The current status of the higher order QCD corrections to the width of the tau is discussed. We report on the result of the first complete calculation of the quadratic quark mass correction to the correlator of the two currents relevant for the strangeness-changing semihadronic tau-decay rate (including its real part at the four-loop level. We discuss phenomenological implications for determination of m_s.

We report the results of the first complete QCD five-loop calculation, viz. analytical contribution of order m_q^2 alpha_s^4, to the (absorptive part of) the vacuum polarization function. The contribution directly leads to the knowledge of the the full O( \als^4 m_q^2/ s)correction to the total cross-section of e^+ e^- annihilation into hadrons. We compare our results with predictions following from various optimization schemes.

The first complete calculation of the quadratic quark mass correction to the correlator of the two currents relevant for the strangeness-changing semihadronic tau-decay rate is presented including its real part at the four-loop level. This allows to perform the extraction of the strange quark mass m_s from the decay width of the tau-lepton with full O(alpha_s^3) accuracy. In agreement with previous estimates the newly computed alpha_s^3 term proves to be rather large. This justifies inclusion of the similarly estimated alpha_s^4 term in phenomenological analysis. Combined with an updated value of V_{us} and an ``'improved'' version of the renormalization group improvement of the perturbative series this leads to an increase of the central value of m_s by about 20% and a partial reduction of the theoretical uncertainty by about 50%.

The study of radiative $\phi$ decays into scalar mesons, with subsequent

decay into $\pi\pi\gamma$, constitutes an important topic at the
electron-positron collider DAPHNE. The interference of the respective 
amplitude with the one for $\pi^+\pi^-\gamma$ production, where
the photon originates from initial state radiation, will allow for unambiguous
tests of models for the $\phi\to\gamma f_0(\to \pi\pi)$ amplitude.
The forward-backward asymmetry of charged pions, which is a clear signal of
such an interference, amounts up to 30 \% and is at the same time
quite sensitive to the details of the various amplitudes.
The results for several characteristic cases are presented and their
implementation into the Monte Carlo generator PHOKHARA is described.

The measurement of the pion form factor and, more generally, of the cross section for electron–positron annihilation into hadrons through the radiative return has become an important task for high luminosity colliders such as the $\Phi$- or $B$-meson factories. For a detailed understanding and analysis of this reaction, the construction of a Monte Carlo program, PHOKHARA, has been undertaken. A brief overview of the most recent developments is presented, which include the combination of initial- and final-state radiation in the case of two-pion production. Baryon pair production is now included and the pion form factor is extended into the region of large $Q^2$. A model for the kaon form factor is discussed which is fitted to $K^+K^-$ and $K^0\bar{K}^0$ data and which leads to predictions for the $\tau$-decay into $K^-K^0\nu$.

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.

In this letter, we extend the known results for the QCD potential between a static quark and its antiquark by computing the two-loop corrections to the colour-octet state.

The correlator of vector heavy-quark currents at small q^2 is considered in the large-beta_0 limit. The leading IR renormalon ambiguity of the sum of the perturbative series is canceled by the UV renormalon ambiguity of the gluon condensate. Asymptotic behaviour of the perturbative series is obtained in a model-independent way, up to a single unknown normalization factor. Gluon-virtuality distribution functions for the perturbative correction are calculated.

We discuss new results obtained for the description of a system of

 two heavy
 quarks close to the production threshold. Special emphasis is put
 on the resummation of logarithms in the quark velocity.
 As physical applications we discuss the determination of the
 mass of the $\eta_b$ meson and the ratio of the photon mediated
 production or annihilation rates of spin triplet and spin singlet
 heavy quarkonium states.

We review a recent calculation of the two-loop next-to-leading logarithmic electroweak corrections to the form factors for massless chiral fermions coupling to an SU(2)xU(1) singlet gauge boson.

New, accurate measurements of the pion and kaon electromagnetic form factors are expected in the near future from experiments at electron-positron colliders,using the radiative return method. We construct a model for the timelike pion electromagnetic form factor, that is valid also at momentum transfers far above the $\rho$ resonance. The ansatz is based on vector dominance and includes a pattern of radial excitations expected from dual resonance models.The form factor is fitted to the existing data in the timelike region, continued to the spacelike region and compared with the measurements there and with the QCD predictions. Furthermore, the model is extended to the kaon electromagnetic form factor. Using isospin and SU(3)-flavour symmetry relations we extract the isospin-one contribution and predict the kaon weak form factor accessible in semileptonic tau decays.

