Searcharxiv⌕ Search

arXiv subjects

D. V. Shirkov

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

At least 37 records · Page 2Linked to original sources
arXiv2003

On the Fourier transformation of Renormalization Invariant Coupling

Integral transformations of the QCD invariant (running) coupling and of some related objects are discussed. Special attention is paid to the Fourier transformation, that is to transition from the space-time to the energy--momentum representation. The conclusion is that the condition of possibility of such a transition provides us with one more argument against the real existence of unphysical singularities observed in the perturbative QCD. The second conclusion relates to the way of "translation" of some singular long--range asymptotic behaviors to the infrared momentum region. Such a transition has to be performed with the due account of the Tauberian theorem. This comment relates to the recent ALPHA collaboration results on the asymptotic behavior of the QCD effective coupling obtained by lattice simulation.

hep-th↗
arXiv2002

On the QCD coupling behavior in the infrared region

The summary of nonperturbative results for the QCD invariant coupling bar{alpha}_s obtained by lattice simulations for functional integral and by solution of approximate Dyson--Schwinger equations reveals a puzzling variety of IR behavior of bar{alpha}_s(Q^2) even on a qualitative level. This, in turn, rises a question of correspondence between the results obtained so far by different groups. We analyze this issue in terms of mass-dependent coupling constant transformations and conclude that the question of the IR behavior of effective QCD coupling and of propagators is not a well--defined one and needs to be more specified.

hep-ph↗
arXiv2001

Analytic Perturbation Theory in analyzing some QCD observables

The paper is devoted to application of recently devised ghost-free Analytic Perturbation Theory (APT) for analysis of some QCD observables. We start with the discussion of the main problem of the perturbative QCD -- ghost singularities and with the resume of this trouble solution within the APT. By a few examples in the various energy and momentum transfer regions (with the flavor number f=3, 4 and 5) we demonstrate the effect of improved convergence of the APT modified perturbative QCD expansion. Our first observation is that in the APT analysis the three-loop contribution $\sim α_s^3$) is as a rule numerically inessential. This gives raise a hope for practical solution of the well-known problem of asymptotic nature of common QFT perturbation series. The second result is that a usual perturbative analysis of time-like events with the big $π^2$ term in the $α_s^3$ coefficient is not adequate at $s\leq 2 \GeV^2$. In particular, this relates to $τ$ decay. Then, for the "high" (f=5) region it is shown that the common two-loop (NLO, NLLA) perturbation approximation widely used there (at $10 \GeV\lesssim\sqrt{s}\lesssim 170 \GeV$) for analysis of shape/events data contains a systematic negative error of a 1--2 per cent level for the extracted $\bar{alpha}_s^{(2)} $ values. Our physical conclusion is that the $\bar{alpha}_s(M^2_Z)$ value averaged over the f=5 data appreciably differs $ _{f=5}\simeq 0.124$ from the currently accepted "world average" (=0.118).}

hep-ph↗
arXiv2001

The $π^2$ terms in the s-channel QCD observables

We analyze the effect of $π^2$-terms in the QCD perturbative expansions for the s-channel effective coupling and observables, the effect known from the 80s. We remind that these terms can be collected into specific functions -- strong s-channel coupling $\tildaα_s$ and its effective powers ${\mathfrak A}(s)$ free of ghost singularities. Further on, we study the structure of perturbation theory for observables and its reformulation in terms of nonpower perturbation expansion over the set $\{\mathfrak A}(s)\}.$\par values of $α_s$ as extracted from experiments. The main result is that the common two-loop (NLO, NLLA) approximation widely used in the five-quark ($10 \GeV\lesssim \sqrt{s}\lesssim 170 \GeV$) region for a shape analysis contains a systematic negative error of a 1-2 per cent order of magnitude for the extracted $\barα_s^{(2)}$. Our physical conclusion is that the $α_s(M_Z)$ value averaged over the f=5 data $<α_s(M_Z)>_{f=5} \simeq 0.124$ appreciably differs from the currently accepted "world average" (=0.118).}

