P. A. Baikov

Order alphas4 QCD corrections to Z and tau decays.

Using recently developed methods for the evaluation of five-loop amplitudes in perturbative QCD, corrections of order alpha_s^4 for the cross section of electron-positron annihilation into hadrons and for the decay rates of the Z-boson and the tau-lepton into hadrons are evaluated. The new terms lead to a significant stabilization of the perturbative series, to a reduction of the theory uncertainly in the strong coupling constant alpha_s, as extracted from these measurements, and to a small shift of the central value, moving two central values closer together. The agreement between two values of alpha_s measured at vastly different energies constitutes a striking test of asymptotic freedom. Combining the results from Z and tau decays we find alpha_s(M_Z)=0.1198 \pm 0.0015 as one of the most precise and presently only result for the strong coupling constant in order alpha_s^4.

Scalar correlator at [symbol: see text](alpha(s)4), Higgs boson decay into bottom quarks, and bounds on the light-quark masses.

We compute, for the first time, the absorptive part of the massless correlator of two quark scalar currents in five loops. As physical applications, we consider the [symbol: see text](alpha(s)4) corrections to the decay rate of the standard model Higgs boson into quarks, as well as the constraints on the strange quark mass following from QCD sum rules.

Hadronic Z- and tau-Decays in Order alpha_s^4

Using recently developed methods for the evaluation of five-loop amplitudes in perturbative QCD, corrections of order alpha_s^4 for the cross section of electron-positron annihilation into hadrons and for the decay rates of the Z-boson and the tau-lepton into hadrons are evaluated. The new terms lead to a significant stabilization of the perturbative series, to a reduction of the theory uncertainly in the strong coupling constant alpha_s, as extracted from these measurements, and to a small shift of the central value, moving two central values closer together. The agreement between two values of alpha_s measured at vastly different energies constitutes a striking test of asymptotic freedom. Combining the results from Z and tau decays we find alpha_s(M_Z)=0.1198 \pm 0.0015 as one of the most precise and presently only result for the strong coupling constant in order alpha_s^4.

Scalar Correlator at O({alpha}{sub s}{sup 4}), Higgs Boson Decay into Bottom Quarks, and Bounds on the Light-Quark Masses

We compute, for the first time, the absorptive part of the massless correlator of two quark scalar currents in five loops. As physical applications, we consider the [symbol: see text](alpha(s)4) corrections to the decay rate of the standard model Higgs boson into quarks, as well as the constraints on the strange quark mass following from QCD sum rules.

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 (nonsinglet) Adler function for the case of a generic color 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).

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.

Top Quark Mediated Higgs Boson Decay into Hadrons to Order alpha~s^5

We present in analytic form the O(alphas5) correction to the H-->gg partial width of the standard-model Higgs boson with an intermediate mass MH<2Mt. Its knowledge is useful because the O(alphas4) correction is sizable (around 20%). For MH=120 GeV, the resulting QCD correction factor reads 1+(215/12)alphas(5)(MH)/pi+152.5[alphas(5)(MH)/pi]2+381.5[alphas(5)(MH)/pi]3 approximately 1+0.65+0.20+0.02. The new four-loop correction increases the total Higgs-boson hadronic width by a small amount of order 1 per thousand and stabilizes significantly the residual scale dependence.

Vector correlator in massless QCD at order \mathcal{O}\left( {\alpha_s^4} \right) and the QED β-function at five loop

A bstractWe present a concise summary of recent results for the vector correlator in massless QCD at order

Adler function, sum rules and Crewther relation of order O(αs4): The singlet case

\mathcal{O}\left( {\alpha_s^4} \right)

A Practical criterion of irreducibility of multi-loop Feynman integrals

, 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