New data for the total cross section $\sigma(e^+e^-\to\mbox{hadrons})$ in the charm and bottom threshold region are combined with an improved theoretical analysis, which includes recent four-loop calculations, to determine the short distance MSbar charm and bottom quark masses. The final result for the MSbar-masses, m_c(3 GeV) = 0.986(13) GeV and m_b(10 GeV) = 3.609(25) GeV is consistent with but significantly more precise than a similar previous study.

D_s K > The analysis of tagged $B_s\to J/\psi \phi$ decays determines the CP phase $\phi_s$ in \bbms\ with a two–fold ambiguity. The solutions differ in the sign of $\cos \phi_s$ which equals the sign of the width difference $\dg_s$ among the two $B_s$ mass eigenstates. We point out that this ambiguity can be removed with the help of $B_s \to D_s K$ decays. We compare untagged and tagged strategies and find the tagged analysis more promising. The removal of the sign ambiguity in $\dg_s$ can be done with relatively low statistics and could therefore be a target for the early stage of $B_s \to D_s K$ studies.

We calculate the $O(\alpha_s)$ and $O(\alpha_s^2)$ gluon radiative corrections to the QCD sum rule for the first Gegenbauer moment $a_1^K$ of the kaon light-cone distribution amplitude. The NNL0 accuracy is achieved for the perturbative term and quark-condensate contributions to the sum rule. A complete factorization is implemented, removing logarithms of $s$-quark mass from the coefficients in the operator-product expansion. The sum rule with radiative corrections yields $a_1^K(1 \GeV)=0.10\pm 0.04$.

We calculate light-cone distribution amplitudes for non-relativistic bound states, including radiative corrections from relativistic gluon exchange to first order in the strong coupling constant. Our results apply to hard exclusive reactions with non-relativistic bound states in the QCD factorization approach like, for instance, [B_c → eta_c l nu] or [e+ e- → J/psi eta_c]. They also serve as a toy model for light-cone distribution amplitudes of light mesons or heavy B and D mesons.

The evolution of the strong coupling constant $\alpha_s$ from $M_Z$ to the GUT scale is presented, involving three-loop running and two-loop decoupling. Accordingly, the two-loop transition from the $\bar{\rm MS}$ to the $\bar{\rm DR}$ scheme is properly taken into account. We find that the three-loop effects are comparable to the experimental uncertainty for $\alpha_s$.

The observed pattern of neutrino mass splittings and mixing angles indicates that their family structure is significantly different from that of the charged fermions. We investigate the implications of these data for the fermion mass matrices in grand unified theories with a type-I seesaw mechanism. We show that, with simple assumptions, naturalness leads to a strongly hierarchical Majorana mass matrix for heavy right-handed neutrinos and a partially cascade form for the Dirac neutrino matrix. We consider various model building scenarios which could alter this conclusion, and discuss their consequences for the construction of a natural model. We find that including partially lopsided matrices can aid us in generating a satisfying model.

We present the first 30 moments of the low energy expansions of the vector, axial-vector, scalar and pseudo-scalar heavy quark correlation functions at three-loop order, including the singlet contribution which appears for the first time at three loops. In addition we compare the behavior of the moments for large n with the prediction from threshold calculations.

A systematic analysis of Higgs-mediated contributions to the Bd and Bs mass differences is presented in the MSSM with large values of tan(beta). In particular, supersymmetric corrections to Higgs self-interactions are seen to modify the correlation between Delta Mq and BR(Bq –> mu+ mu-) for light Higgses. The present experimental upper bound on BR(Bs –> mu+ mu-) is nevertheless still sufficient to exclude noticeable Higgs-mediated effects on the mass differences in most of the parameter space.

The present status of the physics program, which led to the development

of the Monte Carlo event generator PHOKHARA is described. 
 The possibility of using the radiative return method 
in various aspects of hadronic physics, 
from the measurement of the hadronic cross section,
to detailed investigations of  the hadronic dynamics is emphasized.
New results are presented showing how to measure baryon form factors using
the knowledge of their spin in baryon-antibaryon production with subsequent
decay.

We report new results of the NNNLO correction to the S-wave quarkonium wave-functions at the origin, which also provide an estimate of the resonance cross section in t-tbar threshold production at the ILC.

