Elimination of Ghosts in Propagators

Redmond, P. J.

doi:10.1103/physrev.112.1404

Cited by 101 publications

(143 citation statements)

References 12 publications

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“…At the same time, one is still able to incorporate the relevant experimental information about R(s) into the spectral function ρ D (σ) by virtue of Eq. (16), that, however, turns out to be a bit more complicated technically, since the numerical differentiation of the experimental data on R(s) is required.…”

Section: Discussionmentioning

confidence: 99%

A novel integral representation for the Adler function

Нестеренко

Papavassiliou

2006

J. Phys. G: Nucl. Part. Phys.

137

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Abstract. New integral representations for the Adler D-function and the R-ratio of the electron-positron annihilation into hadrons are derived in the general framework of the analytic approach to QCD. These representations capture the nonperturbative information encoded in the dispersion relation for the D-function, the effects due to the interrelation between spacelike and timelike domains, and the effects due to the nonvanishing pion mass. The latter plays a crucial role in this analysis, forcing the Adler function to vanish in the infrared limit. Within the developed approach the D-function is calculated by employing its perturbative approximation as the only additional input. The obtained result is found to be in reasonable agreement with the experimental prediction for the Adler function in the entire range of momenta 0 ≤ Q 2 < ∞.

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Section: Discussionmentioning

confidence: 99%

A novel integral representation for the Adler function

Нестеренко

Papavassiliou

2006

J. Phys. G: Nucl. Part. Phys.

137

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“…The last equation can be obtained by the analytic continuation of α s into the Minkowski space Q 2 → −σ − i0 and calculation of the imaginary partρ (1) (5) is positive monotone decreasing function with maximum at zero α an (Q 2 ) in going to the Minkowski space, so thatρ (1) …”

Section: One-loop Synthetic Running Coupling Of Qcdmentioning

confidence: 99%

“…Let us bring equation (1) for α (1) syn (Q 2 ) to the explicit renormalization invariant form. It can be done without solving the differential renormalization group equations.…”

Section: One-loop Synthetic Running Coupling Of Qcdmentioning

confidence: 99%

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Synthetic Running Coupling of QCD

Алексеев

2006

Few-Body Systems

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Based on a study of the analytic running coupling obtained from the standard perturbation theory results up to four-loop order, the QCD "synthetic" running coupling αsyn is built. In so doing the perturbative time-like discontinuity is preserved and nonperturbative contributions not only remove the nonphysical singularities of the perturbation theory in the infrared region but also decrease rapidly in the ultraviolet region. In the framework of the approach, on the one hand, the running coupling is enhanced at zero and, on the other hand, the dynamical gluon mass mg arises. Fixing the parameter which characterize the infrared enhancement corresponding to the string tension σ and normalization, say, at Mτ completely define the synthetic running coupling. In this case the dynamical gluon mass appears to be fixed and the higher loop stabilization property of mg is observed. For σ = (0.42 GeV) 2 and αsyn(M 2 τ ) = 0.33 ±0.01 it is obtained that mg = 530 ±80 MeV.

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“…The idea of employing the latter together with perturbation theory forms the underlying concept of the so-called analytic approach to QFT, which was first proposed in the framework of Quantum Electrodynamics [1]. Recently, this approach has been extended to Quantum Chromodynamics (QCD) [2] and applied to the "analytization" of the perturbative power series for the QCD observables [3,4,5].…”

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confidence: 99%

Impact of the pion mass on nonpower expansion for QCD observables

Нестеренко

Papavassiliou

2007

Nuclear Physics B - Proceedings Supplements

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A new set of functions, which form a basis of the massive nonpower expansion for physical observables, is presented in the framework of the analytic approach to QCD at the four-loop level. The effects due to the π meson mass are taken into account by employing the dispersion relation for the Adler function. The nonvanishing pion mass substantially modifies the functional expansion at low energies. Specifically, the spacelike functions are affected by the mass of the π meson in the infrared domain below few GeV, whereas the timelike functions acquire characteristic plateaulike behavior below the two-pion threshold. At the same time, all the appealing features of the massless nonpower expansion persist in the considered case of the nonvanishing pion mass.The renormalization group (RG) method plays a key role in the framework of the Quantum Field Theory (QFT) and its applications. Indeed, one is able to handle reliably the strong interaction processes at high energies by employing this method together with perturbative calculations. However, such perturbative solutions to the RG equation possess unphysical singularities in the infrared domain, a fact that contradicts the general principles of the local QFT, and significantly complicates the theoretical description and interpretation of the intermediate-and low-energy experimental data. Nevertheless, an effective way to overcome these difficulties is to complement the perturbative results with a proper nonperturbative insight into the infrared hadron dynamics.One of the sources of the nonperturbative information about the strong interaction processes is the dispersion relations. The idea of employing the latter together with perturbation theory forms the underlying concept of the so-called analytic approach to QFT, which was first proposed in the framework of Quantum Electrodynamics [1]. Recently, this approach has been extended to Quantum Chromodynamics (QCD) [2] and applied to the "analytization" of the perturbative power series for the QCD observables [3,4,5]. The term analytization means the restoring of the correct analytic properties in the kinematic variable of a quantity under consideration by making use of the Källén-Lehmann integral representation (positive q 2 corresponds to a spacelike momentum transfer hereinafter)with the spectral function defined by the initial (perturbative) expression for the quantity at hand:(2) However, there are several ways to embody the analyticity requirement into the RG formalism, that eventually has given rise to different models for the analytic running coupling.Thus, in the original model due to Shirkov and Solovtsov [2] the analyticity requirement (1) is imposed on the perturbative running coupling itself. At the one-loop level this leads towhereas at the higher loop levels the integral representation of the Källén-Lehmann type α(q 2 ) = 4πholds for this invariant charge. Ultimately, the prescription [2] results in the infrared finite limiting value for the running coupling (see papers [3,4,5] and references therein for t...

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Elimination of Ghosts in Propagators

Cited by 101 publications

References 12 publications

A novel integral representation for the Adler function

A novel integral representation for the Adler function

Synthetic Running Coupling of QCD

Impact of the pion mass on nonpower expansion for QCD observables

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