arXiv subjects

D. V. Shirkov

Publications and source records attributed to D. V. Shirkov.

At least 19 recordsLinked to original sources

arXiv2012

"Massive" Perturbative QCD, regular in the IR limit

The goal of research is to devise a modification of the perturbative QCD that should be regular in the low-energy region and could serve as a practical means for the analysis of data below 1 \GeV up to the IR limit. Recent observation of the four-loop pQCD series "blow-up" in the region below 1 \GeV for the Bjorken Sum Rule gave an impetus to this attempt. The proposed {\sf "massive analytic pQCD"} is constructed on the two grounds. The first is the pQCD with only one parameter added, the effective "glueball mass" $m_{gl}\lesssim 1 \GeV,$ serving as an IR regulator. The second stems out of the ghost-free Analytic Perturbation Theory comprising non-power perturbative expansion that makes it compatible with linear integral transformations. In short, the proposed MAPT differs from the minimal APT by simple ansatz $Q^2 \to Q^2+m_{gl}^2.$

hep-th↗

arXiv2012

A Few Lessons from pQCD Analysis at Low Energies

Motivated by the recent 4-loop analysis of the JLab data on Bjorken Sum Rule, where the pQCD series seems to blow up at $|Q|\lesssim 1.5\,\GeV, α_s \gtrsim 0.33\,,$ we overview the general origin of the divergency of common perturbation expansion over powers of a small coupling parameter in QFT and consider in detail the {\it blowing-up phenomenon} and accuracy of finite sums for simple alternating and non-alternating examples of divergent series.

hep-ph↗

arXiv2012

The (2+1)-dim Axial Universes -- Solutions to the Einstein Equations, Dimensional Reduction Points, and Klein-Fock-Gordon Waves

The paper presents a generalization and further development of our recent publications where solutions of the Klein-Fock-Gordon equation defined on a few particular $D=(2+1)$-dim static space-time manifolds were considered. The latter involve toy models of 2-dim spaces with axial symmetry, including dimension reduction to the 1-dim space as a singular limiting case. Here the non-static models of space geometry with axial symmetry are under consideration. To make these models closer to physical reality, we define a set of "admissible" shape functions $ρ(t,z)$ as the $(2+1)$-dim Einstein equations solutions in the vacuum space-time, in the presence of the $Λ$-term, and for the space-time filled with the standard "dust". It is curious that in the last case the Einstein equations reduce to the well-known Monge-Ampère equation, thus enabling one to obtain the general solution of the Cauchy problem, as well as a set of other specific solutions involving one arbitrary function. A few explicit solutions of the Klein-Fock-Gordon equation in this set are given. An interesting qualitative feature of these solutions relates to the dimension reduction points, their classification, and time behavior. In particular, these new entities could provide us with novel insight into the nature of P- and T-violation, and of Big Bang. A short comparison with other attempts to utilize dimensional reduction of the space-time is given.

gr-qc↗

arXiv2012

Dream-land with Classic Higgs field, Dimensional Reduction and all that

This text, on the one hand, is related to the talk delivered at the Conference "Gauge Fields. Yesterday, Today, Tomorrow", dedicated to the Andrej Slavnov 70th anniversary; on the other - in the form of a fairy tale - it summarizes some results of researches performed after this Fest, mainly due to discussion around the talk.

hep-th↗

arXiv2011

Four-loop QCD analysis of the Bjorken sum rule vs data

We study the polarized Bjorken sum rule at low momentum transfers in the range $0.22<Q<1.73 {\rm GeV}$ with the four-loop N$^3$LO expression for the coefficient function $C_{\rm Bj}(α_s)$ in the framework of the common QCD perturbation theory (PT) and the singularity-free analytic perturbation theory (APT). The analysis of the PT series for $C_{\rm Bj}(α_s)$ gives a hint to its asymptotic nature manifesting itself in the region $Q<1$ GeV. It relates to the observation that the accuracy of both the three- and four-loop PT predictions happens to be at the same 10% level. On the other hand, the usage of the two-loop APT allows one to describe the precise low energy JLab data down to $Q\sim 300$ MeV and gives a possibility for reliable extraction of the higher twist (HT) corrections. At the same time, above $Q\sim 700$ MeV the APT two-loop order with HT is equivalent to the four-loop PT with HT compatible to zero and is adequate to current accuracy of the data.

hep-ph↗

arXiv2011

Solutions of the Klein-Gordon equation on manifolds with variable geometry including dimensional reduction