We consider regularisation of a Yang-Mills theory by Dimensional Reduction (DRED). In particular, the anomalous dimensions of fermion masses and gauge coupling are computed to four-loop order. We put special emphasis on the treatment of evanescent couplings which appear when DRED is applied to non-supersymmetric theories. We highlight the importance of distinguishing between the evanescent and the real couplings. Considering the special case of a Super-Yang-Mills theory, we find that Dimensional Reduction is sufficient to preserve Supersymmetry in our calculations.

We present results for the effect of a second massive quark in the relation between the pole and the minimal subtracted quark mass at the three loop level. We also consider the analogous effect for the wave function renormalisation constant. Some technical details of the calculation are given. Our result is phenomenologically relevant for the bottom quark including virtual charm effects.

We perform the non-perturbative (quenched) renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory and its three-loop matching to QCD. At order 1/m of the expansion, the operator is responsible for the mass splitting between the pseudoscalar and vector B-mesons. These new computed factors are affected by an uncertainty negligible in comparison to the known bare matrix element of the operator between B-states. Furthermore, they push the quenched determination of the spin splitting for the Bs-meson much closer to its experimental value than the previous perturbatively renormalized computations. The renormalization factor for three commonly used heavy quark actions and the Wilson gauge action and useful parametrizations of the matching coefficient are provided.

Axigluons are colored heavy neutral gauge boson that couple to quarks through an axial vector current and the same strong coupling as gluons. The most important model-independent manifestation of axigluons is the generation of a forward–backward asymmetry in top-antitop quark production at $p\bar{p}$ collisions which originates from the charge asymmetry. We update our previous analysis for the inclusive QCD induced forward–backward asymmetry and define a new observable which is more sensitive to the effect than the forward–backward asymmetry. Furthermore, we find a lower limit of 1.2 TeV at 90\% C.L. on the axigluon mass from recent measurements of the asymmetry at Tevatron. Also at LHC, the charge asymmetry is sizable in suitably selected samples. We evaluate this asymmetry in the central region for different selection cuts and show that, like at Tevatron, the charge asymmetry can probe larger values of the axigluon mass than the dijet mass distribution.

This contribution summarizes the on-going activities connected to the evaluation of higher order radiative corrections in the context of a future international linear collider (ILC).

In this contribution an improved analysis is described to extract precise charm and bottom quark masses from experimental and theoretical moments of the photon polarization function. The obtained $\bar{\rm MS}$ mass values read $m_c(3 {GeV})=0.986(13)$ GeV and $m_b(10 {GeV})=3.609(25)$ GeV.

We derive the high energy asymptotic behavior of gauge boson production cross section in a spontaneously broken SU(2) gauge theory in the next-to-next-to-leading logarithmic approximation. On the basis of this result we obtain the logarithmically enhanced two-loop electroweak corrections to the differential cross section of W-pair production at ILC/CLIC up to the second power of the large logarithm.

We compute the three-loop relation between the pole and the minimally

 subtracted quark mass allowing for virtual effects from
 a second massive quark. We also consider the analogue effects for
 the on-shell wave function renormalization constant.

We present an analytical calculation of the next-to-next-to-leading order corrections to the partial decay width $H\to gg$ for a Higgs boson in the intermediate mass range. We apply an asymptotic expansion for $M_H\ll 2M_t$ and compute three terms in the expansion. The leading term confirms the results present in the literature. It is argued that our result is equivalent to an exact calculation up to $M_H\approx M_t$. For a Higgs boson mass of 120 GeV the power-suppressed terms lead to corrections of about 9% in the next-to-next-to-leading order coefficient.

To match the precision of present and future measurements of W-boson production at hadron colliders electroweak radiative corrections must be included in the theory predictions. In this paper we consider their effect on the transverse momentum (p_T) distribution of W bosons, with emphasis on large p_T. We evaluate the full electroweak O(alpha) corrections to the processes pp → W+jet and p\bar p → W+jet including virtual and real photonic contributions. We present the explicit expressions in analytical form for the virtual corrections and provide results for the real corrections, discussing in detail the treatment of soft and collinear singularities. We also provide compact approximate expressions which are valid in the high-energy region, where the electroweak corrections are strongly enhanced by logarithms of \hat{s}/M_W^2. These expressions describe the complete asymptotic behaviour at one loop as well as the leading and next-to-leading logarithms at two loops. Numerical results are presented for proton-proton collisions at 14 TeV and proton-antiproton collisions at 2 TeV. The corrections are negative and their size increases with p_T. At the LHC, where transverse momenta of 2 TeV or more can be reached, the one- and two-loop corrections amount up to -40% and +10%, respectively, and will be important for a precise analysis of W production. At the Tevatron, transverse momenta up to 300 GeV are within reach. In this case the electroweak corrections amount up to -10% and are thus larger than the expected statistical error.

