Perturbative expansion of the energy of static sources at large orders in four-dimensional SU(3) gauge theory

Bali, Gunnar S.; Bauer, Clemens; Pineda, A. Morelos; Torrero, C.

doi:10.1103/physrevd.87.094517

Cited by 66 publications

(107 citation statements)

References 71 publications

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“…Irrespective of the scheme, the heavy quark pole mass can only be defined up to an ambiguity of ∼ 0.65 Λ MS . A more detailed analysis is in preparation [32].…”

Section: Figmentioning

confidence: 99%

“…The effects of higher β j start at O(α 5 ), but this uncertainty in our parametrization quickly becomes negligible at high orders where the coefficients f j , governed by the d = 1 renormalon, will dominate. This can be quantified systematically in a large n analysis [32], where any possible renormalon of the lattice β-function is subleading (d > 1). To check this assumption and to justify the truncation at β 2 we have performed fits including β j for j ≤ 0, 1 and 2 (see below).…”

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confidence: 99%

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Compelling Evidence of Renormalons in QCD from High Order Perturbative Expansions

2012

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We compute the static self-energy of SU(3) gauge theory in four spacetime dimensions to order α 20 in the strong coupling constant α. We employ lattice regularization to enable a numerical simulation within the framework of stochastic perturbation theory. We find perfect agreement with the factorial growth of high order coefficients predicted by the conjectured renormalon picture based on the operator product expansion.PACS numbers: 11.15. Bt,12.38.Cy,12.38.Bx,11.10.Jj,12.39.Hg Little is known about properties of quantum field theories from first principles. This is particularly so for asymptotically free gauge theories such as quantum gluodynamics. One of the most salient features of this theory is the confinement of charged objects. Yet this property has not been proven, and the best evidence comes from the linearly rising static potential at large distances obtained in lattice simulations. Another expected property is the asymptotic nature of perturbative weak coupling expansions. In four dimensional non-Abelian gauge theories one particular pattern of asymptotic divergence should be determined by the structure of the operator product expansion (OPE). It is usually named renormalon [1] or, more specifically, infrared renormalon. Its existence has also not been proven but only tested assuming the dominance of β 0 -terms, which amounts to an effective Abelianization of the theory, or in the two dimensional O(N ) model [2], where it is suppressed by powers of 1/N . Moreover, the possible non-existence or irrelevance of renormalons in Quantum Chromodynamics has been suggested in several papers, see, e.g. [3,4] and references therein. This has motivated dedicated high order perturbative expansions of the plaquette, e.g. [5][6][7][8], in lattice regularization, with conflicting conclusions. Powers as high as α 20 were achieved in the most recent simulation [9]. However, the expected asymptotic behaviour was not seen. If confirmed, this non-observation would cast doubt on the well-accepted lore of the OPE and renormalon physics (see [10] for a comprehensive review), and would significantly affect the phenomenological analysis of data from high energy physics experiments on the decay of heavy hadrons, heavy quark masses, the running coupling parameter, parton distributions, etc.. Therefore, this issue should be clarified unambiguously.In this letter we present compelling numerical evidence that the expected renormalons indeed exist not only in models but in real gluodynamics. We also argue why previous analyses based on the plaquette have failed to detect them. The vital and new ingredients of our study are as follows. (a) We consider a perturbative series whose leading renormalon is dictated by a dimension d = 1 operator, rather than by the d = 4 plaquette. (b) Using a higher order integrator and employing twisted boundary conditions, among other improvements, we are able to obtain results of unprecedented precision on an extensive set of spacetime volumes. (c) We carefully extrapolate to the infinite volume limi...