We develop the recent proposal to use dimensional reduction from the four-dimensional space-time D=(1+3) to the variant with a smaller number of space dimensions D=(1+d), d < 3, at sufficiently small distances to construct a renormalizable quantum field theory. We study the Klein-Gordon equation on a few toy examples ("educational toys") of a space-time with variable special geometry, including a transition to a dimensional reduction. The examples considered contain a combination of two regions with a simple geometry (two-dimensional cylindrical surfaces with different radii) connected by a transition region. The new technique of transforming the study of solutions of the Klein-Gordon problem on a space with variable geometry into solution of a one-dimensional stationary Schrödinger-type equation with potential generated by this variation is useful. We draw the following conclusions: (1) The signal related to the degree of freedom specific to the higher-dimensional part does not penetrate into the smaller-dimensional part because of an inertial force inevitably arising in the transition region (this is the centrifugal force in our models). (2) The specific spectrum of scalar excitations resembles the spectrum of the real particles; it reflects the geometry of the transition region and represents its "fingerprints". (3) The parity violation due to the asymmetric character of the construction of our models could be related to violation of the CP symmetry.

hep-th↗

arXiv2010

Coupling running through the Looking-Glass of dimensional Reduction

The dimensional reduction, in a form of transition from four to two dimensions, was used in the 90s in a context of HE Regge scattering. Recently, it got a new impetus in quantum gravity where it opens the way to renormalizability and finite short-distance behavior. We consider a QFT model $g\,φ^4\,$ with running coupling defined in both the two domains of different dimensionality; the $\gbar(Q^2)\,$ evolutions being duly conjugated at the reduction scale $\,Q\sim M.$ Beyond this scale, in the deep UV 2-dim region, the running coupling does not increase any more. Instead, it {\it slightly decreases} and tends to a finite value $\gbar_2(\infty) \,< \, \gbar_2(M^2)\,$ from above. As a result, the global evolution picture looks quite peculiar and can propose a base for the modified scenario of gauge couplings behavior with UV fixed points provided by dimensional reduction instead of leptoquarks.

hep-th↗

arXiv2009

Remembering Nikolai Nikolaevich Bogoliubov

The recollection of souvenirs on great theoretical physicist, addressed to wide physical audience on the occasion of Bogoliubov centenary. Contains four parts: 1. Personal impressions; 2. Joint work; 3. Bogoliubov cp. Landau and 4. Scientist and Teacher.

physics.hist-ph↗

arXiv2009

60 years of Broken Symmetries in Quantum Physics (From the Bogoliubov Theory of Superfluidity to the Standard Model)

A retrospective historical overview of the phenomenon of spontaneous symmetry breaking (SSB) in quantum theory, the issue that has been implemented in particle physics in the form of the Higgs mechanism. The main items are: -- The Bogoliubov's microscopical theory of superfluidity (1946); -- The BCS-Bogoliubov theory of superconductivity (1957); -- Superconductivity as a superfluidity of Cooper pairs (Bogoliubov - 1958); -- Transfer of the SSB into the QFT models (early 60s); -- The Higgs model triumph in the electro-weak theory (early 80s). The role of the Higgs mechanism and its status in the current Standard Model is also touched upon.

physics.hist-ph↗

arXiv2008

Renormalization-group symmetries for solutions of nonlinear boundary value problems

Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concepts of functional self-similarity and of the Bogoliubov renormalization group treated as a Lie group of continuous transformations. Overwhelmingly dominating practical quantum field theory calculations, the renormalization-group method formed the basis for the discovery of the asymptotic freedom of strong nuclear interactions and underlies the Grand Unification scenario. This paper describes the logical framework of a new algorithm based on the modern theory of transformation groups and presents the most interesting results of application of the method to differential and/or integral equation problems and to problems that involve linear functionals of solutions. Examples from nonlinear optics, kinetic theory, and plasma dynamics are given, where new analytical solutions obtained with this algorithm have allowed describing the singularity structure for self-focusing of a laser beam in a nonlinear medium, studying generation of harmonics in weakly inhomogeneous plasma, and investigating the energy spectra of accelerated ions in expanding plasma bunches.

math-ph↗

arXiv2008

Novel Sets of Coupling Expansion Parameters for low-energy pQCD

In quantum theory, physical amplitudes are usually presented in the form of Feynman perturbation series in powers of coupling constant $\al .$ However, it is known that these amplitudes are not regular functions at $α=0 .$ For QCD, we propose new sets of expansion parameters ${\bf w}_k(\as)$ that reflect singularity at $\as=0 $ and should be used instead of powers $\as^k.$ Their explicit form is motivated by the so called Analytic Perturbation Theory. These parameters reveal saturation in a strong coupling case at the level $\as^{eff}(\as\gg1)={\bf w}_1(\as\gg 1) \sim 0.5 .$ They can be used for quanitative analysis of divers low-energy amplitudes. We argue that this new picture with non-power sets of perturbation expansion parameters, as well as the saturation feature, is of a rather general nature.

