arXiv subjects

S. V. Mikhailov

Publications and source records attributed to S. V. Mikhailov.

At least 19 recordsLinked to original sources

arXiv2026

Optimization of perturbation series in QCD for physical quantities using the renormalization group: necessary conditions and partial results

We explore approaches to numerically optimize a segment of the perturbative series for physical quantities using the QCD renormalization group. We apply these methods to the perturbative series for the coefficient function $C_{Bjps}$ of the Bjorken polarized sum rule and the Adler function $D_A$. Using various techniques proposed in the literature, we discuss the consequences of ``optimization.''

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arXiv2025

Extending the LCSR method to the electromagnetic pion form factor at low momenta using QCD renormalization-group summation

We obtain the electromagnetic pion form factor (emFF) $F_π$ for spacelike mid-range of momentum transfer in QCD. We use renormalization group (RG) summation within the light cone sum rules (LCSRs) to obtain the QCD radiative corrections to the $F_π$ and involve contributions of the leading twist 2 and, twists 4, 6. The additional conditions to apply here this RG summation are discussed in details. The strong coupling constants in this approach are free of Landau singularities, which allows one to go down to the lower transferred momentum $Q^2$. The prediction of the calculations performed reproduces the experimental data below/around $Q^2= 1$~GeV$^2$ significantly better than analogous predictions based on a fixed-order power-series expansion in the standard QCD.

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arXiv2024

Adler function, Bjorken polarized sum rule: confirmation of elements of the $\{β\}$-expansion and the diagrams

Different ways exist to obtain the elements of the $\{β\}$-expansion for renormgroup invariant quantities. Here we consider independent confirmation within the standard QCD of a number of our results [1] for the values of elements of this expansion for the nonsinglet Adler $D_A$-function, Bjorken polarized sum rules $S^{Bjp}$ up to the order N$^4$LO. We suggest an approach to estimate the results of high order QCD calculations using a smaller number of diagrams of the specific type. This type is based on a proposed generalization of Naive NonAbelianization.

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arXiv2023

Endpoint behavior of distribution amplitudes of pion and longitudinally polarized rho meson under the influence of renormalon-chain contributions

We calculate the two-point massless QCD correlator of nonlocal (composite) vector quark currents with chains of fermion one-loop radiative corrections inserted into gluon lines. The correlator depends on the Bjorken fraction $x$ related to the composite current and, under large-$β_0$ approximation, gives the main contributions in each order of perturbation theory. In the mentioned approximation, these contributions dominate the endpoint behavior of the leading-twist distribution amplitudes of light mesons in the framework of QCD sum rules. Based on this, we analyze the endpoint behavior of these distribution amplitudes for $π$ and longitudinally polarized $ρ^\|$ mesons and find inequalities for their moments.

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arXiv2023

Correlators of vector, tensor, and scalar composite vertices of order $O(α_s^2β_0)$

We present analytical results for massless correlators of two vector, tensor, and scalar composite vertices with the Bjorken fractions $x$ and $y$ of order $α_s^2 β_0$ of QCD. The structure of these correlators $Π^\text{V,T,S}(x,y; p^2)$ and properties of its main elements are discussed in detail. Special attention is paid to verifying the results and comparing them with known particular cases. We apply the correlators to evaluate radiative corrections to the distribution amplitudes of light mesons within the QCD sum rules.

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arXiv2023

Renormalon-chain contributions to two-point correlators of nonlocal quark currents

We calculate, within massless QCD, a two-point correlator of nonlocal (composite) vector quark currents with arbitrary-length chains of the simplest fermion loops being inserted into gluon lines. Within the large $n_f$ (or large $β_0$) approximation, the correlator defines a perturbative contribution to the leading-twist distribution amplitudes for light mesons. Our results are consistent with a number of special cases in the literature. We consider functionals of the correlator, which are important for the phenomenology, and their properties as function series.

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arXiv2022

The $\{β\}$-expansion for Adler function, Bjorken Sum Rule, and the Crewther-Broadhurst-Kataev relation at order $O(α_s^4)$

We derive explicit expressions for the elements of the $\{ β\}$-expansion for the nonsinglet Adler $D_A$-function and Bjorken polarized sum rules $S^{Bjp}$ in the N$^4$LO using recent results by Chetyrkin for these quantities computed within extended QCD including any number of fermion representations. We discuss the properties of the $\{ β\}$-expansion for $D_A$ and $S^{Bjp}$ at higher orders which follow from the Crewther [1] and the Broadhurst-Kataev [2] relation.

