Perturbative expansions in QCD and analytic properties of alpha_s

Abstract

It is shown that analytic properties of standard QCD perturbation theory contradict known spectral properties,and contain in particular IR generated ghost poles and cuts. As an outcome the rigorous background perturbation theory is developed and its analytic properties are shown to be in agreement with general requirements. In a limiting case of large Nc, when QCD amplitudes contain only pole singularities, the strong coupling constant alpha_s(Q) is shown to be also meromorfic function of external momenta. Some simple models and examples are given when nonperturbative beta function and alpha_s(Q) can be written explicitly. General form of amplitudes at large Nc is given in the framework of background perturbation theory and its correspondence with standard perturbation theory at large momenta is demonstrated in the example of e^+e^- annihilation. For time-like momenta the background coupling constant differs drastically from the standard one but the background series averaged over energy intervals has the same (AF) asymptotics at large momenta as in the standard perturbation theory.

38 pages, no figures

References in corpus (1)

• Nonperturbative corrections to the quark self-energy

Cited by in corpus (35)

• Quark Antiscreening at Strong Magnetic Field and Inverse Magnetic Catalysis
• Relating a gluon mass scale to an infrared fixed point in pure gauge QCD
• Bjorken Sum Rule and pQCD frontier on the move
• Matching Regge Theory to the OPE
• Nucleon spin structure and pQCD frontier on the move
• Parity doubling in particle physics
• Higher excitations of the $D$ and $D_s$ mesons
• Asymptotic freedom in strong magnetic field
• FAPT: a Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory
• Quark condensate and deviations from string-like behaviour of meson spectra
• Dimension-two gluon condensate from large-Nc Regge models
• Holographic like models as a five-dimensional rewriting of large-Nc QCD
• Qualitative solution of QCD sum rules
• Reconciling the analytic QCD with the ITEP operator product expansion philosophy
• Pion transition form factor in the Regge approach and incomplete vector-meson dominance
• Asymptotic freedom and IR freezing in QCD: the role of gluon paramagnetism
• Scalar-isoscalar states in the large-Nc Regge approach
• Pion transition form factor and distribution amplitudes in large-Nc Regge models
• Cluster duality
• Field Correlator Method for the confinement in QCD
• The Hyperfine Splittings in Bottomonium and the $B_q(q=n,s,c)$ Mesons
• Gluon Propagator in Fractional Analytic Perturbation Theory
• Techniques of evaluation of QCD low-energy physical quantities with running coupling with infrared fixed point
• Dimension-2 condensates, zeta-regularization and large-Nc Regge Models
• The Hyperfine Splittings in Heavy-Light Mesons and Quarkonia
• Current correlators in QCD: OPE versus large distance dynamics
• Boosting QED and QCD bound states in the path integral formalism
• Matching meson resonances to OPE in QCD
• The sigma meson from QCD sum rules for large-$N_c$ Regge spectra
• The fundamental scale of QCD
• Electromagnetic couplings of radially excited light vector mesons from QCD sum rules
• The large-Nc limit of borelized spectral sum rules and the slope of radial Regge trajectories
• The case of equivalence of low and high energy constraints on Regge vector spectrum in AdS/QCD
• The linear radial spectrum of scalar mesons within the QCD sum rules in the planar limit
• Resummation in QCD Fractional Analytic Perturbation Theory