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K. G. Chetyrkin

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

At least 73 records · Page 4Linked to original sources
arXiv2005

Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions

The anomalous dimensions of the gluon and ghost fields as well as the ghost-ghost-gluon and quark-quark-gluon vertexes are analytically computed in pQCD. Taken together with already available anomalous dimensions of the coupling constant, the quark field and the mass the results lead to complete knowledge of all renormalization constant entering into the renormalization of the QCD Lagrangian at the four-loop level. As a by-product we get scale and scheme invariant gluon and ghost propagators at NNNLO. Using a theorem due to Dudal, Verschelde and Sorella, we also construct the four-loop anomalous dimension of the ``gluon mass operator'', A^2, in the Landau gauge.

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arXiv2005

Heavy-quark vacuum polarization: first two moments of the O(alphas^3 nf^2) contribution

The vacuum polarization due to a virtual heavy quark pair and specifically the coefficients of its Taylor expansion in the external momentum are closely related to moments of the cross section for quark-antiquark pair production in electron-positron annihilation. Relating measurement and theoretically calculated Taylor coefficients, an accurate value for charm- and bottom-quark mass can be derived, once corrections from perturbative QCD are sufficiently well under control. Up to three-loop order these have been evaluated previously. We now present a subset of four-loop contributions to the lowest two moments, namely those from diagrams which involve two internal loops from massive and massless fermions coupled to virtual gluons, hence of order alphas^3 nf^2. The calculation demonstrates the applicability of Laporta's algorithm to four-loop vacuum diagrams with both massive and massless propagators and should be considered a first step towards the full evaluation of the order alphas^3 contribution.

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arXiv2003

QCD Corrections to Hadronic Z and tau Decays

We present a brief (mainly bibliographical) report on recently performed calculations of terms of order O(α_s^4 n_f^2) and O(α_s^4 n_f^2 m_q^2) for hadronic Z and τdecay rates. A few details about the analytical evaluation of the masters integrals appearing in the course of calculations are presented.

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arXiv2003

Five-loop vacuum polarization in pQCD: O(m_q^2α_s^4 n_f^2) contribution

We present the analytical calculation of the contribution of order m_q^2 α_s^4 n_f^2 to the absorptive part of the vacuum polarization function of vector currents. This term constitutes an important gauge-invariant part of the full O(m_q^2 alpha_s^4) correction to the total cross-section of e^+ e^- annihilation into hadrons. The results are compared to predictions following from various optimization schemes.

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arXiv2002

Towards Order alpha_s^4 Accuracy in tau-decays

Recently computed terms of orders O(α_s^4 n_f^2) in the perturbative series for the tau decay rate, and similar (new) strange quark mass corrections, are used to discuss the validity of various optimization schemes. The results are then employed to arrive at improved predictions for the complete terms order O(α_s^4) and O(α_s^5) in the massless limit as well as for terms due to the strange quark mass. Phenomenological implications are presented.

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arXiv2002

A closed analytical formula for two-loop massive tadpoles with arbitrary tensor numerators

Using the integration by parts method we derive a closed analytical expression for the result of the integration of an arbitrary dimensionally regulated tadpole diagram composed of a massless propagator and two massive ones, each raised into an arbitrary power, and including an arbitrary tensor numerator. We also briefly discuss the implementation of the formula in the algebraic manipulation language of FORM.

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arXiv2002

Quartic mass corrections to R_had at order α_s^3

The total cross section for the production of massive quarks in electron positron annihilation can be predicted in perturbative QCD. After expansion in m^2/s the quartic terms, i.e. those proportional to m^4/s^2, are calculated up to order α_s^3 for vector and axial current induced rates. Predictions relevant for charm, bottom and top quarks production are presented. The α_s^3 corrections are shown to be comparable to terms of order α_s and α_s^2. As a consequence, the predictions exhibit a sizeable dependence on the renormalization scale. The stability of the prediction is improved and, at the same time, the relative size of the large order terms decreases by replacing the running mass \bar{m}(μ) with the scheme independent invariant one \hat{m}. By combining these results with the prediction for massless case and the quadratic mass terms the cross section for massive quark production at electron positron colliders is put under control in order α_s^3 from the high energy region down to fairly low energies.

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arXiv2001

The Cross Section of e^+ e^- Annihilation into Hadrons of Order alpha_s^4 n_f^2 in Perturbative QCD

We present the first genuine QCD five-loop calculation of the vacuum polarization functions: analytical terms of order alpha_s^4 n_f^2 to the absorptive parts of vector and scalar correlators. These corrections form an important gauge-invariant subset of the full O(alpha_s^4) correction to $e^+ e^- annihilation into hadrons and the Higgs decay rate into hadrons respectively. They discriminate between different widely used estimates of the full result.

