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A. V. Nesterenko

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

At least 19 recordsLinked to original sources
arXiv2026

Window quantities for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment in spacelike and timelike domains

The relations between the window quantities for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment $a^{\text{HVP}}_μ$ in spacelike and timelike domains are studied. Two types of window functions (abrupt and smooth) as well as two kinds of kinematic intervals (symmetric and asymmetric with respect to the spacelike/timelike flip) are addressed. It is shown that the window quantities for $a^{\text{HVP}}_μ$ represented in terms of the hadronic vacuum polarization function $\barΠ(Q^2)$, the Adler function $D(Q^2)$, and the $R$-ratio of electron-positron annihilation into hadrons are mutually equivalent only if the additional contributions due to the window edge effects are properly taken into account and the explicit expressions for such contributions are derived. The obtained results enable one to evaluate $a^{\text{HVP}}_μ$ by making simultaneous use of the inputs for functions $\barΠ(Q^2)$, $D(Q^2)$, and $R(s)$ at various energies and an example of such hybrid assessment is provided. The obtained results also enable one to accurately compare the window quantities for $a^{\text{HVP}}_μ$ based, e.g., on MUonE or lattice data with the ones based on $R$-ratio data, even if the window function covers different kinematic ranges in spacelike and timelike domains.

hep-ph↗
arXiv2025

The anomalous magnetic moment of the muon in the Standard Model: an update

We present the current Standard Model (SM) prediction for the muon anomalous magnetic moment, $a_μ$, updating the first White Paper (WP20) [1]. The pure QED and electroweak contributions have been further consolidated, while hadronic contributions continue to be responsible for the bulk of the uncertainty of the SM prediction. Significant progress has been achieved in the hadronic light-by-light scattering contribution using both the data-driven dispersive approach as well as lattice-QCD calculations, leading to a reduction of the uncertainty by almost a factor of two. The most important development since WP20 is the change in the estimate of the leading-order hadronic-vacuum-polarization (LO HVP) contribution. A new measurement of the $e^+e^-\toπ^+π^-$ cross section by CMD-3 has increased the tensions among data-driven dispersive evaluations of the LO HVP contribution to a level that makes it impossible to combine the results in a meaningful way. At the same time, the attainable precision of lattice-QCD calculations has increased substantially and allows for a consolidated lattice-QCD average of the LO HVP contribution with a precision of about 0.9%. Adopting the latter in this update has resulted in a major upward shift of the total SM prediction, which now reads $a_μ^\text{SM} = 116\,592\,033(62)\times 10^{-11}$ (530 ppb). When compared against the current experimental average based on the E821 experiment and runs 1-6 of E989 at Fermilab, one finds $a_μ^\text{exp} - a_μ^\text{SM} =38(63)\times 10^{-11}$, which implies that there is no tension between the SM and experiment at the current level of precision. The final precision of E989 (127 ppb) is the target of future efforts by the Theory Initiative. The resolution of the tensions among data-driven dispersive evaluations of the LO HVP contribution will be a key element in this endeavor.

hep-ph↗
arXiv2024

The strong coupling constant: State of the art and the decade ahead

Theoretical predictions for particle production cross sections and decays at colliders rely heavily on perturbative Quantum Chromodynamics (QCD) calculations, expressed as an expansion in powers of the strong coupling constant $α_s$. The current $\mathcal{O}(1\%)$ uncertainty of the QCD coupling evaluated at the reference Z boson mass, $α_s(m_Z) = 0.1179 \pm 0.0009$, is one of the limiting factors to more precisely describe multiple processes at current and future colliders. A reduction of this uncertainty is thus a prerequisite to perform precision tests of the Standard Model as well as searches for new physics. This report provides a comprehensive summary of the state-of-the-art, challenges, and prospects in the experimental and theoretical study of the strong coupling. The current $α_s(m_Z)$ world average is derived from a combination of seven categories of observables: (i) lattice QCD, (ii) hadronic $τ$ decays, (iii) deep-inelastic scattering and parton distribution functions fits, (iv) electroweak boson decays, hadronic final-states in (v) $e^+e^-$, (vi) e-p, and (vii) p-p collisions, and (viii) quarkonia decays and masses. We review the current status of each of these seven $α_s(m_Z)$ extraction methods, discuss novel $α_s$ determinations, and examine the averaging method used to obtain the world-average value. Each of the methods discussed provides a ``wish list'' of experimental and theoretical developments required in order to achieve the goal of a per-mille precision on $α_s(m_Z)$ within the next decade.

hep-ph↗
arXiv2023

Effects of the quark flavour thresholds in the hadronic vacuum polarization contributions to the muon anomalous magnetic moment