I summarize the observables constraining the B_s-B_s-bar mixing complex and present a new calculation of the element Gamma_{12}^s of the decay matrix. Gamma_{12}^s enters the prediction of the width difference Delta Gamma_s, for which we obtain Delta Gamma_s^SM = 0.088 +/- 0.017 ps^(-1), if no new physics enters B_s-B_s-bar mixing. Applying our formulae to Tevatron data we find a deviation of the B_s-B_s-bar mixing phase phi_s from its Standard Model value by 2 standard deviations. I stress that present data do not give any information on the sign of Delta Gamma_s.

We present four-loop results for the gauge beta-function and the fermion mass anomalous dimension for a gauge theory with a general gauge group and a multiplet of fermions transforming according to an arbitrary representation, calculated using the dimensional reduction scheme. In the special case of a supersymmetric theory we confirm previous calculations of both the gauge beta-function and the gaugino mass beta-function.

Using recent CLEO III results for the cross section for $e^+e^- \to {\rm hadrons}$ at seven center-of-mass energies between 6.964 and 10.538~GeV, we derive a value for the strong coupling constant $\alpha_s(M_Z^2)=0.110_{-0.012}^{-0.010}{}_{-0.011}^{+0.010}$ where the uncertainties are uncorrelated and correlated, respectively. Our result differs by more than one standard deviation from the one derived by CLEO III, as a consequence of inclusion of quark mass effects and the proper matching between the effective theories with four and five flavours, respectively.

A short review of both theoretical and experimental aspects of the radiative return method is presented with the emphasize on the results obtained within the EURIDICE network. It is shown that the method gives not only possibility of an independent from the scan method measurement of the hadronic cross section, but also can provide information concerning details of the hadronic interactions.

We compute the three-loop QCD corrections to the quark chromomagnetic

 moment and thus obtain the matching coefficient and the anomalous
 dimension of the chromomagnetic interaction in HQET. As a byproduct we
 obtain the three-loop corrections to the quark anomalous magnetic
 moment.

Recent developments in higher order calculations within the framework of Dimensional Reduction, the preferred regularization scheme for supersymmetric theories, are reported on. Special emphasis is put on the treatment of evanescent couplings, the equivalence to Dimensional Regularization, and the evaluation of $\alpha_s(M_{\rm GUT})$ from $\alpha_s(M_{\rm Z})$.

A consistent evolution of the strong coupling constant $\alpha_s$ from $M_Z$ to the GUT scale is presented, involving three-loop running and two-loop decoupling. The two-loop transition from the MS- to the DR-scheme is properly taken into account. In the second part of the paper, the bottom quark mass in the DR- scheme at the electroweak/SUSY scale is evaluated with four-loop accuracy. We find that the three-loop effects are comparable to the experimental uncertainty both for $\alpha_s$ and $m_b$.

We compute the third-order correction to electromagnetic S-wave quarkonium production and annihilation rates due to the emission and absorption of an ultrasoft gluon. Our result completes the analysis of the non-relativistic quarkonium bound-state dynamics in the next-to-next-to-next-to-leading order. The impact of the ultrasoft correction on the Upsilon(1S) leptonic width and the top quark-antiquark threshold production cross section is estimated.

We compute the third-order correction to the S-wave quarkonium wave functions |\psi_n(0)|^2 at the origin from non-Coulomb potentials in the effective non-relativistic Lagrangian. Together with previous results on the Coulomb correction and the ultrasoft correction computed in a companion paper, this completes the third-order calculation up to a few unknown matching coefficients. Numerical estimates of the new correction for bottomonium and toponium are given.

New data for the total cross section σ(e^+e^- → hadrons) in the charm and bottom threshold region are combined with an improved theoretical analysis, which includes recent four-loop calculations, to determine the short distance \overline{MS} charm and bottom quark masses. The final result for the \overline{MS}-masses, m_c(3 GeV)=0.986(13) GeV and m_b(10 GeV)=3.609(25) GeV is consistent with but significantly more precise than a similar previous study.

