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P. A. Baikov

Publications and source records attributed to P. A. Baikov.

At least 19 recordsLinked to original sources
arXiv2026

Solving recurrence relations for multiloop integrals in the limit of large values of the dimensional regularization parameter

A method for calculating the $1/d$ expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive form. A possible type of such substitutions is proposed for the case of vacuum integrals. Its applicability is shown for several families of massless (with one massive line) vacuum integrals up to the 7-loop level.

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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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arXiv2019

Transcendental structure of multiloop massless correlators and anomalous dimensions

We give a short account of recent advances in our understanding of the $π$-dependent terms in massless (Euclidean) 2-point functions as well as in generic anomalous dimensions (ADs) and $β$-functions. We extend the considerations of \cite{Baikov:2018wgs} by two more loops, that is for the case of 6- and 7-loop correlators and 7- and 8-loop renormalization group (RG) functions. Our predictions for the ($π$-dependent terms) of the 7-loop RG functions for the case of the $O(n)$ $ϕ^4$ theory are in full agreement with the recent results from \cite{Schnetz:2016fhy}. All available 7- and 8-loop results for QCD and the scalar $O(n)$ $φ^4$ theory obtained within the large $N_f$ approach to the quantum field theory (see, e.g. \cite{Gracey:2018ame}) are also in full agreement with our results.

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arXiv2019

$α_s$(2019): Precision measurements of the QCD coupling

This document collects a written summary of all contributions presented at the workshop "$α_s$(2019): Precision measurements of the strong coupling" held at ECT* (Trento) in Feb. 11--15, 2019. The workshop explored in depth the latest developments on the determination of the QCD coupling $α_s$ from the key categories where high precision measurements are available: (i) lattice QCD, (ii) hadronic $τ$ decays, (iii) deep-inelastic scattering and parton distribution functions, (iv) event shapes, jet cross sections, and other hadronic final-states in $e^+e^-$ collisions, (v) Z boson and W boson hadronic decays, and (vi) hadronic final states in p-p collisions. The status of the current theoretical and experimental uncertainties associated to each extraction method, and future perspectives were thoroughly reviewed. Novel $α_s$ determination approaches were discussed, as well as the combination method used to obtain a world-average value of the QCD coupling at the Z mass pole.

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arXiv2018

No-$π$ Theorem for Euclidean Massless Correlators

We provide the reader with a (very) short review of recent advances in our understanding of the $π$-dependent terms in massless (Euclidean) 2-point functions as well as in generic anomalous dimensions and $β$-functions. We extend the considerations of [1] by one more loop, that is for the case of 6-loop correlators and 7-loop renormalization group (RG) functions.

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arXiv2018

The structure of generic anomalous dimensions and no-$π$ theorem for massless propagators

Extending an argument of [Baikov:2010hf] for the case of 5-loop massless propagators we prove a host of new exact model-independent relations between contributions proportional to odd and even zetas in generic \MSbar\ anomalous dimensions as well as in generic massless correlators. In particular, we find a new remarkable connection between coefficients in front of $ζ_3$ and $ζ_4$ in the 4-loop and 5-loop contributions to the QCD $β$-function respectively. It leads to a natural explanation of a simple mechanics behind mysterious cancellations of the $π$-dependent terms in one-scale Renormalization Group (RG) invariant Euclidian quantities recently discovered in \cite{Jamin:2017mul}. We give a proof of this no-$π$ theorem for a general case of (not necessarily scheme-independent) one-scale massless correlators. All $π$-dependent terms in the {\bf six-loop} coefficient of an anomalous dimension (or a $β$-function) are shown to be explicitly expressible in terms of lower order coefficients for a general one-charge theory. For the case of a scalar $O(n)$ $ϕ^4$ theory all our predictions for $π$-dependent terms in 6-loop anomalous dimensions are in full agreement with recent results of [Batkovich:2016jus],[Schnetz:2016fhy],[Kompaniets:2017yct].

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arXiv2017

Higgs Decay, Z Decay and the QCD Beta-Function

Recent developments in perturbative QCD, leading to the beta function in five-loop approximation are presented. In a first step the two most important decay modes of the Higgs boson are discussed: decays into a pair of gluons and, alternatively, decays into a bottom-antibottom quark pair. Subsequently the quark mass anomalous dimension is presented which is important for predicting the value of the bottom quark mass at high scales and, consequently, the Higgs boson decay rate into pair of massive quarks, in particular into $b\bar b$. In the next section the $α_s^4$ corrections to the vector- and axial-vector correlator are discussed. These are the essential ingredients for the evaluation of the QCD corrections to the cross section for electron-positron annihilation into hadrons at low and at high energies, to the hadronic decay rate of the $τ$ lepton and for the $Z$-boson decay rate into hadrons. Finally we present the prediction for the QCD beta-function in five-loop approximation, discuss the analytic structure of the result and compare with experiment at low and at high energies.