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arXiv2022

Two-loop kite master integral for a correlator of two composite vertices

We consider the most general two-loop massless correlator $I(n_1,n_2,n_3,n_4,n_5; x,y;D)$ of two composite vertices with the Bjorken fractions $x$ and $y$ for arbitrary indices $\{n_i\}$ and space-time dimension $D$; this correlator is represented by a "kite" diagram. The correlator $I(\{n_i\};x,y;D)$ is the generating function for any scalar Feynman integrals related to this kind of diagrams. We calculate $I(\{n_i\};x,y;D)$ and its Mellin moments in a direct way by evaluating hypergeometric integrals in the $α$ representation. The result for $I(\{n_i\};x,y;D)$ is given in terms of a double hypergeometric series -- the Kampé de Férriet function. In some particular but still quite general cases it reduces to a sum of generalized hypergeometric functions $_3F_2$. The Mellin moments can be expressed through generalized Lauricella functions, which reduce to the Kampé de Férriet functions in several physically interesting situations. A number of Feynman integrals involved and relations for them are obtained.

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arXiv2021

Cross-link relations between $π$ and $ρ$-meson channels and the QCD vacuum

We discuss cross-link relations between the $π$ and $ρ$-meson channels emerging from two different descriptions of the QCD vacuum: Instanton physics and QCD sum rules with nonlocal condensates (NLC). We derive in both schemes an intriguing linear relation between the $π$ and the $ρ^\|$-meson distribution amplitudes in terms of their conformal coefficients and work out the specific impact of the scalar NLC in these two channels. Using a simple model with Gaussian decay of the scalar NLC, we are able to relate it to the moments of the pion non-singlet parton distribution function measurable in experiment -- a highly nontrivial result. The implications for the pion and the $ρ^\|$-meson DAs entailed by the obtained cross-link relations are outlined in terms of two generic scenarios.

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arXiv2021

Extending the application of the LCSR method to low momenta using QCD renormalization-group summation. Theory and phenomenology

We show that using renormalization-group summation to generate the QCD radiative corrections to the $π-γ$ transition form factor, calculated with lightcone sum rules (LCSR), renders the strong coupling free of Landau singularities while preserving the QCD form-factor asymptotics. This enables a reliable applicability of the LCSR method to momenta well below 1 GeV$^2$. This way, one can use the new preliminary BESIII data with unprecedented accuracy below 1.5 GeV$^2$ to fine tune the prefactor of the twist-six contribution. Using a combined fit to all available data below 3.1 GeV$^2$, we are able to determine all nonperturbative scale parameters and a few Gegenbauer coefficients entering the calculation of the form factor. Employing these ingredients, we determine a pion distribution amplitude with conformal coefficients $(b_2,b_4)$ that agree at the $1σ$ level with the data for $Q^2 \leqslant 3.1$ GeV$^2$ and fulfill at the same time the lattice constraints on $b_2$ at N$^3$LO together with the constraints from QCD sum rules with nonlocal condensates.The form-factor prediction calculated herewith reproduces the data below 1 GeV$^2$ significantly better than analogous predictions based on a fixed-order power-series expansion in the strong coupling constant.

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arXiv2020

Calculation of the pion-photon transition form factor using dispersion relations and renormalization-group summation

We consider the lightcone sum-rule description of the pion-photon transition form factor, based on dispersion relations, in combination with the renormalization group of QCD, in terms of the formal solution of the Efremov-Radyushkin-Brodsky-Lepage evolution equation, and show that the emerging scheme amounts to a certain version of Fractional Analytic Perturbation Theory (FAPT). In order to ensure the correct asymptotic behavior of the considered physical quantity, this modified FAPT version has to be supplemented by process-specific boundary conditions---in contrast to the standard one. However, it provides the advantage of significantly improving the inclusion of radiative corrections in the low-momentum regime of QCD perturbation theory using renormalization-group summation.

