We report first results of an ongoing project devoted to the analytical calculation of the QCD $\beta$-function and the quark mass anomalous dimension at the five loop level.

The impact of improved measurements of the cross section for electron-positron annihilation into hadrons in the charm threshold region is discussed. Two aspects are studied in detail: i.)~A significant reduction of the experimental error of the electronic width of the narrow resonances $J/\psi$ and $\psi'$ and of the continuum cross section from the open charm threshold up to 4.6~GeV will lead to a correspondingly improved determination of the charmed quark mass. ii)~A high luminosity measurement with 24~pb${}^{-1}$ at three points and with a spacing of 2~MeV around $\sqrt{s}=3511\,{\rm MeV}$ may allow to observe the direct, resonant production of $\chi_{c1}$.

Weak corrections for top-quark pair production at hadron colliders are revisited. Predictions for collider energies of 8 TeV, adopted to the present LHC run, and for 14 TeV, presumably relevant for the next round of LHC experiments, are presented. Kinematic regions with large momentum transfer are identified, where the corrections become large and may lead to strong distortions of differential distributions, thus mimicking anomalous top quark couplings. As a complementary case we investigate the threshold region, corresponding to configurations with small relative velocity between top and antitop quark, which is particularly sensitive to the top-quark Yukawa coupling. We demonstrate, that nontrivial upper limits on this coupling are well within reach of ongoing experiments.

In the context of inter-jet energy flow, we present the first quantitative result of the resummation of non-global logarithms at finite N_c. This is achieved by refining Weigert's approach in which the problem is reduced to the simulation of associated Langevin dynamics in the space of Wilson lines. We find that, in e+e- annihilation, the exact result is rather close to the result previously obtained in the large-N_c mean field approximation. However, we observe enormous event-by-event fluctuations in the Langevin process which may have significant consequences in hadron collisions.

We extend the low-energy effective field theory relevant for b to s transitions up to operators of mass-dimension 7 and compute the associated anomalous-dimension matrix. We then compare our findings to the known results for dimension 6 operators and derive a solution for the renormalization group equations involving operators of dimension 7. We finally apply our analysis to a particularly simple case where the Standard Model is extended by an electroweak-magnetic operator and consider limits on this scenario from the decays Bs to mu+ mu- and B to K nu nubar.

We analytically compute the QCD, electroweak, Higgs and third generation Yukawa contributions to the $\beta$-function for the Higgs self-coupling as well as for the Higgs mass parameter in the unbroken phase of the Standard Model at three-loop level.

We present $O(\alpha_s^2)$ QCD corrections to the fully-differential decay rate of a $b$-quark into inclusive semileptonic charmless final states. Our calculation provides genuine two-loop QCD corrections, beyond the Brodsky-Lepage-Mackenzie (BLM) approximation, to any infra-red safe partonic observable that can be probed in $b \to X_u e \bar \nu$ decays. Kinematic cuts that closely match those used in experiments can be fully accounted for. To illustrate these points, we compute the non-BLM corrections to moments of the hadronic invariant mass and the hadronic energy with cuts on the lepton energy and the hadronic invariant mass. Our results remove one of the sources of theoretical uncertainty that affect the extraction of the CKM matrix element $|V_{ub}|$ from charmless inclusive B-decays.

We describe a calculation of the fully-differential decay rate of a top quark to a massless $b$-quark and a lepton pair at next-to-next-to-leading order in perturbative QCD. Technical details of the calculation are discussed and selected results for kinematic distributions are shown.

In this paper analytical results are presented for higher order corrections to coefficient functions of the operator product expansion (OPE) for the correlator of two pseudoscalar gluonium operators \tilde{O}_1=G^{\mu \nu}\tilde{G}_{\mu \nu}. The Wilson coefficient in front of the scalar gluon condensate operator O_1=-1/4 G^{\mu \nu}G_{\mu \nu} is given at three-loop accuracy. The leading coefficient C_0 in front of the unity operator O_0=1 has been calculated up to three-loop order some time ago but has been checked independently in this work. It is interesting to see that the coefficient C_1 in the pseudoscalar case is finite, whereas contact terms appear in C_0 in this case and in both coefficients C_0 and C_1 in the cases of the scalar gluonium correlator and the energy momentum tensor correlator. For the corresponding Renormalization Group invariant Wilson coefficients which are also constructed the results are partially extended to four-loop accuracy. All results are given in the MSbar-scheme at zero temperature.