arXiv subjects

A. V. Nesterenko

Publications and source records attributed to A. V. Nesterenko.

52 records · Page 3Linked to original sources

arXiv2005

Impact of the pion mass on nonpower expansion for QCD observables

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.

hep-ph↗

arXiv2005

Infrared enhanced analytic coupling and chiral symmetry breaking in QCD

We study the impact on chiral symmetry breaking of a recently developed model for the QCD analytic invariant charge. This charge contains no adjustable parameters, other than the QCD mass scale $Λ$, and embodies asymptotic freedom and infrared enhancement into a single expression. Its incorporation into the standard form of the quark gap equation gives rise to solutions for the dynamically generated mass that display a singular confining behaviour at the origin. Using the Pagels-Stokar method we relate the obtained solutions to the pion decay constant $f_π$, and estimate the scale parameter $Λ$, in the presence of four active quarks, to be about 880 MeV.

hep-ph↗

arXiv2004

The massive analytic invariant charge in QCD

The low energy behavior of a recently proposed model for the massive analytic running coupling of QCD is studied. This running coupling has no unphysical singularities, and in the absence of masses displays infrared enhancement. The inclusion of the effects due to the mass of the lightest hadron is accomplished by employing the dispersion relation for the Adler D function. The presence of the nonvanishing pion mass tames the aforementioned enhancement, giving rise to a finite value for the running coupling at the origin. In addition, the effective charge acquires a "plateau-like" behavior in the low energy region of the timelike domain. This plateau is found to be in agreement with a number of phenomenological models for the strong running coupling. The developed invariant charge is applied in the processing of experimental data on the inclusive $τ$ lepton decay. The effects due to the pion mass play an essential role here as well, affecting the value of the QCD scale parameter $Λ$ extracted from these data. Finally, the massive analytic running coupling is compared with the effective coupling arising from the study of Schwinger-Dyson equations, whose infrared finiteness is due to a dynamically generated gluon mass. A qualitative picture of the possible impact of the former coupling on the chiral symmetry breaking is presented.

hep-ph↗

arXiv2004

The QCD analytic running coupling and chiral symmetry breaking

We study the dependence on the pion mass of the QCD effective charge by employing the dispersion relations for the Adler D function. This new massive analytic running coupling is compared to the effective coupling saturated by the dynamically generated gluon mass. A qualitative picture of the possible impact of the former coupling on the chiral symmetry breaking is presented.

hep-ph↗

arXiv2004

Analytic Invariant Charge in QCD

This paper gives an overview of recently developed model for the QCD analytic invariant charge. Its underlying idea is to bring the analyticity condition, which follows from the general principles of local Quantum Field Theory, in perturbative approach to renormalization group (RG) method. The concrete realization of the latter consists in explicit imposition of analyticity requirement on the perturbative expansion of $β$ function for the strong running coupling, with subsequent solution of the corresponding RG equation. In turn, this allows one to avoid the known difficulties originated in perturbative approximation of the RG functions. Ultimately, the proposed approach results in qualitatively new properties of the QCD invariant charge. The latter enables one to describe a wide range of the strong interaction processes both of perturbative and intrinsically nonperturbative nature.

hep-ph↗

arXiv2004

The QCD analytic effective charge and its dependence on the pion mass

A new model for the QCD analytic running coupling, which incorporates the effects due to the $π$ meson mass, is proposed. The properties of this invariant charge in spacelike and timelike regions are examined. Its main distinctive features are a finite infrared limiting value, which depends on the pion mass, and the "plateau-like" behavior in the deep infrared domain of the timelike region.

hep-ph↗

arXiv2003

Analytic invariant charge and the lattice static quark-antiquark potential

A recently developed model for the QCD analytic invariant charge is compared with quenched lattice simulation data on the static quark-antiquark potential. By employing this strong running coupling one is able to obtain the confining quark-antiquark potential in the framework of the one-gluon exchange model. To achieve this objective a technique for evaluating the integrals of a required form is developed. Special attention is paid here to removing the divergences encountered the calculations. All this enables one to examine the asymptotic behavior of the potential at both small and large distances with high accuracy. An explicit expression for the quark-antiquark potential, which interpolates between these asymptotics, and satisfies the concavity condition, is proposed. The derived potential coincides with the perturbative results at small distances, and it is in a good agreement with the lattice data in the nonperturbative physically-relevant region. An estimation of the parameter $Λ_{QCD}$ is obtained for the case of pure gluodynamics. It is found to be consistent with all the previous estimations of $Λ_{QCD}$ in the framework of approach in hand.

hep-ph↗

arXiv2003

Nonperturbative aspects of the QCD analytic invariant charge

In the framework of the analytic approach to Quantum Chromodynamics a new model for the strong running coupling has recently been developed. Its underlying idea is to impose the analyticity requirement on the perturbative expansion of the renormalization group $β$ function for restoring the correct analytic properties of the latter. The proposed model possesses a number of appealing features. Namely, the analytic invariant charge has no unphysical singularities at any loop level; it contains no free parameters; it has universal behavior both in ultraviolet and infrared regions at any loop level; and it possesses a fair higher loop and scheme stability. The extension of this model to the timelike region revealed the asymmetrical behavior of the running coupling in the intermediate- and low-energy domains of spacelike and timelike regions, that is essential when one handles the experimental data. The developed approach enables one to describe, in a consistent way, various strong interaction processes both of perturbative and intrinsically nonperturbative nature.