We compute the imaginary part of the 2-loop vertex corrections in the QCD Factorization framework for hadronic two-body decays as B → pi pi. This completes the NNLO calculation of the imaginary part of the topological tree amplitudes and represents an important step towards a NNLO prediction of direct CP asymmetries in QCD Factorization. Concerning the technical aspects, we find that soft and collinear infrared divergences cancel in the hard-scattering kernels which demonstrates factorization at the 2-loop order. All results are obtained analytically including the dependence on the charm quark mass. The numerical impact of the NNLO corrections is found to be significant, in particular they lead to an enhancement of the strong phase of the colour-suppressed tree amplitude.

To match the precision of present and future measurements of W-boson production at hadron colliders, electroweak radiative corrections must be included in the theory predictions. In this paper we consider their effect on the transverse momentum (p_T) distribution of W bosons, with emphasis on large p_T. We evaluate the full electroweak O(\alpha) corrections to the process pp → Wj including virtual and real photonic contributions. We also provide compact approximate expressions which are valid in the high-energy region, where the electroweak corrections are strongly enhanced by logarithms of \hat{s}/M_W^2. These expressions include quadratic and single logarithms at one loop as well as quartic and triple logarithms at two loops. Numerical results are presented for proton-proton collisions at 14 TeV. The corrections are negative and their size increases with p_T. At the LHC, where transverse momenta of 2 TeV or more can be reached, the one- and two-loop corrections amount up to -40% and +10%, respectively.

We present TFORM, the version of the symbolic manipulation system FORM that can make simultaneous use of several processors in a shared memory architecture. The implementation uses Posix threads, also called pthreads, and is therefore easily portable between various operating systems. Most existing FORM programs will be able to take advantage of the increased processing power, without the need for modifications. In some cases some minor additions may be needed. For a computer with two processors a typical improvement factor in the running time is 1.7 when compared to the traditional version of FORM. In the case of computers with 4 processors a typical improvement factor in the execution time is slightly above 3.

The non-factorizable two-loop corrections to the formfactor both for a $U(1)\times U(1)$ and a $SU(2)\times U(1)$ gauge theory with massive and massless gauge bosons respectively are evaluated at arbitrary momentum transfer $q^2$. The asymptotic behaviour for $q^2\to\infty$ is compared to a recent calculation of Sudakov logarithms. The result is an important ingredient for the calculation of radiative corrections to $Z$-boson production at hadron and lepton colliders.

We compute the relation between the pole quark mass and the minimally subtracted quark mass in the framework of QCD applying dimensional reduction as a regularization scheme. Special emphasis is put on the evanescent couplings and the renormalization of the epsilon-scalar mass. As a by-product we obtain the three-loop on-shell renormalization constants Zm(OS) and Z2(OS) in dimensional regularization and thus provide the first independent check of the analytical results computed several years ago.

Exclusive baryon pair production through the radiative return

is a unique tool to determine the electric and the magnetic form factors
in the timelike region over a wide range of energies. The decay of 
$\Lambda$-baryons into $p +\pi^-$ can be used to measure
their spin and to analyze
spin-spin correlations in the  $\bar\Lambda\Lambda$ system.
We evaluate the spin dependent hadronic tensor, which describes this reaction,
calculate the corresponding cross section for 
$e^+e^- \to \Lambda\bar\Lambda$ and $e^+e^- \to \Lambda\bar\Lambda\gamma$
with subsequent decays of  $\Lambda$ and $\bar\Lambda$ and present a compact
formula for the correlated distribution. We demonstrate that the relative
phase between the electric and the magnetic form factor can be determined
in this analysis by considering single spin asymmetries and correlated
decay distributions. The reaction is implemented in the event generator
 PHOKHARA. It is demonstrated that the relative phase can be measured 

with the event sample presently accumulated at $B$- factories.

New data for the total cross section $\sigma(e^+e^-\to\mbox{hadrons})$ in the charm and bottom threshold region are combined with an improved theoretical analysis, which includes recent four-loop calculations, to determine the short distance $\overline{\rm MS}$ charm and bottom quark masses. A detailed discussion of the theoretical and experimental uncertainties is presented. The final result for the $\overline{\rm MS}$-masses, $m_c(3~\mbox{GeV})=0.986(13)$~GeV and $m_b(10~\mbox{GeV})=3.609(25)$~GeV, can be translated into $m_c(m_c)=1.286(13)$~GeV and $m_b(m_b)=4.164(25)$~GeV. This analysis is consistent with but significantly more precise than a similar previous study.

Recent results on four-loop tadpoles amplitudes and their implications for precision calculations are presented.