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arXiv2019

Form factor $π^0 γ^* γ$ in lightcone sum rules combined with renormalization-group summation vs experimental data

We consider the lightcone sum-rule (LCSR) description of the pion-photon transition form factor in combination with the renormalization group of QCD. The emerging scheme represents a certain version of Fractional Analytic Perturbation Theory and significantly extends the applicability domain of perturbation theory towards lower momenta $Q^2\lesssim 1$ GeV$^2$. We show that the predictions calculated herewith agree very well with the released preliminary data of the BESIII experiment, which have very small errors just in this region, while the agreement with other data at higher $Q^2$ is compatible with the LCSR predictions obtained recently by one of us using fixed-order perturbation theory.

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arXiv2019

Optimized determination of the polarized Bjorken sum rule in pQCD

We present the method of numerical optimization for the perturbative series using the renormalization group in quantum chromodynamics. We apply our approach to the perturbation series in $α_s$ for the coefficient function $C_\text{Bjp}(α_s)$ of the Bjorken sum rule for the polarized deep inelastic lepton-hadron scattering. We optimize the Bjorken sum rule value, $Γ_1^\text{p-n}$, at the COMPASS, SLAC and JLab kinematics and compare the obtained results with the experimental measurements and also with the truncated Bjorken sum rule predictions.

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arXiv2017

Nucleon structure functions in the truncated moments approach

We demonstrate advantages of the truncated Mellin moments (TMM) approach in the analysis of DIS data. We present a novel method for determination of the Bjorken sum rule (BSR) from restricted in $x$ variable experimental data. We show how to incorporate different uncertainties for each kinematic bin. We apply our analysis to recent COMPASS data.

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arXiv2017

Cut Moments approach in the analysis of DIS data

We review the main results on the generalization of the DGLAP evolution equations within the cut Mellin moments (CMM) approach, which allows one to overcome the problem of kinematic constraints in Bjorken $x$. CMM obtained by multiple integrations as well as multiple differentiations of the original parton distribution also satisfy the DGLAP equations with the simply transformed evolution kernel. The CMM approach provides novel tools to test QCD; here we present one of them. Using appropriate classes of CMM, we construct the generalized Bjorken sum rule that allows us to determine the Bjorken sum rule value from the experimental data in a restricted kinematic range of $x$. We apply our analysis to COMPASS data on the spin structure function $g_1$.

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arXiv2017

On a realization of $\{β\}$-expansion in QCD

We suggest a simple algebraic approach to fix the elements of the $\{ β\}$-expansion for renormalization group invariant quantities, which uses additional degrees of freedom. The approach is discussed in detail for N$^2$LO calculations in QCD with the MSSM gluino -- an additional degree of freedom. We derive the formulae of the $\{ β\}$-expansion for the nonsinglet Adler $D$-function and Bjorken polarized sum rules in the actual N$^3$LO within this quantum field theory scheme with the MSSM gluino and the scheme with the second additional degree of freedom. We discuss the properties of the $\{ β\}$-expansion for higher orders considering the N$^4$LO as an example.

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arXiv2016

The $\{β\}$-expansion formalism in perturbative QCD and its extension

We discuss the $\{ β\}$-expansion for renormalization group invariant quantities tracing this expansion to the different contractions of the corresponding incomplete BPHZ $R$-operation. All of the coupling renormalizations, which follow from these contractions, should be taken into account for the $\{ β\}$-expansion. We illustrate this feature considering the nonsinglet Adler function $D^\text{NS}$ in the third order of perturbation. We propose a generalization of the $\{ β\}$-expansion for the renormalization group covariant quantities -- the $\{ β,γ\}$-expansion.

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arXiv2016

Improved estimates of the pion-photon transition form factor in the $(\mathbf{1\leq Q^2\leq5})$~GeV$^\mathbf{2}$ range and their theoretical uncertainties

We consider the pion-photon transition form factor at low to intermediate spacelike momenta within the theoretical framework of light-cone sum rules. We derive predictions which take into account all currently known contributions stemming from QCD perturbation theory up to the next-to-next-to-leading order (NNLO) and by including all twist terms up to order six. In order to enable a more detailed comparison with forthcoming high-precision data, we also estimate the main systematic theoretical uncertainties, stemming from various sources, and discuss their influence on the calculations --- in particular the dominant one related to the still uncalculated part of the NNLO contribution. The analysis addresses, in broad terms, also the role of the twist-two pion distribution amplitude derived with different approaches.

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