The next-to-leading order (NLO) QCD corrections to the production and decay rate of a Higgs boson are computed within the framework of the Minimal Supersymmetric Standard Model (MSSM). The calculation is based on an effective theory for light and intermediate mass Higgs bosons. We provide a Fortran routine for the numerical evaluation of the coefficient function. For most of the MSSM parameter space, the relative size of the NLO corrections is typically of the order of 5% smaller than the Standard Model value. We exemplify the numerical results for two scenarios: the benchmark point SPS1a, and a parameter region where the gluon-Higgs coupling at leading order is very small due to a cancellation of the squark and quark contributions.

We consider hadronic production of a Z boson in association with a jet and study one- and two-loop electroweak logarithmic corrections in the region of high Z-boson transverse momentum, p_T » M_Z, including leading and next-to-leading logarithms. Numerical results for the LHC and Tevatron colliders are presented. At the LHC these corrections amount to tens of per cent and will be important for interpretation of the measurements.

We present an algorithm to compute arbitrary multi-loop massive Feynman diagrams in the region where the typical energy scale \sqrt{s} is much larger than the typical mass scale M, i.e. s»M^2, while various different energy and mass parameters may be present. In this region we perform an asymptotic expansion and, using sector decomposition, we extract the leading contributions resulting from ultraviolet and mass singularities, which consist of large logarithms log(s/M^2) and 1/\epsilon poles in D=4-2\epsilon dimensions. To next-to-leading accuracy, at L loops all terms of the form \alpha^L \epsilon^{-k} log^j(s/M^2) with j+k=2L and j+k=2L-1 are taken into account. This algorithm permits, in particular, to compute higher-order next-to-leading logarithmic electroweak corrections for processes involving various kinematical invariants of the order of hundreds of GeV and masses M_W \sim M_Z \sim M_H \sim M_t of the order of the electroweak scale, in the approximation where the masses of the light fermions are neglected.

After an introduction to the sequential version of FORM and the mechanisms behind, we report on the status of our project of parallelization. We have now a parallel version of FORM running on Cluster- and SMP-architectures. This version can be used to run arbitrary FORM programs in parallel.

We present a semi-numerical approach which allows the calculation of four-loop tadpole diagrams. The method is introduced by presenting the results for a scalar four-loop diagram. Finally, the application of the method to the calculation of a physical quantity like the four-loop vacuum polarization in QCD is discussed.

Determinations of |Vud| and |Vus| along with their implications for the unitarity test |Vud|^2+|Vus|^2+|Vub|^2=1 are discussed. The leading two loop radiative corrections to neutron beta-decay are evaluated and used to derive a refined relationship |Vud|^2 tau_n (1+3g_A^2)=4908(4)sec. Employing |Vud| =0.9740(5) from superallowed nuclear decays and the measured neutron lifetime, tau_n = 885.7(7)sec leads to the precise prediction g_A=1.2703(8) which is compared with current direct experimental values. Various extractions of |Vus| are described and updated. The long accepted Particle Data Group value of |Vus| from fitted K_{e3} decay rates suggests a deviation from CKM unitarity but it is contradicted by more recent experimental results which confirm unitarity with good precision. An outlook for possible future advances is given.

The status of the theoretical predictions for the most important Higgs production processes at the Large Hadron Collider is reviewed. Both the Standard Model and neutral Higgs production in the \mssm{} are considered.

The ratio of the photon mediated production or annihilation rates of spin triplet and spin singlet heavy quarkonium states is computed to the next-to-next-to-leading logarithmic accuracy within the nonrelativistic renormalization group approach. The result is presented in analytical form and applied to the phenomenology of $t\bar{t}$, $b\bar{b}$ and $c\bar{c}$ systems. The use of the nonrelativistic renormalization group considerably improves the behaviour of the perturbative expansion and is crucial for accurate theoretical analysis. For bottomonium decays we predict $\Gamma(\eta_b(1S) \rightarrow \gamma\gamma)=0.659\pm 0.089 ({\rm th.}) {}^{+0.019}_{-0.018} (\delta \alpha_{\rm s})\pm 0.015 ({\rm exp.})\; {\rm keV}$. Our results question the accuracy of the existing extractions of the strong coupling constant from the bottomonium annihilation. As a by-product we obtain novel corrections to the ratio of the ortho- and parapositronium decay rates: the corrections of order $\alpha^4\ln^2\alpha$ and $\alpha^5\ln^3\alpha$.

