Related papers: Evaluations of low-energy physical quantities in Q…
Perturbative QCD (pQCD) running coupling a(Q^2) (=alpha_s(Q^2)/pi) is expected to get modified at low spacelike momenta 0 < Q^2 < 1 GeV^2 so that, instead of having unphysical (Landau) singularities it remains smooth and finite there, due…
We try to review the main current ideas and points of view on the running coupling constant in QCD. We begin by recalling briefly the classic analysis based on the Renormalization Group with some emphasis on the exact solutions of the RG…
We investigate a large class of perturbative QCD (pQCD) renormalization schemes whose beta functions $\beta(a)$ are meromorphic functions of the running coupling and give finite positive value of the coupling $a(Q^2)$ in the infrared regime…
Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite nonzero. This leads to a definition of the QCD running coupling, in a specific scheme, that…
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…
Analytic versions of QCD are those whose coupling alpha_s(Q^2) does not have the unphysical Landau singularities on the space-like axis (-q^2=Q^2 > 0). The coupling is analytic in the entire complex plane except the time-like axis (Q^2 <…
We consider a phenomenologycal parametrization of the QCD running coupling which arises from the dispersion relation respecting the holomorphic properties of the physical QCD observables in the complex momentum plane. The parameters are…
In contrast to perturbative QCD, the analytic QCD models have running coupling whose analytic properties correctly mirror those of spacelike observables. The discontinuity (spectral) function of such running coupling is expected to agree…
Analytic QCD models are those where the QCD running coupling has the physically correct analytic behavior, i.e., no Landau singularities in the Euclidean regime. We present a simple analytic QCD model in which the discontinuity function of…
We consider quantum rotors or Ising spins in a transverse field on a $d$-dimensional lattice, with random, frustrating, short-range, exchange interactions. The quantum dynamics are associated with a finite moment of inertia for the rotors,…
The new model for the QCD analytic running coupling, proposed recently, is extended to the timelike region. This running coupling naturally arises under unification of the analytic approach to QCD and the renormalization group (RG)…
Starting from the Schr\"odinger functional, we give a non-perturbative definition of the running coupling constant in QCD. The spatial boundary conditions for the quark fields are chosen such that the massless Dirac operator in the…
Effective coupling constant in quantum electrodynamics is investigated. A pole appears in the effective coupling constant for the space-like momentum if it is calculated by perturbation. The pole can be eliminated by the analytic…
It is shown that the commonly accepted relationship between the Landau singularity in the running coupling constant of QED or QCD and the renormalon singularities in the Borel sums of perturbation theory expansions is only a particular…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
We discuss symmetry-driven squeezing and coherent states of few-particle systems in magnetic fields. An operator approach using canonical transformations and the SU(1,1) algebras is developed for considering Coulomb correlations in the…
Methods described in the literature for the computation of the QCD running coupling are essentially all defined with respect to the renormalization group equations and these equations are associated with the method of renormalization for…
A non-perturbative expansion method which gives a well-defined analytic continuation of the running coupling constant from the spacelike to the timelike region is applied to the inclusive semileptonic decay of the $\tau$--lepton. The method…
The frozen QCD coupling is a parameter often used as an effective fixed coupling. It is supposed to mimic both the running coupling effects and the lack of knowledge of alpha_s in the infrared region. Usually the value of the frozen…
The difference between the timelike and spacelike meson form factors is analysed in the framework of perturbative QCD with Sudakov effects included. It is found that integrable singularities appear but that the asymptotic behavior is the…