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K. G. Chetyrkin

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

At least 37 records · Page 2Linked to original sources
arXiv2015

High-precision $α_s$ measurements from LHC to FCC-ee

This document provides a writeup of all contributions to the workshop on "High precision measurements of $α_s$: From LHC to FCC-ee" held at CERN, Oct. 12--13, 2015. The workshop explored in depth the latest developments on the determination of the QCD coupling $α_s$ from 15 methods where high precision measurements are (or will be) available. Those include low-energy observables: (i) lattice QCD, (ii) pion decay factor, (iii) quarkonia and (iv) $τ$ decays, (v) soft parton-to-hadron fragmentation functions, as well as high-energy observables: (vi) global fits of parton distribution functions, (vii) hard parton-to-hadron fragmentation functions, (viii) jets in $e^\pm$p DIS and $γ$-p photoproduction, (ix) photon structure function in $γ$-$γ$, (x) event shapes and (xi) jet cross sections in $e^+e^-$ collisions, (xii) W boson and (xiii) Z boson decays, and (xiv) jets and (xv) top-quark cross sections in proton-(anti)proton collisions. The current status of the theoretical and experimental uncertainties associated to each extraction method, the improvements expected from LHC data in the coming years, and future perspectives achievable in $e^+e^-$ collisions at the Future Circular Collider (FCC-ee) with $\cal{O}$(1--100 ab$^{-1}$) integrated luminosities yielding 10$^{12}$ Z bosons and jets, and 10$^{8}$ W bosons and $τ$ leptons, are thoroughly reviewed. The current uncertainty of the (preliminary) 2015 strong coupling world-average value, $α_s(m_Z)$ = 0.1177 $\pm$ 0.0013, is about 1\%. Some participants believed this may be reduced by a factor of three in the near future by including novel high-precision observables, although this opinion was not universally shared. At the FCC-ee facility, a factor of ten reduction in the $α_s$ uncertainty should be possible, mostly thanks to the huge Z and W data samples available.

hep-ph↗
arXiv2015

Charm and Bottom Quark Masses: an Update

Using new four-loop results for the heavy quark vacuum polarization and new data for bottom quark production in electron-positron annihilation, an update on the determination of charm- and bottom-quark masses through sum rules has been performed. The previous result for the charm-quark mass, $m_c(3 {\rm GeV})= 0.986(13) {\rm GeV}$, based on the lowest moment, is supported by the new results from higher moments which lead to consistent values with comparable errors. The new value for the bottom quark, $m_b(10 {\rm GeV})= 3.610(16) {\rm GeV}$, corresponding to $m_b(m_b)= 4.163(16) {\rm GeV}$, makes use both of the new data and the new perturbative results and is consistent with the earlier determination.

hep-ph↗
arXiv2014

OPE of the energy-momentum tensor correlator in massless QCD

We analytically calculate higher order corrections to coefficient functions of the operator product expansion (OPE) for the Euclidean correlator of two energy-momentum tensors in massless QCD. These are the three-loop contribution to the coefficient C_0 in front of the unity operator O_0=1 and the one and two-loop contributions to the coefficient C_1 in front of the gluon "condensate" operator O_1=-1/4 G^{μν} G_{μν}. For the correlator of two operators O_1 we present the coefficient C_1 at two-loop level.

hep-ph↗
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.

hep-ph↗
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).

hep-ph↗
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.

hep-ph↗
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.

hep-ph↗
arXiv2012

Three-loop β-functions for top-Yukawa and the Higgs self-interaction in the Standard Model

We analytically compute the dominant contributions to the β-functions for the top-Yukawa coupling, the strong coupling and the Higgs self-coupling as well as the anomalous dimensions of the scalar, gluon and quark fields in the unbroken phase of the Standard Model at three-loop level. These are mainly the QCD and top-Yukawa corrections. The contributions from the Higgs self-interaction which are negligible for the running of the top-Yukawa and the strong coupling but important for the running of the Higgs self-coupling are also evaluated.

hep-ph↗
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.

hep-ph↗
arXiv2010

Massless correlators of vector, scalar and tensor currents in position space at orders alpha_s^3 and alpha_s^4: explicit analytical results

We present analytical results both in momentum and position space for the massless correlators of the vector and scalar currents to order alpha_s^4 as well as for the tensor currents to order alpha_s^3. The evolution equations for the correlators together with all relevant anomalous dimensions are discussed in detail. As an application we present explicit conversion formulas relating the MSbar-renormalized vector, scalar and tensor currents to their counterparts renormalized in the X-space renormalization scheme more appropriate for lattice calculations.

hep-ph↗
arXiv2010

Adler Function, DIS sum rules and Crewther Relations

The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is presented: an analytical calculation of the coefficient function of the latter sum rule in a generic gauge theory in order O(alpha_s^4). It is demonstrated that the corresponding Crewther relation allows to fix two of three colour structures in the O(alpha_s^4) contribution to the singlet part of the Adler function.

hep-ph↗
arXiv2010

Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals

The old "glue--and--cut" symmetry of massless propagators, first established in [1], leads --- after reduction to master integrals is performed --- to a host of non-trivial relations between the latter. The relations constrain the master integrals so tightly that they all can be analytically expressed in terms of only few, essentially trivial, watermelon-like integrals. As a consequence we arrive at explicit analytical results for all master integrals appearing in the process of reduction of massless propagators at three and four loops. The transcendental structure of the results suggests a clean explanation of the well-known mystery of the absence of even zetas (zeta_{2n}) in the Adler function and other similar functions essentially reducible to the massless propagators. Once a reduction of massless propagators at five loops is available, our approach should be also applicable for explicit performing the corresponding five-loop master integrals.

hep-ph↗
arXiv2010

Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory

We compute, for the first time, the order alpha_s^4 contributions to the Bjorken sum rule for polarized electron-nucleon scattering and to the (non-singlet) Adler function for the case of a generic colour gauge group. We confirm at the same order a (generalized) Crewther relation which provides a strong test of the correctness of our previously obtained results: the QCD Adler function and the five-loop beta-function in quenched QED. In particular, the appearance of an irrational contribution proportional to zeta_3 in the latter quantity is confirmed. We obtain the commensurate scale equation relating the effective strong coupling constants as inferred from the Bjorken sum rule and from the Adler function at order alpha_s^4.

hep-ph↗
arXiv2009

Wilson Expansion of QCD Propagators at Three Loops: Operators of Dimension Two and Three

In this paper we construct the Wilson short distance operator product expansion for the gluon, quark and ghost propagators in QCD, including operators of dimension two and three, namely, A^2, m^2, m A^2, \ovlψ ψand m^3. We compute analytically the coefficient functions of these operators at three loops for all three propagators in the general covariant gauge. Our results, taken in the Landau gauge, should help to improve the accuracy of extracting the vacuum expectation values of these operators from lattice simulation of the QCD propagators.

hep-ph↗