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“…Irrespective of the scheme, the heavy quark pole mass can only be defined up to an ambiguity of ∼ 0.65 Λ MS . A more detailed analysis is in preparation [32].…”

Section: Figmentioning

confidence: 99%

mentioning

confidence: 99%

Compelling Evidence of Renormalons in QCD from High Order Perturbative Expansions

2012

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“…The perturbative expansion of aδm(α) = n c n α n+1 was obtained in Refs. [39,40] up to O(α 20 ), and its intrinsic ambiguity δΛ = √ n 0 c n0 α n0+1 = 0.748(42)Λ MS = 0.450(44)r −1 0 in Refs. [40,41].…”

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confidence: 99%

“…[39,40] up to O(α 20 ), and its intrinsic ambiguity δΛ = √ n 0 c n0 α n0+1 = 0.748(42)Λ MS = 0.450(44)r −1 0 in Refs. [40,41]. MC data for the ground state energy E MC of a static-light meson with the Wilson gauge action can be found in Refs.…”

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confidence: 99%

Model Independent Determination of the Gluon Condensate in Four Dimensional SU(3) Gauge Theory

2014

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We determine the non-perturbative gluon condensate of four-dimensional SU(3) gauge theory in a model-independent way. This is achieved by carefully subtracting high order perturbation theory results from non-perturbative lattice QCD determinations of the average plaquette. No indications of dimension two condensates are found. The value of the gluon condensate turns out to be of a similar size as the intrinsic ambiguity inherent to its definition. We also determine the binding energy of a B meson in the heavy quark mass limit.PACS numbers: 12.38. Gc,12.38.Bx,11.55.Hx,12.38.Cy,11.15.Bt The operator product expansion (OPE) [1] is a fundamental tool for theoretical analyses in quantum field theories. Its validity is only proven rigorously within perturbation theory, to arbitrary finite orders [2]. The use of the OPE in a non-perturbative framework was initiated by the ITEP group [3] (see also the discussion in Ref. [4]), which postulated that the OPE of a correlator could be approximated by the following series:where the expectation values of local operators O d are suppressed by inverse powers of a large external momentum Q ≫ Λ QCD , according to their dimensionality d.The Wilson coefficients C d (α) encode the physics at momentum scales larger than Q. These are well approximated by perturbative expansions in the strong coupling parameter α. The large-distance physics is described by the matrix elements O d that usually have to be determined non-perturbatively. Almost all QCD predictions of relevance to particle physics phenomenology are based on factorizations that are generalizations of the above generic OPE.For correlators where O 0 = 1, the first term of the OPE expansion is a perturbative series in α. In pure gluodynamics the first non-trivial gauge invariant local operator has dimension four. Its expectation value is the so-called non-perturbative gluon condensate

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“…In addition, for lattices with L/a ≤ 24 we found perfect agreement with the results obtained using a Langevin implementation of NSPT based on the 2nd-order integrator of ref. [23]. In conclusion, we are confident that within the statistical precision our results are not affected by step-size errors, and we can thus proceed discussing their continuum extrapolation.…”

Section: Resultsmentioning

confidence: 99%

The gradient flow coupling from numerical stochastic perturbation theory

Brida¹,

Lüscher²

2017

Proceedings of 34th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2016)

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Perturbative calculations of gradient flow observables are technically challenging. Current results are limited to a few quantities and, in general, to low perturbative orders. Numerical stochastic perturbation theory is a potentially powerful tool that may be applied in this context. Precise results using these techniques, however, require control over both statistical and systematic uncertainties. In this contribution, we discuss some recent algorithmic developments that lead to a substantial reduction of the cost of the computations. The matching of the MS coupling with the gradient flow coupling in a finite box with Schrödinger functional boundary conditions is considered for illustration.

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Perturbative expansion of the energy of static sources at large orders in four-dimensional SU(3) gauge theory

Cited by 66 publications

References 71 publications

Compelling Evidence of Renormalons in QCD from High Order Perturbative Expansions

Compelling Evidence of Renormalons in QCD from High Order Perturbative Expansions

Model Independent Determination of the Gluon Condensate in Four Dimensional SU(3) Gauge Theory

The gradient flow coupling from numerical stochastic perturbation theory

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