hep-ph↗
arXiv2000

Analytic Perturbation Theory for QCD observables

The connection between ghost-free formulations of RG-invariant perturbation theory in the both Euclidean and Minkowskian regions is studied. Our basic tool is the "double spectral representation", similar to definition of Adler function, that stems from first principles of local QFT. It relates real functions defined in the Euclidean and Minkowskian regions. On this base we establish a simple relation between -- The trick of resummation of the $π^2$-terms (known from early 80s) for the invariant QCD coupling and observables in the time-like region and -- Invariant Analytic Approach (devised a few years ago) with the "analyticized" coupling $α_{\rm an}(Q^2)$ and nonpower perturbative expansion for observables in the space-like domain which are free of unphysical singularities . As a result, we formulate a self-consistent scheme, Analytic Perturbation Theory (APT), that relates a renorm-invariant, effective coupling functions $α_{an}(Q^2) $ and $\tilda{alpha}(s),$ as well as non-power perturbation expansions for observables in both space- and time-like domains, that are free of extra singularities and obey better convergence in the infrared region. Then we consider the quark threshold crossing and devise a global APT scheme for the data analysis in the whole accessible space-like and time-like domain with various numbers of active quarks. Preliminary estimates indicate that this global scheme produces results a bit different, sometimes even in the five-flavour region, on a few per cent level for $\barα_s$ -- from the usual one, thus influencing the total picture of the QCD parameter correlation.

hep-ph↗
arXiv2000

Toward the correlated analysis of perturbative QCD observables

We establish direct connection between ghost-free formulations of RG-invariant perturbation theory in the both Euclidean and Minkowskian regions. By combining the trick of resummation of the $π^2$-terms for the invariant QCD coupling and observables in the time-like region with fresh results on the "analyticized" coupling $α_{\rm an}(Q^2)$ and observables in the space-like domain we formulate a self-consistent scheme, free of ghost troubles. The basic point of this joint construction is the "dipole spectral relation" emerging from axioms of local QFT. Then we consider the issue of the heavy quark thresholds and devise a global scheme for the data analysis in the whole accessible space-like and time-like domain with various numbers of active quarks. Observables in both the regions are presented in a form of non-power perturbation series with improved convergence properties. Preliminary estimates indicate that this global scheme produces results a bit different - on a few per cent level for $\barα_s$ - from the usual one, thus influencing the total picture of the QCD parameters correlation.

hep-ph↗
arXiv1999

Analytic Approach in Quantum Chromodynamics

We investigate a new ``renormalization invariant analytic formulation'' of calculations in quantum chromodynamics, where the renormalization group summation is correlated with the analyticity with respect to the square of the transferred momentum $Q^2$. The expressions for the invariant charge and matrix elements are then modified such that the unphysical singularities of the ghost pole type do not appear at all, being by construction compensated by additional nonperturbative contributions. Using the new scheme, we show that the results of calculations for a number of physical processes are stable with respect to higher-loop effects and the choice of the renormalization prescription. Having in mind applications of the new formulation to inelastic lepton-nucleon scattering processes, we analyze the corresponding structure functions starting from the general principles of the theory expressed by the Jost-Lehmann-Dyson integral representation. We use a nonstandard scaling variable that leads to modified moments of the structure functions possessing Källén-Lehmann analytic properties with respect to $Q^2$. We find the relation between these ``modified analytic moments'' and the operator product expansion.

hep-ph↗
arXiv1999

Evolution of the Bogoluibov Renormalization Group

We start with a simple introduction into the renormalization group (RG) in quantum field theory and give an overview of the renormalization group method. The third section is devoted to essential topics of the renorm-group use in the QFT. Here, some fresh results are included. Then we turn to the remarkable proliferation of the RG ideas into various fields of physics. The last section summarizes an impressive recent progress of the "QFT renormalization group" application in mathematical physics.

hep-th↗
arXiv1999

$e^+e^-$ annihilation at low energies in analytic approach to QCD

We begin with short review of the analytic approach (AA) to QCD recently developed and applied to the process of $e^+e^-$ annihilation into hadrons at low energies. Besides summary of the theoretical description of smeared experimental data for the $R$ cross-section ratio we give fresh analogous result for the corresponding Adler function, $D(Q^2)$, and demonstrate excellent agreement between the AA theoretical results and data in the low $Q^2$ region.

hep-ph↗
arXiv1999

The Unitary Mechanism of Infrared Freezing in QCD with massive gluons

A "natural" model for the QCD invariant (running) coupling, free of the IR singularity, is proposed. It is based upon the hypothesis of finite gluon mass $ m_{gl}$ existence and, technically, uses an accurate treating of threshold behavior of Feynman diagram contribution. The model correlates with the unitarity condition. Quantitative estimate, performed in the one-loop approximation yields a reasonable lower bound for this mass $m_{gl} > 150$ MeV and a smooth IR freezing at the level $α_s(Q^2)\lesssim 1$.

hep-ph↗
arXiv1999

The Bogoluibov Renormalization Group in Theoretical and Mathematical Physics

This text follows the line of a talk on Ringberg symposium dedicated to Wolfhart Zimmermann 70th birthday. The historical overview (Part 1) partially overlaps with corresponding text of my previous commemorative paper. At the same time second part includes some recent results in QFT and summarize an impressive progress of the "QFT renormalization group" application in mathematical physics.

