Analytic extension of the modified minimal subtraction renormalization scheme

Brodsky, Stanley J.; Gill, M. S.; Melles, Michael; Rathsman, Johan

doi:10.1103/physrevd.58.116006

Cited by 80 publications

(145 citation statements)

References 51 publications

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“…Its higher order value has artificial strong residual renormalization-scale dependence due to the large numerical value of Π 3 in QCD with five active flavors. These final scales determine the effective number of quarks flavors at each order of perturbation theory [16].…”

Section: The Final Pqcd Expression For the Observable Readsmentioning

confidence: 99%

Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in Perturbative QCD

2013

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We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of nonconformal {βi} terms, and reveals a special degeneracy of the terms in the perturbative coefficients. It allows us to systematically determine the argument of the running coupling order by order in pQCD in a form which can be readily automatized. The new method satisfies all of the principles of the renormalization group and eliminates an unnecessary source of systematic error.PACS numbers: 12.38. Aw, 12.38.Bx, 11.10.Gh, 11.15.Bt An important goal in high energy physics is to make perturbative QCD (pQCD) predictions as precise as possible, not only to test QCD itself, but also to expose new physics beyond the standard model. In this letter we present a systematic method which determines the argument of the running coupling order by order in pQCD and which can be readily automatized. The resulting predictions for physical processes are independent of theoretical conventions such as the choice of renormalization scheme and the initial choice of renormalization scale. The resulting scales also determine the effective number of quark flavors at each order of perturbation theory. The method can be applied to processes with multiple physical scales and is consistent with QED scale setting in the limit N c → 0. The new method satisfies all of the principles of the renormalization group [1], and it eliminates an unnecessary source of systematic error.The starting point for our analysis is to introduce a generalization of the conventional schemes used in dimensional regularization in which a constant −δ is subtracted in addition to the standard subtraction ln 4π − γ E of the MS-scheme. This amounts to redefining the renormalization scale by an exponential factor; i.e. µ 2 δ = µ 2 MS exp(δ). In particular, the MS-scheme is recovered for δ = ln 4π − γ E . The δ-subtraction defines an infinite set of renormalization schemes which we call * mojaza@cp3-origins.net † sjbth@slac.stanford.edu ‡ wuxg@cqu.edu.cn δ-Renormalization (R δ ) schemes; since physical results cannot depend on the choice of scheme, predictions must be independent of δ. Moreover, since all R δ schemes are connected by scale-displacements, the β-function of the strong QCD coupling constant a = α s /4π is the same in any R δ -scheme:The R δ -scheme exposes the general pattern of nonconformal {β i }-terms, and it reveals a special degeneracy of the terms in the perturbative coefficients which allows us to resum the perturbative series. The resummed series matches the conformal series, which is itself free of any scheme and scale ambiguities as well as being free of a divergent renormalon series. It is the final expression one should use for physical predictions. It also makes it possible to set up an algorithm for automatically computing the conformal series and setting the effective scales for the coupling constant at each pertu...

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Section: The Final Pqcd Expression For the Observable Readsmentioning

confidence: 99%

Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in Perturbative QCD

2013

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“…Even so, the Monte Carlo results still are not completely stable for small values of Q/m, especially in the light of the numerical differentiation required in Eq. (24). Nevertheless, accurate results can be obtained by fitting the numerical calculation to a suitable analytic function.…”

Section: Momentum Space Resultsmentioning

confidence: 99%

“…(23) and (24). Rather, ψ (0) V and ψ (1) V are functions of the ratio of the physical momentum transfer Q = √ −q 2 and the pole mass m only.…”

Section: Momentum Space Resultsmentioning

confidence: 99%

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Static QCD potential in coordinate space with quark masses through two loops

Melles

2000

Phys. Rev. D

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The potential between infinitely heavy quarks in a color singlet state is of fundamental importance in QCD. While the confining long distance part is inherently non-perturbative, the short-distance (Coulomb-like) regime is accessible through perturbative means. In this paper we present new results of the short distance potential in coordinate space with quark masses through two loops. The results are given in explicit form based on reconstructed solutions in momentum space in the Euclidean regime. Thus, a comparison with lattice results in the overlap region between the perturbative and non-perturbative regime is now possible with massive quarks. We also discuss the definition of the strong coupling based on the force between the static sources. * Michael.Melles@psi.ch

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“…However, we can use this commensurate scale relation to define an extended MS scheme which is continuous and analytic at any scale. The new modified scheme inherits all of the good properties of the α V scheme, including its correct analytic properties as a function of the quark masses and its unambiguous scale fixing [126].…”

Section: Extension Of the M S Schemementioning

confidence: 99%

New directions in Quantum Chromodynamics

Brodsky¹

1999

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I review the light-cone Fock state represention and its associated light-cone factorization scheme as a method for encoding the flavor, momentum, and helicity properties of hadrons in the form of universal process-independent and frame-independent amplitudes. Discrete light-cone quantization (DLCQ) provides a matrix representation of the QCD Hamiltonian and a nonperturbative method for computing the quark and gluon bound state wavefunctions. A number of applications of the light-cone formalism are discussed, including an exact light-cone Fock state representation of semileptonic B decay amplitudes. Hard exclusive and diffractive reactions are shown to be sensitive to hadron distribution amplitudes, the valence Fock state hadronic wavefuctions at small impact separation. Semi-exclusive reactions are shown to provide new flavor-dependent probes of distribution amplituds and new types of deep inelastic currents. "Self-resolving" diffractive processes and Coulomb dissociation are discussed as a direct measure of the light-cone wavefunctions of hadrons. Alternatively, one can use Coulomb dissociation to resolve nuclei in terms of their nucleonic and mesonic degrees of freedom. I also discuss several theoretical tools which eliminate theoretical ambiguities in perturbative QCD predictions. For example, commensurate scale relations are perturbative QCD predictions based on conformal symmetry which relate observable to observable at fixed relative scale; such relations have no renormalization scale or scheme ambiguity. I also discuss the utility of the α V coupling, defined from the QCD heavy quark potential, as a useful physical expansion parameter for perturbative QCD and grand unification. New results on the analytic fermion masses dependence of the α V coupling at two-loop order are presented.

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Analytic extension of the modified minimal subtraction renormalization scheme

Cited by 80 publications

References 51 publications

Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in Perturbative QCD

Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in Perturbative QCD

Static QCD potential in coordinate space with quark masses through two loops

New directions in Quantum Chromodynamics

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