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arXiv2001

Heavy-light current correlators at order $α_s^2$ in QCD and HQET

The non-diagonal correlators of vector and scalar currents are considered at three-loop order in QCD. The full mass dependence is computed in the case where one of the quarks is massless and the other one carries mass $M$. We exploit the decoupling relations between the full theory and the heavy quark effective theory (HQET) in order to obtain the logarithmic parts of the leading threshold terms. With the help of conformal mapping and Padé approximation numerical estimates for the non-logarithmic terms are extracted which in turn lead to a prediction of the correlator in HQET at order $α_s^2$. As applications of the vector and scalar correlator we consider the single-top-quark production via the process $q\bar{q}\to t\bar{b}$ and the decay rate of a charged Higgs boson into hadrons, respectively. In both cases the computed NLO corrections are shown to be numerically much less important than the leading ones. On the contrary, the NLO order QCD corrections to the HQET sum rule for the leptonic decay rate of a heavy-light meson proves to be comparable to the leading one.

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arXiv2001

Vacuum Saturation Hypothesis and QCD Sum Rules

The accuracy of the vacuum saturation hypothesis is discussed using the examples of vacuum expectation values of four-quark operators and the parameter $B$, which determines the short-distance contribution to the $K^0 - \bar K^0$ mixing. Note added: The approach based on sum rules in position (x-)space as elaborated in the paper is relevant and useful tool for the current phenomenology. In particular, it provides the unique possibility of direct non-perturbative estimation of the VEV's of four-quark operators renormalized in any scheme, including the MSbar one.

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arXiv2001

Calculation of the K^0-\bar{K}^0 mixing parameter via the QCD sum rules at finite energies

The QCD finite energy sum rules method is used to show that the parameter of the K^0-\bar{K}_0 mixing \hat{B} is mainly determined by the value of g m_s< \bar{d} G_{μν} σ_{μν} d > and the vacuum expectation values of four-quark operators. Assuming the hypothesis of vacuum dominance and/or unitarity symmetry to estimate latter, it is found that \hat{B}=1.2\pm 0.1. (The updated (March 2001) prediction reads \hat{B} = 1.0 +- 0.1 (for more details, see Comments after the main text).

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arXiv2000

Three-Loop Leading Top Mass Contributions to the rho Parameter

We present analytical results for the leading contributions of the top quark to the electroweak rho parameter at order GF^3 Mt^6 and GF^2 Mt^4 alpha_s. The Higgs boson and the gauge bosons are taken to be massless in this limit. The correction of order GF^3 Mt^6 is found to be sizeable in comparison to the the leading two-loop GF^2 Mt^4 correction, however it is much smaller than the subleading GF^2 Mt^2 MZ^2 correction.

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arXiv2000

Three-loop non-diagonal current correlators in QCD and NLO corrections to single-top-quark production

The non-diagonal correlators of vector and scalar currents are considered at three-loop order in QCD. The full mass dependence is computed in the case where one of the quarks is massless and the other one carries the mass $M$. As applications we consider the single-top-quark production via the process $q\bar{q}\to t\bar{b}$ and the decay rate of a charged Higgs into hadrons. In both cases the computed NLO corrections are shown to be numerically much less important than the leading ones.

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arXiv2000

Two Loop QCD Vertices and Three Loop MOM $β$ functions

We present numerical results for the two loop QCD corrections to the ghost gluon vertex, the quark gluon vertex, and the triple gluon vertex in the massless limit at the symmetric point. We restrict ourselves to the tensor structures existing in the tree level. The corrections are used to examine different coupling constant definitions in momentum subtraction schemes and the corresponding three-loop $β$ functions.

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arXiv2000

Three-loop Three-Linear Vertices and Four-Loop MOM beta functions in massless QCD

In this paper we present a full set of 2- and 3-point functions for massless QCD at three-loop order in the MSbar scheme. The vertex functions are evaluated at the asymmetric point with one vanishing momentum. These results are used to relate the MSbar coupling constant to that of various momentum subtraction renormalization schemes at three-loop order. With the help of the known four-loop MS-bar beta-function we then determine the four-loop coefficients of the corresponding MOM beta-functions. As an application we consider the momentum dependence (running) of the three-gluon asymmetrical vertex recently computed within the lattice approach by Ph. Boucaud et al. (JHEP 04 006 (2000)). An account of the four-loop term in the corresponding beta-function leads to a significant (around 30%) decrease of the value of the non-perturbative power-suppressed correction to the running.

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arXiv2000

Light Hybrid Mesons in QCD

Including the radiative perturbative corrections and the short distance tachyonic gluon mass effects which mimic the ones of UV renormalons, we re-estimate the decay amplitudes, masses and widths of light hybrid mesons from QCD spectral sum rules. We show that the effects are tiny and confirm the previous lowest order results. We discuss the phenomenological impacts of our results for the vector hybrids.

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arXiv2000

The relation between the $\bar{\rm MS}$ and the on-shell quark mass at order $α_s^3$

The relation between the on-shell and $\bar{\rm MS}$ mass can be expressed through scalar and vector part of the quark propagator. In principle these two-point functions have to be evaluated on-shell which is a non-trivial task at three-loop order. Instead, we evaluate the quark self energy in the limit of large and small external momentum and use conformal mapping in combination with Padé improvement in order to construct a numerical approximation for the relation [1]. The errors of our final result are conservatively estimated to be below 3%. The numerical implications of the results are discussed in particular in view of top and bottom quark production near threshold. We show that the knowledge of new ${\cal O}(α_s^3)$ correction leads to a significant reduction of the theoretical uncertainty in the determination of the quark masses.

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