The equivalent representations for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment $a^{\text{HVP}}_μ$ in the presence of the quark flavour thresholds are studied. Specifically, the explicit relations between the contributions given by the integration over a finite kinematic interval to $a^{\text{HVP}}_μ$ expressed in terms of the hadronic vacuum polarization function, Adler function, and the $R$-ratio of electron-positron annihilation into hadrons are derived. It is shown that the quark flavour thresholds of the hadronic vacuum polarization function generate additional contributions to $a^{\text{HVP}}_μ$ expressed in terms of the Adler function and the $R$-ratio and the explicit expressions for such contributions are obtained. The commonly employed dispersion relations, which bind together hadronic vacuum polarization function, Adler function, and $R$-ratio, are extended to account for the effects due to the quark flavour thresholds. The examined additional contributions due to the heavy quark thresholds to $a^{\text{HVP}}_μ$ expressed in terms of the $R$-ratio appear to be quite sizable, that can be of a particular relevance for the data-driven method of assessment of the hadronic part of the muon anomalous magnetic moment.

hep-ph↗
arXiv2022

Addendum: Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment (2022 J. Phys. G: Nucl. Part. Phys. 49 055001)

This addendum provides results complementary to those obtained in [J. Phys. G49, 055001 (2022)]. Specifically, an equivalent form of the relation, which binds together the "spacelike" kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment $a^{\text{HVP}}_μ$, is obtained. It is shown that the infrared limiting value of the "spacelike" and "timelike" kernel functions, which enter the representations for $a^{\text{HVP}}_μ$ involving the Adler function and the $R$-ratio, is identical to the corresponding QED contribution to the muon anomalous magnetic moment of the preceding order in the electromagnetic coupling. The next-to-leading order contributions $a^{\text{HVP}(3b)}_μ$ (which includes the leptonic and hadronic insertions) and $a^{\text{HVP}(3c)}_μ$ (which includes the double hadronic insertion), are studied. The three kernel functions appearing in the representations for $a^{\text{HVP}(3b)}_μ$, which involve the hadronic vacuum polarization function, Adler function, and the $R$-ratio, are presented for the cases of the electron and $τ$-lepton loop insertions.

hep-ph↗
arXiv2022

Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment

The complete set of relations, which mutually express the spacelike and timelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment $a^{\text{HVP}}_μ$ in terms of each other, is obtained. By making use of the derived relations the explicit expression for the next-to-leading order spacelike kernel function, which enters the representation for $a^{\text{HVP}}_μ$ involving the hadronic vacuum polarization function, is obtained. The corresponding next-to-leading order spacelike kernel function, which appears in the representation for $a^{\text{HVP}}_μ$ involving the Adler function, is calculated numerically. The obtained results can be employed in the assessments of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment in the framework of the spacelike methods, such as lattice studies, MUonE project, and others.

hep-ph↗
arXiv2022

Mini-Proceedings of the STRONG2020 Virtual Workshop on "Space-like and Time-like determination of the Hadronic Leading Order contribution to the Muon $g-2$"

The mini-proceedings of the STRONG2020 Virtual Workshop "Space-like and Time-like determination of the Hadronic Leading Order contribution to the Muon $g-2$", November 24--26 2021, are presented. This is the first workshop of the STRONG2020 WP21: JRA3-PrecisionSM: Precision Tests of the Standard Model (http://www.strong-2020.eu/joint-research-activity/jra3-precisionsm.html). The workshop was devoted to review of the working group activitity on: $(\it i)$ Radiative Corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^+ e^-$ collisions; $(\it ii)$ Annotated database for $e^+e^-$ into hadrons processes at low energy; $(\it iii)$ Radiative Corrections and Monte Carlo tools for $μ$-$e$ elastic scattering.

hep-ph↗
arXiv2020

Recurrent form of the renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients

The renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients are studied. The folded recurrent and unfolded explicit forms of such relations are obtained. The explicit expression for the coefficients, which incorporate the contributions of the $π^{2}$-terms in the perturbative expansion of the R-ratio of electron-positron annihilation into hadrons, is derived at an arbitrary loop level. The obtained results can be employed as an independent crosscheck of the higher-order perturbative calculations of the hadronic vacuum polarization function and in the studies of the renormalization scale setting in the relevant physical observables.

hep-ph↗
arXiv2019

Explicit form of the R-ratio of electron-positron annihilation into hadrons

The explicit expression for the R-ratio of electron-positron annihilation into hadrons, which properly accounts for all the effects due to continuation of the spacelike perturbative results into the timelike domain, is obtained at an arbitrary loop level. Several equivalent ways to derive a commonly employed approximation of the R-ratio are recapped and the impact of discarded in the latter higher-order pi2-terms on the evaluation of the strong running coupling is elucidated. The obtained results substantially facilitate the theoretical study of electron-positron annihilation into hadrons and the related strong interaction processes.

