon (dimension-4) condensate and the dimension-6 condensate, which reproduce the measured OPAL and ALEPH data to a significantly better precision than the perturbative MS coupling approach.3 It is possible to show that pQCD renormalization schemes exist in which pQCD coupling a(Q 2 ) is holomorphic for Q 2 ∈ C\(−∞, −M 2 thr ] and at the same time reproduces the high-energy QCD phenomenology as well as the semihadronic τ -lepton decay physics [23][24][25]. 4 MiniMOM scheme is known at present to four loops [18][19][20].…”
mentioning
confidence: 89%
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“…The coupling is constructed in a dispersive way, resulting as a byproduct in the holomorphic behavior of A(Q 2 ) in the complex Q 2 -plane which reflects the holomorphic behavior of the spacelike QCD observables. Application of the Borel sum rules to τ -decay V + A spectral functions allows us to obtain values for the gluon (dimension-4) condensate and the dimension-6 condensate, which reproduce the measured OPAL and ALEPH data to a significantly better precision than the perturbative MS coupling approach.3 It is possible to show that pQCD renormalization schemes exist in which pQCD coupling a(Q 2 ) is holomorphic for Q 2 ∈ C\(−∞, −M 2 thr ] and at the same time reproduces the high-energy QCD phenomenology as well as the semihadronic τ -lepton decay physics [23][24][25]. 4 MiniMOM scheme is known at present to four loops [18][19][20].…”
mentioning
confidence: 89%
“…If in Eq. (25) we increased the power index, i.e., N max > 5, the numerical results for A(Q 2 ) would change insignificantly: A would merge even slightly better with a in the UV regime, but the number of conditions and parameters in A would increase. On the other hand, N max = 5 is sufficiently high for the application of OPE.…”
Section: Construction Of the Coupling A(q 2 )mentioning
confidence: 99%
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“…A of [72]], giving in this scheme the value a = 0.28043/π at Q 2 = (2m c ) 2 and N f = 3, and the Lambert scale value Λ L = 1.153 GeV. For more details on this procedure, we refer to [37,48,62,73]. We point out that we construct our coupling A(Q 2 ) in (Lambert-)MiniMOM renormalization scheme, and not in the usual MS scheme, in order to make the comparison of Fig.…”
Section: Construction Of the Nearly Perturbative Holomorphic Coumentioning
confidence: 99%
“…For further literature on various analytic QCD models, we refer to review articles [10,20,21]. Some newer constructions of analytic models in QCD of A 1 (Q 2 ) include those based on specific classes of β functions with nonperturbative contributions [22] or without such contributions [23][24][25] and those based on modifications of the the spectral density ρ…”
Section: Introductionmentioning
confidence: 99%