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I. L. Solovtsov

Publications and source records attributed to I. L. Solovtsov.

At least 19 recordsLinked to original sources
arXiv2007

On statistical methods of structure function extraction

Several methods of statistical analysis are proposed and analyzed in application for a specific task -- extraction of the structure functions from the cross sections of deep inelastic interactions of any type. We formulate the method based on the orthogonal weight functions and on an optimization procedure of errors minimization as well as methods underlying common $χ^2$ minimization. Effectiveness of these methods usage is analyzed by comparison of the statistical parameters such as bias, extraction variance etc., for sample deep inelastic scattering data set.

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↗
arXiv2005

An analytic method of describing $R$-related quantities in QCD

A model based on the analytic approach to QCD, involving a summation of threshold singularities and taking into account the nonperturbative character of the light quark masses, is applied to find hadronic contributions to different physical quantities. It is shown that the suggested model allows us to describe well such objects as the hadronic contribution to the anomalous magnetic moment of the muon, the ratio of hadronic to leptonic $τ$-decay widths in the vector channel, the Adler $D$-function, the smeared $R_Δ$-function, and the hadronic contribution to the evolution of the fine structure constant.

hep-ph↗
arXiv2002

Remark on the perturbative component of inclusive $τ$-decay

In the context of the inclusive $τ$-decay, we analyze various forms of perturbative expansions which have appeared as modifications of the original perturbative series. We argue that analytic perturbation theory, which combines renormalization-group invariance and $Q^2$-analyticity, has significant merits favoring its use to describe the perturbative component of $τ$-decay.

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

The Adler Function for Light Quarks in Analytic Perturbation Theory

The method of analytic perturbation theory, which avoids the problem of ghost-pole type singularities and gives a self-consistent description of both spacelike and timelike regions, is applied to describe the "light" Adler function corresponding to the non-strange vector channel of the inclusive decay of the $τ$ lepton. The role of threshold effects is investigated. The behavior of the quark-antiquark system near threshold is described by using a new relativistic resummation factor. It is shown that the method proposed leads to good agreement with the ``experimental'' Adler function down to the lowest energy scale.

hep-ph↗
arXiv2000

Renormalization Scheme and Higher Loop Stability in Hadronic $τ$ Decay within Analytic Perturbation Theory

We apply an analytic description to the inclusive decay of the $τ$ lepton. We argue that this method gives not only a self-consistent description of the process both in the timelike region by using the initial expression for $R_τ$ and in the spacelike domain by using the analytic properties of the hadronic correlator, but also leads to the fact that theoretical uncertainties associated with unknown higher-loop contributions and renormalization scheme dependence can be reduced dramatically.

hep-ph↗
arXiv2000

Timelike and spacelike QCD characteristics of the $e^+e^-$ annihilation process

We consider the Adler $D$-function, which is defined in the spacelike region, and the $e^+e^-$ annihilation ratio smeared, according to the Poggio, Quinn, and Weinberg method, which is determined for timelike argument. We show that the method of the nonperturbative $a$-expansion allows one to describe these Euclidean and Minkowskian characteristics of the process of $e^+e^-$ annihilation down to the lowest energy scales.

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

$e^+e^-$ 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↗
arXiv1998

The Bjorken Sum Rule in the Analytic Approach to Perturbative QCD

Results of applying analytic perturbation theory (APT) to the Bjorken sum rule are presented. We study the third-order QCD correction within the analytic approach and investigate its renormalization scheme dependence. We demonstrate that, in the framework of the method, theoretical predictions of the Bjorken sum rule are, practically, scheme independent for the entire interval of momentum transfer.

hep-ph↗
arXiv1998

The Gross--Llewellyn Smith Sum Rule in the Analytic Approach to Perturbative QCD

We apply analytic perturbation theory to the Gross--Llewellyn Smith sum rule. We study the $Q^2$ evolution and the renormalization scheme dependence of the analytic three-loop QCD correction to this sum rule, and demonstrate that the results are practically renormalization scheme independent and lead to rather different $Q^2$ evolution than the standard perturbative correction possesses.

hep-ph↗
arXiv1998

Analytic Perturbative Approach to QCD

A technique called analytic perturbation theory, which respects the required analytic properties, consistent with causality, is applied to the definition of the running coupling in the timelike region, to the description of inclusive $τ$-decay, to deep-inelastic scattering sum rules, and to the investigation of the renormalization scheme ambiguity. It is shown that in the region of a few GeV the results are rather different from those obtained in the ordinary perturbative description and are practically renormalization scheme independent.

hep-ph↗
arXiv1998

Conformal Mapping, Power Corrections, and the QCD Bound State Spectrum

We analyze the heavy quark bound state spectrum using an order-dependent conformal mapping to re-sum the perturbative expansion for current correlators. The procedure consists of two main steps. Firstly, the Borel plane structure of the truncated perturbative expression is modified to ensure consistency with the operator product expansion. This is analogous to a resummation of infrared renormalon chains. Secondly, this perturbative expansion is conformally mapped to a new series with improved convergence properties. This approach may be shown to induce power corrections consistent with existing condensates, and the resulting expansion may be ordered in powers of an infrared-analytic effective coupling. The technique is then applied to $c\bar{c}$ and $b\bar{b}$ sum rules without any explicit introduction of vacuum condensate parameters. Ground state masses for the vector, axial--vector, and $A'$ channels are well reproduced, while results for the scalar--pseudoscalar mass splitting are less impressive.

hep-ph↗
arXiv1998

Analytic Perturbation Theory and Renormalization Scheme Dependence in Tau Decay

We apply analytic perturbation theory in next-to-next-to-leading order to inclusive semileptonic $τ$-decay and study the renormalization scheme dependence. We argue that the renormalization scheme ambiguity is considerably reduced in the analytic perturbation theory framework and we obtain a rather stable theoretical prediction.

hep-ph↗
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

Analytic Perturbation Theory and Inclusive Tau Decay

We apply analytic perturbation theory to the inclusive decay of a $τ$ lepton into hadrons. It is shown that the resulting analyticity of the coupling constant strongly influences the value of the QCD $Λ$-parameter extracted from the experimental data on $τ$ decay.

hep-ph↗