hep-ph↗

arXiv2007

Bound state approach to the QCD coupling at low energy scales

We exploit theoretical results on the meson spectrum within the framework of a Bethe-Salpeter (BS) formalism adjusted for QCD, in order to extract an ``experimental'' coupling α_s^{exp}(Q^2) below 1 GeV by comparison with the data. Our results for α_s^{exp}(Q^2) exhibit a good agreement with the infrared safe Analytic Perturbation Theory (APT) coupling from 1 GeV down to 200 MeV. As a main result, we claim that the combined BS-APT theoretical scheme provides us with a rather satisfactory correlated understanding of very high and low energy phenomena.

hep-ph↗

arXiv2006

Ten years of the Analytic Perturbation Theory in QCD

The renormalization group method enables one to improve the properties of the QCD perturbative power series in the ultraviolet region. However, it ultimately leads to the unphysical singularities of observables in the infrared domain. The Analytic Perturbation Theory constitutes the next step of the improvement of perturbative expansions. Specifically, it involves additional analyticity requirement which is based on the causality principle and implemented in the Källen--Lehmann and Jost--Lehmann representations. Eventually, this approach eliminates spurious singularities of the perturbative power series and enhances the stability of the latter with respect to both higher loop corrections and the choice of the renormalization scheme. The paper contains an overview of the basic stages of the development of the Analytic Perturbation Theory in QCD, including its recent applications to the description of hadronic processes.

hep-ph↗

arXiv2006

Analytic Perturbation Theory for Practitioners and Upsilon Decay

Within the ghost-free Analytic Perturbation Theory (APT), devised in the last decade for low energy QCD, simple approximations are proposed for 3-loop analytic couplings and their effective powers, in both the space-like (Euclidean) and time-like (Minkowskian) regions, accurate enough in the large range (1--100 GeV) of current physical interest.\par Effectiveness of the new Model is illustrated by the example of $Υ(1\mathrm{S})$ decay where the standard analysis gives $α_s(M_Υ)=0.170\pm 0.004$ value that is inconsistent with the bulk of data for $α_s$. Instead, we obtain $α_s^{Mod}(M_Υ)=0.185\pm 0.005$ that corresponds to $α_s^{Mod}(M_Z)=0.120\pm 0.002 $ that is close to the world average.\par The issue of scale uncertainty for $Υ$ decay is also discussed.

hep-ph↗

arXiv2006

Analytic Perturbation Theory Model for QCD and Upsilon Decay

An elegant and more precise formula for the 3-loop perturbative QCD coupling is discussed. It improves the common expression (e.g., canonized by PDG) in few GeV region. On its base, we propose simple analytic Model for ghost-free QCD running couplings and their effective powers within the Analytic Perturbation Theory, in both the space-like (Euclidean) and time-like (Minkowskian) regions, very accurate in the range above 1 GeV. Effectiveness of the new Model is illustrated by the example of Upsilon(1S) decay where the standard analysis gives $α_s(M_{\Ups})=0.170\pm 0.004$ value that is inconsistent with the bulk of data. Instead, we obtain $α_s(M_{\Ups})=0.185\pm 0.005$ that corresponds to $α_s(M_Z)=0.120\pm 0.002 $ that is close to the world average.

hep-ph↗

arXiv2005

QCD Effective Couplings in Minkowskian and Euclidean Domains

We argue for essential upgrading of the defining equations (9.5) and (9.6) in Section 9.2 "The QCD coupling ... " of PDG review and their use for data analysis in the light of recent development of the QCD theory. Our claim is twofold. First, instead of universal expression (9.5) for QCD coupling $\barα_s$, one should use various ghost-free couplings $α_E(Q^2), α_M(s)...$ specific for a given physical representation, Euclidean, Mincowskian etc. Second, instead of power expansion (9.6) for observable, we recommend to use nonpower functional ones over particular functional sets ${{\cal A}_k(Q^2)}$, ${{\mathfrak A}_k(s)}...$ related by suitable integral transformations. We remind that use of this modified prescription results in a better correspondence of reanalyzed low energy data with the high energy ones.

hep-ph↗

arXiv2005

Renormgroup symmetry for solution functionals

The paper contains generalization of the renormgroup algorithm for boundary value problems of mathematical physics and related concept of the renormgroup symmetry, formulated earlier by authors with reference to models based on differential equations. These algorithm and symmetry are formulated now for models with non local (integral) equations. We discuss in detail and illustrate by examples applications of the generalized algorithm to models with not local terms which appear as linear functionals of the solution.

math-ph↗

arXiv2004

Nonpower Expansions for QCD Observables at Low Energies

A comprehensive review is presented of the progress made in further developing the ghost-free Analytic Approach to low-energy QCD since "QCD-97" meeting. It is now formulated as a logically closed ``Analytic Perturbation Theory" algorithm. Its most essential feature is nonpower functional expansions for QCD observables.

hep-ph↗