According to our present understanding many J/Psi production processes proceed through a coloured c\bar{c} state followed by the emission of soft particles in the quarkonium rest frame. The kinematic effect of soft particle emission is usually a higher-order effect in the non-relativistic expansion, but becomes important near the kinematic endpoint of quarkonium energy (momentum) distributions. In an intermediate region a systematic resummation of the non-relativistic expansion leads to the introduction of so-called shape functions'. In this paper we provide an implementation of the kinematic effect of soft gluon emission which is consistent with the non-relativistic shape function formalism in the region where it is applicable and which models the extreme endpoint region. We then apply the model to photoproduction of J/Psi and J/Psi production in B meson decay. A satisfactory description of B decay data is obtained. For inelastic charmonium photoproduction we conclude that a sensible comparison of theory with data requires a transverse momentum cut larger than the currently used 1 GeV.

We apply the strategy of regions within dimensional regularization to find functions involved in evolution equations which govern the asymptotic dynamics of the Abelian form factor and four-fermion amplitude in the SU(N) gauge theory in the Sudakov limit up to the next-to-leading logarithmic approximation. The results are used for the analysis of the dominant electroweak corrections to the fermion-antifermion pair production in the electron positron annihilation at high energy.

One-particle inclusive CP asymmetries in the decays of the type B → D(*) X are considered in the framework of a QCD based method to calculate the rates for one-particle inclusive decays.

The integration by parts recurrence relations allow to reduce some Feynman integrals to more simple ones (with some lines missing). Nevertheless the possibility of such reduction for the given particular integral was unclear. The recently proposed technique for studying the recurrence relations as by-product provides with simple criterion of the irreducibility.

The analytic relation between the \bar {MS} and the pole quark masses is computed to O(\alpha_s^3) in QCD. Using this exact result, the accuracy of the large \beta_0 approximation is critically examined and the implications of the obtained relation for semileptonic B decays are discussed.

Top quark production in electron-positron annihilation is one of the benchmark reactions at a future linear collider. Both electroweak and QCD corrections are large, amounting to 10% or even more in specific kinematic regions. In this note we present a method which allows to combine the dominant terms from both sources, thus improving considerably the result based on a simple addition of both corrections.

At variance with fully inclusive quantities, which have been computed already at the two- or three-loop level, most exclusive observables are still known only at one-loop, as further progress was hampered so far by the greater computational problems encountered in the study of multi-leg amplitudes beyond one loop. We show in this paper how the use of tools already employed in inclusive calculations can be suitably extended to the computation of loop integrals appearing in the virtual corrections to exclusive observables, namely two-loop four-point functions with massless propagators and up to one off-shell leg. We find that multi-leg integrals, in addition to integration-by-parts identities, obey also identities resulting from Lorentz-invariance. The combined set of these identities can be used to reduce the large number of integrals appearing in an actual calculation to a small number of master integrals. We then write down explicitly the differential equations in the external invariants fulfilled by these master integrals, and point out that the equations can be used as an efficient method of evaluating the master integrals themselves. We outline strategies for the solution of the differential equations, and demonstrate the application of the method on several examples.

To establish the Higgs mechanism {\it sui generis} experimentally, the Higgs self-interaction potential must be reconstructed. This task requires the measurement of the trilinear and quadrilinear self-couplings, as predicted in the Standard Model or in supersymmetric theories. The couplings can be probed in multiple Higgs production at high-luminosity e+e- linear colliders. We present the theoretical analysis for the production of neutral Higgs-boson pairs in the relevant channels of double Higgs-strahlung and associated multiple Higgs production.

The relation between the on-shell and $\overline{\rm MS}$ mass can be expressed through scalar and vector part of the quark propagator. In principle these two-point functions have to be evaluated on-shell which is a non-trivial task at three-loop order. Instead, we evaluate the quark self energy in the limit of large and small external momentum and use conformal mapping in combination with Pad\'e improvement in order to construct a numerical approximation for the relation [1]. The errors of our final result are conservatively estimated to be below 3\%. The numerical implications of the results are discussed in particular in view of top and bottom quark production near threshold. We show that the knowledge of new ${\cal O}(\alpha_s^3)$ correction leads to a significant reduction of the theoretical uncertainty in the determination of the quark masses.

Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta. Several recent applications also for other limiting cases are touched upon. Finally, the pros and cons of the different approaches are briefly discussed.

We report on the analytical calculation of the ${\cal O}(\alpha_s^3)$ conversion factor between the $\overline{\mbox{MS}}$ quark mass and the one defined in the so-called ``Regularization Invariant'' scheme.

The last unknown contribution to hydrogen energy levels at order m alpha ^7, due to the slope of the Dirac form factor at three loops, is evaluated in a closed analytical form. The resulting shift of the hydrogen nS energy level is found to be 3.016/n^3 kHz. Using the QED calculations of the 1S Lamb shift, we extract a precise value of the proton charge radius r_p=0.883 \pm 0.014 fm.