hep-th↗
arXiv1999

Renorm-group, Causality and Non-power Perturbation Expansion in QFT

The structure of the QFT expansion is studied in the framework of a new "Invariant analytic" version of the perturbative QCD. Here, an invariant (running) coupling $a(Q^2/Λ^2)=β_1α_s(Q^2)/4π$ is transformed into a "$Q^2$--analytized" invariant coupling $a_{\rm an}(Q^2/Λ^2) \equiv {\cal A}(x)$ which, by constuction, is free of ghost singularities due to incorporating some nonperturbative structures. Meanwhile, the "analytized" perturbation expansion for an observable $F$, in contrast with the usual case, may contain specific functions ${\cal A}_n(x)= [a^n(x)]_{\rm an}$, the "n-th power of $a(x)$ analytized as a whole", instead of $({\cal A}(x))^n$. In other words, the pertubation series for $F(x)$, due to analyticity imperative, may change its form turning into an {\it asymptotic expansion à la Erdélyi over a nonpower set} $\{{\cal A}_n(x)\}$. We analyse sets of functions $\{{\cal A}_n(x)\}$ and discuss properties of non-power expansion arising with their relations to feeble loop and scheme dependence of observables. The issue of ambiguity of the invariant analytization procedure and of possible inconsistency of some of its versions with the RG structure is also discussed.

hep-th↗
arXiv1997

Analytic Approach to Perturbative QCD and Renormalization Scheme Dependence

We further develop the approach recently used to construct an analytic ghost-free model for the QCD running coupling based on the requirement of the $Q^2$-analyticity and apply it to the process of $e^+e^-$ annihilation into hadrons to study the renormalization scheme dependence of the $R(s)$ cross-section ratio. \par By transforming the relevant QCD corrections up to the three-loop level into the "analytized" form we show that the $R_{AA}(s)$ expression thus obtained is remarkably stable (as compared to the conventional perturbative approach) with respect to the renormalization scheme dependence for the whole low-energy region.

hep-ph↗
arXiv1997

On the Analytic "Causal" Model for the QCD Running Coupling

We discuss the model $\barα_{an}(Q^2)$ recently proposed for the QCD running coupling $\barα_s(Q^2)$ in the Euclidean domain on the basis of the "asymptotic-freedom" expression and on causality condition in the form of the $Q^2$-analyticity. The model contains no adjustable parameters and obeys the important features: (i) Finite ghost-free behavior in the "low $Q^2$" region and correspondence with the standard RG-summed UV expressions;%\item~ % (ii) The universal limiting value $\barα_{an}(0)$ expressed only via group symmetry factors. This value as well as the $\barα_{an}$ behavior in the whole IR region $Q^2 \leq Λ^2$ turns out to be stable with respect to higher loop corrections; %\item~ (iii) Coherence between observed $\barα_s(M_τ^2)$ value and integral information on the IR $\barα_s(Q^2)$ behavior extracted from jet physics.

hep-ph↗
arXiv1997

Continuous mass-dependent analysis of the non-singlet $xF_3$ CCFR data

We consider the issue of an accurate description of the evolution of the non-singlet structure function moments $M_n(Q)$ near heavy quark threshold. To this aim we propose a simple modification of the standard massless \MSbar scheme approach to the next-to-leading QCD analysis of DIS data. We apply it to the processing of the modern CCFR'97 data for $xF_3$ structure function and extract the value of $α_s(M_z) \approx 0.122 \pm 0.004$ We check also the consistency of light gluino hypothesis with CCFR'97 data.

hep-ph↗
arXiv1997

Group analysis and renormgroup symmetries

An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries, based on modern group analysis are described. Application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model.

hep-th↗
arXiv1997

Analytic Model for the QCD Running Coupling with Universal $\barα_s(0)$ Value

We discuss the new model expression $\barα_{an}(Q^2)$ recently obtained for the QCD running coupling with a regular ghost-free behavior in the "low $Q^2$" region. Being deduced from the standard "asymptotic-freedom" expression by imposing the $Q^2$-analyticity -- without any adjustable parameters -- it obeys nice features: (i) The universal limiting value $\barα_{an}(0)=4π/β_0 \simeq 1.4$ expressed only via group symmetry factors and independent of experimental estimates on the running coupling $\barα_s(Q^2)$ (of QCD scale parameter $Λ$). This value turns out to be stable with respect to higher order corrections; (ii) Stability of IR behavior with respect to higher-loop effects; (iii) Coherence between the experimental $\barα_{an}(M_τ^2)$ value and integral information on IR $\barα_s(Q^2)$ behavior as extracted from jet physics data.

hep-ph↗