hep-ph↗
arXiv2017

Electron-positron annihilation into hadrons at the higher-loop levels

The strong corrections to the R-ratio of electron-positron annihilation into hadrons are studied at the higher-loop levels. Specifically, the essentials of continuation of the spacelike perturbative results into the timelike domain are elucidated. The derivation of a general form of the commonly employed approximate expression for the R-ratio (which constitutes its truncated re-expansion at high energies) is delineated, the appearance of the pertinent $π^2$-terms is expounded, and their basic features are examined. It is demonstrated that the validity range of such approximation is strictly limited to $\sqrt{s}/Λ> \exp(π/2) \simeq 4.81$ and that it converges rather slowly when the energy scale approaches this value. The spectral function required for the proper calculation of the R-ratio is explicitly derived and its properties at the higher-loop levels are studied. The developed method of calculation of the spectral function enables one to obtain the explicit expression for the latter at an arbitrary loop level. By making use of the derived spectral function the proper expression for the R-ratio is calculated up to the five-loop level and its properties are examined. It is shown that the loop convergence of the proper expression for the R-ratio is better than that of its commonly employed approximation. The impact of the omitted higher-order $π^2$-terms on the latter is also discussed.

hep-ph↗
arXiv2016

Ponderomotive forces in electrodynamics of moving media: The Minkowski and Abraham approaches

In the general setting of the problem, the explicit compact formulae are derived for the ponderomotive forces in the macroscopic electrodynamics of moving media in the Minkowski and Abraham approaches. Taking account of the Minkowski constitutive equations and making use of a special representation for the Abraham energy-momentum tensor enable one to obtain a compact expression for the Abraham force in the case of arbitrary dependence of the medium velocity on spatial coordinates and the time and for nonstationary external electromagnetic field. We term the difference between the ponderomotive forces in the Abraham and Minkowski approaches as the Abraham force not only under consideration of media at rest but also in the case of moving media. The Lorentz force is found which is exerted by external electromagnetic field on the conduction current in a medium, the covariant Ohm law and the constitutive Minkowski relations being taken into account. The physical argumentation is traced for definition of the 4-vector of the ponderomotive force as the 4-divergence of the energy-momentum tensor of electromagnetic field in a medium.

physics.class-ph↗
arXiv2016

Symmetric energy-momentum tensor: The Abraham form and the explicitly covariant formula

We compare the known in literature, explicitly covariant 4-dimensional formula for the symmetric energy-momentum tensor of electromagnetic field in a medium and the energy-momentum tensor derived by Abraham in the 3-dimensional vector form. It is shown that these two objects coincide only on the physical configuration space $\overlineΓ$, formed by the field vectors and the velocity of the medium, which satisfy the Minkowski constitutive relations. It should be emphasized that the 3-dimensional vector formulae for the components of the energy-momentum tensor were obtained by Abraham only on $\overlineΓ$, and the task of their extension to the whole unconditional configuration space $Γ$ was not posed. In order to accomplish the comparison noted above we derive the covariant formula anew by another method, namely, by generalizing the Abraham reasoning. The comparison conducted enables one to treat the explicitly covariant formula as a unique consistent extension of the Abraham formulae to the whole configuration space $Γ$. Thus the question concerning the relativistic covariance of the original 3-dimensional Abraham formulae defined on $\overlineΓ$ is solved positively. We discuss in detail the relativistic covariance of the 3-dimensional vector formulae for individual components of the 4-dimensional tensors in electrodynamics which is manifested in the form-invariance of these formulae under Lorentz transformations.

physics.class-ph↗
arXiv2016

R-ratio of electron-positron annihilation into hadrons: higher-order pi2-terms

High-energy behavior of R-ratio of electron-positron annihilation into hadrons is studied. In particular, it is argued that at any given order of perturbation theory the re-expansion of the R-ratio in the ultraviolet asymptotic can be reduced to the form of power series in the naive continuation of the strong running coupling into the timelike domain. The convergence range of the re-expanded R-ratio and the corresponding higher-order pi2-terms are discussed.

hep-ph↗
arXiv2016

Hadronic contributions to electroweak observables in the framework of DPT

The hadronic contributions to the muon anomalous magnetic moment and to the shift of the electromagnetic fine structure constant at the scale of Z boson mass are evaluated within dispersively improved perturbation theory (DPT). The latter merges the corresponding perturbative input with intrinsically nonperturbative constraints, which originate in the respective kinematic restrictions. The obtained results conform with recent assessments of the quantities on hand.

hep-ph↗
arXiv2015

Hadronic contributions to electroweak observables within DPT

Dispersive approach to quantum chromodynamics is applied to the assessment of hadronic contributions to electroweak observables. The employed approach merges the corresponding perturbative input with intrinsically nonperturbative constraints, which originate in the respective kinematic restrictions. The evaluated hadronic contributions to the muon anomalous magnetic moment and to the shift of the electromagnetic fine structure constant at the scale of Z boson mass conform with recent assessments of these quantities.

hep-ph↗
arXiv2015

Inclusive tau lepton hadronic decay in vector and axial-vector channels within dispersive approach to QCD

The dispersive approach to QCD, which properly embodies the intrinsically nonperturbative constraints originating in the kinematic restrictions on relevant physical processes and extends the applicability range of perturbation theory towards the infrared domain, is briefly overviewed. The study of OPAL (update 2012) and ALEPH (update 2014) experimental data on inclusive tau lepton hadronic decay in vector and axial-vector channels within dispersive approach is presented.

hep-ph↗