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K. G. Chetyrkin

Publications and source records attributed to K. G. Chetyrkin.

At least 19 recordsLinked to original sources
arXiv2025

The $γ^\ast\to ηγ$ and $γ^\ast\to η'γ$ form factors to NNLO accuracy in perturbative QCD

We use conformal symmetry to calculate the NNLO anomalous dimension matrix (three loops) for flavor-singlet axial-vector QCD operators for spin $N \le 8$ from a set of gauge-invariant two-point correlation functions. Combining this result with the recent calculation of the two-loop coefficient functions, we carry out the calculation of the $γγ^\ast\to η$ and $γγ^\ast\to η'$ form factors at large momentum transfers to the NNLO accuracy in perturbative QCD.

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arXiv2022

NNLO anomalous dimension matrix for twist-two flavor-singlet operators

Conformal symmetry of QCD is restored at the Wilson-Fisher critical point in noninteger $4-2ε$ space-time dimensions. Correlation functions of multiplicatively renormalizable operators with different anomalous dimensions at the critical point vanish identically. We show that this property allows one to calculate off-diagonal parts of the anomalous dimension matrices for leading-twist operators from a set of two-point correlation functions of gauge-invariant operators which can be evaluated using standard computer algebra techniques. As an illustration, we present the results for the NNLO anomalous dimension matrix for flavor-singlet QCD operators for spin $N\le 8$.

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arXiv2021

Operator product expansion for the non-local gluon condensate

We consider the short-distance expansion of the product of two gluon field strength tensors connected by a straight-line-ordered Wilson line. The vacuum expectation value of this nonlocal operator is a common object in studies of the QCD vacuum structure, whereas its nucleon expectation value is known as the gluon quasi-parton distribution and is receiving a lot of attention as a tool to extract gluon distribution functions from lattice calculations. Extending our previous study, we calculate the three-loop coefficient functions of the scalar operators in the operator product expansion up to dimension four. As a by-product, the three-loop anomalous dimension of the nonlocal two-gluon operator is obtained as well.

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arXiv2020

Renormalization of parton quasi-distributions beyond the leading order: spacelike vs. timelike

We argue that the renormalization factors for nonlocal quark-antiquark and gluon operators at space-like and time-like separations connected by a Wilson line coincide to all orders in perturbation theory. We calculate the anomalous dimensions and renormalization constants of quark-antiquark and gluon operators to three- and two-loop accuracy, respectively, and also compute vacuum expectation values of these operators to three-loop accuracy.

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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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arXiv2018

Five-loop renormalisation of QCD in covariant gauges

We present the complete set of vertex, wave function and charge renormalisation constants in QCD in a general simple gauge group and with the complete dependence on the covariant gauge parameter $ξ$ in the minimal subtraction scheme of conventional dimensional regularisation. Our results confirm all already known results, which were obtained in the Feynman gauge, and allow the extraction of other useful gauges such as the Landau gauge. We use these results to extract the Landau gauge five-loop anomalous dimensions of the composite operator $A^2$ as well as the Landau gauge scheme independent gluon, ghost and fermion propagators at five loops.

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arXiv2018

The method of global R* and its applications

The global R* operation is a powerful method for computing renormalisation group functions. This technique, based on the principle of infrared rearrangement, allows to express all the ultraviolet counterterms in terms of massless propagator integrals. In this talk we present the main features of global R* and its application to the renormalisation of QCD. By combining this approach with the use of the program Forcer for the evaluation of the relevant Feynman integrals, we renormalise for the first time QCD at five loops in covariant gauges.

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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

Four-loop renormalization of QCD with a reducible fermion representation of the gauge group: anomalous dimensions and renormalization constants

We present analytical results at four-loop level for the renormalization constants and anomalous dimensions of an extended QCD model with one coupling constant and an arbitrary number of fermion representations. One example of such a model is the QCD plus gluinos sector of a supersymmetric theory where the gluinos are Majorana fermions in the adjoint representation of the gauge group. The renormalization constants of the gauge boson, ghost and fermion fields are analytically computed as well as those for the ghost-gluon vertex, the fermion-gluon vertex and the fermion mass. All other renormalization constants can be derived from these. Some of these results were already produced in Feynman gauge for the computation of the beta-function of this model, which was recently published. Here we present results for an arbitrary gauge parameter.

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arXiv2017

Combinatorics of $\mathbf{R}$-, $\mathbf{R^{-1}}$-, and $\mathbf{R^*}$-operations and asymptotic expansions of feynman integrals in the limit of large momenta and masses

A generalization of the forest technique procedure --- the $R^{-1}$-operation---is elaborated and then employed to treat a variety of problems. First, it is employed to reveal the underlying simple structure of the Bogoliubov-Parasiuk renormalization prescription based on momentum subtractions. Second, we use this structure to derive a generalized Zimmermann identity connecting two different renormalized versions of a given Feynman integral. Third, the recursive procedure to minimally subtract the ultraviolet and infrared divergences from euclidean, dimensionally regularized Feynman integrals---the $R^*$-operation--- is simplified by reformulating it in terms of the R-operation alone. The new formulation is shown to lead immediately to a simple and regular algorithm for evaluating the overall ultraviolet divergences of arbitrary dimensionally regularized Feynman integrals, (including the ones appearing in two-dimensional field-theoretical models), the algorithm neatly reducing the problem to computing some massless propagator-type integrals. Finally, we construct a brief and concise proof of a general theorem which gives an explicitly finite large momenta and/or masses asymptotic expansion of an arbitrary (minimally subtracted) euclidean Feynman integral.

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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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arXiv2016

Leading QCD-induced four-loop contributions to the $β$-function of the Higgs self-coupling in the SM and vacuum stability

We present analytical results for the leading top-Yukawa and QCD contribution to the $β$-function for the Higgs self-coupling $λ$ of the Standard Model at four-loop level, namely the part $\propto y_t^4 g_s^6$ independently confirming a result given in [1]. We also give the contribution $\propto y_t^2 g_s^6$ of the anomalous dimension of the Higgs field as well as the terms $\propto y_t g_s^8$ to the top-Yukawa $β$-function which can also be derived from the anomalous dimension of the top quark mass. We compare the results with the RG functions of the correlators of two and four scalar currents in pure QCD and find a new relation between the anomalous dimension $γ_0$ of the QCD vacuum energy and the anomalous dimension $γ_m^{SS}$ appearing in the RG equation of the correlator of two scalar currents. Together with the recently computed top-Yukawa and QCD contributions to $β_{g_s}$ [2,3] the $β$-functions presented here constitute the leading four-loop contributions to the evolution of the Higgs self-coupling. A numerical estimate of these terms at the scale of the top-quark mass is presented as well as an analysis of the impact on the evolution of $λ$ up to the Planck scale and the vacuum stability problem.

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arXiv2016

Six loop analytical calculation of the field anomalous dimension and the critical exponent $η$ in $O(n)$-symmetric $φ^4$ model

We report on a completely analytical calculation of the field anomalous dimension $γ_φ$ and the critical exponent $η$ for the $O(n)$-symmetric $φ^4$ model at the record six loop level. We successfully compare our result for $γ_φ$ with $n=1$ with the predictions based on the method of the Borel resummation combined with a conformal mapping. Predictions for seven loop contribution to the field anomalous dimensions are given.

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