hep-ph↗

arXiv2002

Analytic invariant charge: non-perturbative aspects

A brief review of the recently developed model for the QCD analytic invariant charge is presented. The main idea of this approach is invoking the analyticity condition into the framework of the renormalization group method. More precisely, the analyticity requirement is explicitly imposed on the perturbative expansion of the $β$ function for restoring its correct analytic properties. The model possesses a number of profitable features. Namely, the analytic invariant charge has no unphysical peculiarities at any loop level; it contains no free parameters; it incorporates ultraviolet asymptotic freedom with infrared enhancement; it has universal behavior both in ultraviolet and infrared regions at any loop level; it possesses a good higher loop and scheme stability. There is considerable difference between the respective values of analytic invariant charge in the low-energy domain of spacelike and timelike regions. The approach proposed enables one to describe various strong interaction processes both of perturbative and intrinsically non-perturbative nature.

hep-ph↗

arXiv2001

New analytic running coupling in QCD: higher loop levels

The properties of the new analytic running coupling are investigated at the higher loop levels. The expression for this invariant charge, independent of the normalization point, is obtained by invoking the asymptotic freedom condition. It is shown that at any loop level the relevant $β$ function has the universal behaviors at small and large values of the invariant charge. Due to this feature the new analytic running coupling possesses the universal asymptotics both in the ultraviolet and infrared regions irrespective of the loop level. The consistency of the model considered with the general definition of the QCD invariant charge is shown.

hep-ph↗

arXiv2001

New analytic running coupling in spacelike and timelike regions

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) formalism. A new method for determining the coefficients of the "analytized" RG equation is elaborated. It enables one to take into account the higher loop contributions to the new analytic running coupling (NARC) in a consistent way. The expression for the new analytic running coupling, independent of the normalization point, is obtained by invoking the asymptotic freedom condition. It is shown that the difference between the values of the NARC in respective spacelike and timelike regions is rather valuable for intermediate energies. This is essential for the correct extracting of the running coupling from experimental data. The new analytic running coupling is applied to the description of the inclusive $τ$ lepton decay. The consistent estimation of the parameter $Λ_{QCD}$ is obtained here.

hep-ph↗

arXiv2001

New Model for the QCD Analytic Running Coupling

As an elaboration of the analytic approach to Quantum Chromodynamics (QCD), a new model for the QCD analytic running coupling is proposed. A self-evident advantage of the new analytic running coupling (NARC) is that it incorporates the infrared enhancement and the ultraviolet asymptotic freedom in a single expression. It is essential that additional parameters are not introduced in the theory. The absence of unphysical singularities in the physical region $q^2>0$ and a fairly well loop and scheme stability are the remarkable features of the NARC. By making use of practically the same values of $Λ_{QCD}$ in the approach developed, one succeeded in description of various physical phenomena, from quark confinement to the $τ$ lepton decay. This undoubtedly implies that the new analytic running coupling substantially involves both the nonperturbative and the perturbative behavior of Quantum Chromodynamics.

hep-ph↗

arXiv2001

Investigation of a new analytic running coupling in QCD

The mathematical properties of the new analytic running coupling (NARC) in QCD are investigated. This running coupling naturally arises under ``analytization'' of the renormalization group equation. One of the crucial points in our consideration is the relation established between the NARC and its inverse function. The latter is expressed in terms of the so-called Lambert $W$ function. This relation enables one to present explicitly the NARC in the renorminvariant form and to derive the corresponding $β$ function. The asymptotic behavior of this $β$ function is examined. The consistent estimation of the parameter $Λ_{QCD}$ is given.

hep-ph↗

arXiv2000

Quark confinement in the analytic approach to QCD

The interquark potential is constructed by making use of the new analytic running coupling in QCD. This running coupling arises under ``analytization'' of the renormalization group equation. The rising behavior of the interquark potential at large distances, which provides the quark confinement, is shown explicitly. The estimation of the parameter $Λ_{QCD}$ is obtained.

hep-ph↗

arXiv2000

Quark-antiquark potential in the analytic approach to QCD

The quark-antiquark potential is constructed by making use of a new analytic running coupling in QCD. This running coupling arises under ``analytization'' of the renormalization group equation. The rising behavior of the quark-antiquark potential at large distances, which provides the quark confinement, is shown explicitly. At small distances, the standard behavior of this potential originating in the QCD asymptotic freedom is revealed. The higher loop corrections and the scheme dependence of the approach are briefly discussed.

hep-ph↗

arXiv1998

Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder

Using the mode-by-mode summation technique the zero point energy of the electromagnetic field is calculated for the boundary conditions given on the surface of an infinite solid cylinder. It is assumed that the dielectric and magnetic characteristics of the material which makes up the cylinder $(ε_1, μ_1)$ and of that which makes up the surroundings $(ε_2, μ_2)$ obey the relation $ε_1μ_1= ε_2μ_2$. With this assumption all the divergences cancel. The divergences are regulated by making use of zeta function techniques. Numerical calculations are carried out for a dilute dielectric cylinder and for a perfectly conducting cylindrical shell. The Casimir energy in the first case vanishes, and in the second is in complete agreement with that obtained by DeRaad and Milton who employed a Green's function technique with an ultraviolet regulator.

hep-th↗