The two-loop Sudakov form factor is computed in a $U(1)$ model with a massive gauge boson and a $U(1)\times U(1)$ model with mass gap. We analyze the result in the context of hard and infrared evolution equations and establish a matching procedure which relates the theories with and without mass gap setting the stage for the complete calculation of the dominant two-loop corrections to electroweak processes at high energy.

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.

Muon pair production through the radiative return is of importance for a measurement of the hadronic production cross section in two ways: it provides an independent calibration and it may give rise to an important background for a measurement of the pion form factor. With this motivation the Monte Carlo event generator PHOKHARA is extended to include next-to-leading order radiative corrections to the reaction $e^+e^-\to \mu^+\mu^-\gamma$. Furthermore, virtual ISR corrections to FSR from pions are introduced, which extends the applicability of the generator into a new kinematical regime. Finally, the effect of photon vacuum polarization is introduced into this new version of the generator.

We compute the hyperfine splitting in a heavy quarkonium composed of different flavors in next-to-leading logarithmic approximation using the nonrelativistic renormalization group. We predict the mass difference of the vector and pseudoscalar charm-bottom mesons to be $M(B^*_c)-M(B_c)=65 \pm 24\,{(\rm th)}\,{}^{+19}_{-16}\,(\delta\alpha_s)$~MeV.

The feasibility of a measurement of the electric and magnetic nucleon form factors at $B$-meson factories through the radiative return is studied. Angular distributions allow a separation of the contributions from the two form factors. The distributions are presented for the laboratory and the hadronic rest frame, and the advantages of different coordinate systems are investigated. It is demonstrated that $Q^2$ values up to 8 or even 9 GeV$^2$ are within reach. The Monte Carlo event generator PHOKHARA is extended to nucleon final states, and results are presented which include Next-to-Leading Order radiative corrections from initial-state radiation. The impact of angular cuts on rates and distributions is investigated and the relative importance of radiative corrections is analysed.

Two different two-loop relations between the pole- and the MS-mass of the top quark have been derived in the literature

which were based on different treatments of the tadpole

diagrams. In addition, the limit M_W^2/m_t^2 \to 0 was employed in one of the calculations. It is shown that, after appropriate transformations, the results of the two calculations are in perfect agreement. Furthermore we demonstrate that the inclusion of the non-vanishing mass of the W-boson leads to small modifications only.

In ongoing and upcoming hadron collider experiments, top quark physics will play an important r\^ole in testing the Standard Model and its possible extensions. In this work we present analytic results for the differential cross sections of top quark pair production in hadronic collisions at next-to-leading order in the QCD coupling, keeping the full dependence on the spins of the top quarks. These results are combined with the corresponding next-to-leading order results for the decay of polarized top quarks into dilepton, lepton plus jets, and all jets final states. As an application we predict double differential angular distributions which are due to the QCD-induced top quark spin correlations in the intermediate state. In addition to the analytic results, we give numerical results in terms of fit functions that can easily be used in an experimental analysis.

Recently the next-to-next-to-leading order QCD corrections and the electroweak O(\alpha) corrections to the Higgs-strahlung processes p\bar p → WH/ZH+X have been calculated. Both types of corrections are of the order of 5-10%. In this article the various corrections are briefly discussed and combined into state-of-the-art predictions for the cross sections. The theoretical uncertainties from renormalization/factorization scales and from the parton distribution functions are discussed.

We consider virtual electroweak corrections to the form factors for massless chiral fermions coupling to an SU(2)xU(1) singlet gauge boson in the asymptotic region $s\gg M_W^2\sim M_Z^2$, where the invariant mass $s$ of the external gauge boson is much higher than the weak-boson mass scale. Using the sector-decomposition method we compute mass singularities, which arise as logarithms of $s/M_W^2$ and $1/\epsilon$ poles in $D=4-2\epsilon$ dimensions, to one- and two-loop next-to-leading logarithmic accuracy. In this approximation we include all contributions of order $\alpha^l\epsilon^{k}\log^{j+k}(s/M_W^2)$, with $l=1,2$ and $j=2l,2l-1$. We find that the electroweak two-loop leading- and next-to-leading-logarithmic mass singularities can be written in a form that corresponds to a generalization of Catani's formula for massless QCD.