arXiv subjects
Publications and source records attributed to K. G. Chetyrkin.
In this paper the three-loop polarization functions Π(q^2) are calculated for the cases of an external vector, axial-vector, scalar or pseudo-scalar current. Results are presented for the imaginary part which directly leads to the cross section $σ(e^+e^- \to Z \to hadrons)$ and to the Higgs decay rates, respectively.
We present in analytic form the three-loop O(α_s^2) correction to the H -> gg partial width of the standard-model Higgs boson with intermediate mass M_H << 2 M_t. Its knowledge is required because the O(α_s) correction is so sizeable that the theoretical prediction to this order is unlikely to be reliable. For M_H=100 GeV, the resulting QCD correction factor reads $1+(215/12)α_s^{(5)}(M_H)/π+150.419 (α_s^{(5)}(M_H)/π)^2 \approx 1+0.66+0.21$. The new three-loop correction increases the Higgs-boson hadronic width by an amount of order 1%.
Three-loop QCD corrections to the vector current correlator are considered. The large momentum procedure is applied in order to evaluate mass corrections up to order $(m^2/q^2)^6$. The inclusion of the first seven terms to the ratio $R=σ(e^+e^- \to hadrons)/σ(e^+e^- \to μ^+μ^-)$ leads to reliable predictions from the high energy region down to relatively close to threshold.
We present a QCD sum rule calculation of the strange-quark mass including four-loop QCD corrections to the correlator of scalar currents. We obtain $\bar m_s(1$ GeV$)=205.5\pm 19.1$ MeV.
We present the results of analytic calculation of the quark mass anomalous dimension to alpha_s**4.
A simple procedure to estimate O(alpha_s^3) and O(alpha_s^4) corrections to mass-dependent observables is conjectured. The method is tested in a number of cases where the O(alpha_s^3) contribution is exactly known, and reasonable agreement is found.
We calculate the top-quark-induced three-loop corrections of O(alpha_s^2 G_F M_t^2) to the Yukawa couplings of the first five quark flavours in the framework of the minimal standard model with an intermediate-mass Higgs boson, with mass M_H << 2M_t. The calculation is performed using an effective-Lagrangian approach implemented with the hard-mass procedure. As an application, we derive the O(alpha_s^2 G_F M_t^2) corrections to the H -> q q-bar partial decay widths, including the case q=b. The couplings of the Higgs boson to pairs of leptons and intermediate bosons being known to O(alpha_s^2 G_F M_t^2), this completes the knowledge of such corrections in the Higgs sector. We express the results both in the MS-bar and on-shell schemes of mass renormalization. We recover the notion that the QCD perturbation expansions exhibit a worse convergence behaviour in the on-shell scheme than they do in the MS-bar scheme.
We discuss the calculation of two-point three-loop functions with an arbitrary number of massive propagators and one large external momentum. The relevant subdiagrams are generated automatically. The resulting massless two-point integrals and massive tadpoles are transformed on-line to FORM-expressions ready to be used by existing FORM packages which calculate them analytically. As an example we compute the quartic mass corrections to the photon polarization function.
The talk briefly reviews the current state of the art in doing multiloop QCD calculations in a completely analytic way. In particular, we discuss recent analytical calculation of 4-loop O(alpha_s**3) gluino contribution to R(s) and its implications to the Z boson and tau-lepton decay rates.
By means of a heavy-top-quark effective Lagrangian, we calculate the three-loop corrections of O(alpha_s^2 G_F M_t^2) to the H->bb-bar partial decay width of the standard-model Higgs boson with intermediate mass M_H<<2M_t. We take advantage of a soft-Higgs theorem to construct the relevant coefficient functions. We present our result both in the MS-bar and on-shell schemes of mass renormalization. The MS-bar formulation turns out to be favourable with regard to the convergence behaviour. We also test a recent idea concerning the naive non-abelianization of QCD.
We analytically compute quadratic mass corrections of order $α_s^3 m_q^2/s$ to the absorptive part of the (non-diagonal) correlator of two axial vector currents. This allows us to find the correction of order $α_s^3 m_q^2/M^2_W$ to the $Γ(W -->hadrons)$ as well as similar corrections to $Γ(Z -->hadrons)$.
By a completely independent analytic calculation made in general covariant gauge we confirm the known result for the massless $α_s^3$ correction to $R_{had}$ and check explicitly its gauge independence. We extend the calculations to include contributions due to a hypothetical existence of a colour octet of (light) neutral fermions known also under the name of gluinos.
We present the results of the analytical evaluation of the massless four-loop O(alpha_s^3) correction to the correlator of the quark scalar currents and the Higgs decay rate into hadrons.
We present analytical calculation of the first seven moments of the heavy quark vacuum polarization function in the three-loop order. The obtained results are compared against the asymptotic formulas following from the threshold singularities. We also discuss the $μ$ dependence of the moments within the BLM procedure.
The three-loop vacuum polarization function $Π(q^2)$ induced by a massive quark is calculated. A comprehensive description of the method is presented. From the imaginary part the ${\cal O}(α_s^2)$ result for the production of heavy quarks $R(s)=σ(e^+e^-\to \mbox{hadrons})/σ(e^+e^-\to μ^+μ^-)$ can be extracted. Explicit formulae separated into the different colour factors are given.
The cross-section for the production of $t\bar{t}$ pairs in $e^+e^-$-annihilation via a virtual photon is determined up to order $α_s^2$. For the cm-energies of interest the effect of the top mass may not be considered as a small parameter and the full mass dependence must be included.
Second order ${\cal O}(α_s^2)$ corrections to the heavy quark production cross-section due to massless quarks and coloured scalars are calculated for all energies above threshold. Based on the method introduced in this letter also the gauge non-invariant second order corrections due to the pure gluonic selfenergy insertion and a certain class of ${\cal{O}}(α_s^3)$ and ${\cal{O}}(α_s^4)$ corrections are determined. For the special choice of the gauge parameter, $ξ=4$, the leading threshold and high energy behaviour of the pure second order gluonic corrections to the cross-section are governed by the gluonic self energy insertion.
The real and imaginary part of the vacuum polarisation function $Π(q^2)$ induced by a massive quark is calculated in perturbative QCD up to order $α_s^2$. The method is described and the results are presented. This extends the calculation by Källén and Sabry from two to three loops.