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arXiv2017

Five-loop fermion anomalous dimension for a general gauge group from four-loop massless propagators

We extend the ${\cal O}(α_s^5)$ result of the analytic calculation of the quark mass anomalous dimension in pQCD [1] to the case of a generic gauge group. We present explicit formulas which express the relevant renormalization constants in terms of four-loop massless propagators. We also use our result to shed new light on the old puzzle of the absence of even zetas in results of perturbative calculations for a class of physical observables.

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arXiv2016

Five-Loop Running of the QCD coupling constant

We analytically compute the five-loop term in the beta function which governs the running of $α_s$ --- the quark-gluon coupling constant in QCD. The new term leads to a reduction of the theory uncertainty in $α_s$ taken at the Z-boson scale as extracted from the $τ$-lepton decays as well as to new, improved by one more order of perturbation theory, predictions for the effective coupling constants of the Standard Model Higgs boson to gluons and for its total decay rate to the quark-antiquark pairs.

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arXiv2014

The QED vacuum polarization function at four loops and the anomalous magnetic moment at five loops

The anomalous magnetic moment of the muon is one of the most fundamental observables. It has been measured experimentally with a very high precision and on theory side the contributions from perturbative QED have been calculated up to five-loop level by numerical methods. Contributions to the muon anomalous magnetic moment from certain diagram classes are also accessible by alternative methods. In this paper we present the evaluation of contributions to the QED corrections due to insertions of the vacuum polarization function at five-loop level.

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arXiv2012

The relation between the QED charge renormalized in MSbar and on-shell schemes at four loops, the QED on-shell beta-function at five loops and asymptotic contributions to the muon anomaly at five and six loops

In this paper we compute the four-loop corrections to the QED photon self-energy Pi(Q^2) in the two limits of q=0 and Q^2->infinity. These results are used to explicitly construct the conversion relations between the QED charge renormalized in on-shell(OS) and MSbar scheme. Using these relations and results of Baikov et al. [1] we construct the momentum dependent part of Pi(Q^2,m,alpha) at large Q^2 at five loops in both MSbar and OS schemes. As a direct consequence we arrive at the full result for the QED beta-function in the OS scheme at five loops. These results are applied, in turn, to analytically evaluate a class of asymptotic contributions to the muon anomaly at five and six loops.

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arXiv2012

R(s) and Z decay in order α_s^4: complete results

We report on our calculation of the order α_s^4 axial singlet contributions for the decay rates of the Z-boson as well as the vector singlet contribution to the cross section for electron-positron annihilation into hadrons. Together with recently finished O(α_s^4) calculations of the non-signlet corrections [1,2], the new results directly lead us to the first complete O(α_s^4) predictions for the total hadronic decay rate of the Z-boson and the ratio R(s).

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arXiv2012

Vector Correlator in Massless QCD at Order O(alpha_s^4) and the QED beta-function at five loop

We present a concise summary of recent results for the vector correlator in massless QCD at order ${\cal O}(α_s^4)$, with all colour factors being given for a generic colour group. As a direct consequence we arrive at: (i) the full QCD contribution to the QED $β$--function of order $α^2\, α_s^4$ in the MSbar- and MOM-schemes; (ii) the full five-loop result of order $α^6$ for the $β$-function of QED with a generic number of single-charged fermions, again for the MSbar- and MOM-schemes.

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arXiv2012

Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case

The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule [1], we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available non-singlet part of the Adler function [2,3] we arrive at the complete ${\cal O}(α_s^4)$ expression for the Adler function and, as a direct consequence, at the complete ${\cal O}(α_s^4)$ correction to the $e^+ e^-$ annihilation into hadrons in a general gauge theory.

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arXiv2012

Complete QCD Corrections to Hadronic $Z$--Decays in Order $α_s^4$

Corrections of order $α_s^4$ for the axial singlet contributions for the decay rates of the $Z$-boson into hadrons are evaluated in the limit of the heavy top quark mass. Combined with recently finished ${\cal O}(α_s^4)$ calculations of the non-signlet corrections, the new results directly lead us to the first {\em complete} ${\cal O}(α_s^4)$ prediction for the total hadronic decay rate of the Z-boson. The new ${\cal O}(α_s^4)$ term in Z-decay rate lead to a significant stabilization of the perturbative series, to a reduction of the theory uncertainty in the strong coupling constant $α_s$, as extracted from these measurements, and to a small shift of the central value.

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