We derive explicit transformation formulae relating the renormalized quark mass and field as defined in the $\msbar$-scheme with the corresponding quantities defined in any other scheme. By analytically computing the three-loop quark propagator in the high-energy limit (that is keeping only massless terms and terms of first order in the quark mass) we find the NNNLO conversion factors transforming the $\msbar$ quark mass and the renormalized quark field to those defined in a ``Regularization Invariant'' (\RI) scheme which is more suitable for lattice QCD calculations. The NNNLO contribution in the mass conversion factor turns out to be large and comparable to the previous NNLO contribution at a scale of 2 GeV — the typical normalization scale employed in lattice simulations. Thus, in order to get a precise prediction for the $\msbar$ masses of the light quarks from lattice calculations the latter should use somewhat higher scale of around, say, 3 GeV where the (apparent) convergence of the perturbative series for the mass conversion factor is better. We also compute two more terms in the high-energy expansion of the $\msbar$ renormalized quark propagator. The result is then used to discuss the uncertainty caused by the use of the high energy limit in determining the $\msbar$ mass of the charmed quark. Finally, as a by-product of our calculations we determine the four-loop anomalous dimensions of quark mass and field in the Regularization Invariant scheme.

hadrons) at O(\alpha_s^3) > The calculation of the quartic mass terms at order \alpha_s^3 to the hadronic R ratio is described. It is based on the operator product expansion for the quark current correlator, combined with an application of the renormalization group equation.

We report on a recent calculation of the top decay rate up to order \alpha_s^2. It is based on asymptotic expansions of the off-shell top propagator, followed by a Pad\'e approximation in order to reach the physically relevant point q^2=Mt^2.

For the S-states of muonium and positronium, the hyperfine shifts to the order $\alpha^6$ of a recently derived two-fermion equation with explicit $\cal CPT$-invariance are checked against the results of a nonrelativistic reduction, and the leading $\alpha^8$ shifts are calculated. An additional hyperfine operator is discovered which can milden the singularity for $r\to 0$ of the Dirac hyperfine operator, such that the resulting extended operator can be used nonperturbatively. The binding correction to magnetic moments is mentioned.

We report on the analytical calculation of NNNLO (of order alpha_s^3) conversion factor between the MS-bar quark mass and the one defined in the so-called Regularization Invariant scheme. The NNNLO contribution in the conversion factor turns out to be relatively large and comparable to the known NNLO term.

In this article two-loop QED corrections to the muon decay and corrections of order $\alpha_s^2$ to the semileptonic decay of the bottom quark are considered. We compute the imaginary part of the four-loop diagrams contributing to the corresponding fermion propagator in the limit of small external momentum. The on-shell condition is obtained with the help of a conformal mapping and Pad\'e approximation. Via this method we confirm the existing results by an independent calculation.

One year of Z- and WW-Threshold running of TESLA can provide the possibility to measure electroweak precision observables to an extremely high accuracy. At the Z peak O(10^9) Z bosons and about 6 times 10^8 b quarks can be collected. We employ the expected uncertainties Delta(M_W) = 6 MeV and Delta(sin^2 theta_eff) = 0.00001 and demonstrate in this way that very stringent consistency tests of the Standard Model (SM) and the Minimal Supersymmetric Standard Model (MSSM) will be possible. The indirect determination of the Higgs-boson mass within the SM can reach an accuracy of about 5 %. The 6 times 10^8 b quarks can be used to investigate various b physics topics.

The spin physics parallel sessions at this workshop made a critical review of the physics potential of future experiments on polarized nucleons, with an emphasis on the potential impact of polarized electron-proton collisions at HERA. A summary of the results and discussions from these sessions is presented in this article.

The electromagnetic and weak structure functions of the photon can be studied in the deep inelastic electron-photon processes e+gamma → e+X and e+gamma → nu+X. While at low energies only virtual photon exchange is operative in the neutral-current process, additional Z-exchange becomes relevant for high Q2 of order MZ^2 at e+e- linear colliders. Likewise the charged-current process can be observed at these high energy colliders. By measuring the electroweak neutral- and charged-current structure functions, the up- and down-type quark content of the photon can be determined separately.

Extending earlier investigations, we analyze the quasi-elastic scattering of strongly interacting electroweak bosons at high-energy e+-e- colliders. The three processes e+e- → bar-nu nu W+W-, bar-nu nu ZZ, and e-e- → W-W- are examined at a c.m. energy of 1 TeV for high-luminosity runs. The expected experimental error on the scattering amplitude, parameter-free to leading order in the chiral expansion of the WW interactions, is estimated for 1 TeV colliders at the level of ten percent, providing a stringent test of strong interaction mechanisms for breaking the electroweak symmetries.

The relation between the on-shell quark mass and the mass defined in the modified minimal subtraction scheme is computed up to order \alpha_s^3. Implications for the numerical values of the top and bottom quark masses are discussed. We show that the new three-loop correction significantly reduces the theoretical uncertainty in the determination of the quark masses.

We study the production of photons accompanied by jets in large-$Q^2$ deep inelastic scattering. Numerical results for the cross section differential with respect to the fraction of momentum $z_{\gamma}$ carried by a photon inside a jet at large $z_{\gamma}, up to $ O(\alpha \alpha_s)$ in perturbative QCD, are presented. The sensitivity to the fragmentation contribution allows one to study the quark-to-photon fragmentation function. Our results can be confronted with future experimental data from HERA.

We discuss one-particle inclusive B decays in the limit of heavy b and c quarks. Using the large-N_C limit we factorize the non-leptonic matrix elements, and we employ a short distance expansion. Modeling the remaining nonperturbative matrix elements we obtain predictions for various decay channels and compare them with existing data.

We present the results of a calculation of deep inelastic electron-photon scattering at a linear collider for very high virtuality of the intermediate gauge boson up to NLO in perturbative QCD. The real photon is produced unpolarized via the Compton back scattering of laser light of the incoming beam. For $Q^2$ values close to the masses squared of the Z and W gauge bosons, the deep inelastic electron-photon scattering process receives important contributions not only from virtual photon exchange but also from the exchange of a Z-boson and a W-boson. We find that the total cross section for center of mass energies above $500 \rm{GeV}$ is at least of ${\cal O}(pb)$ and has an important charged current contribution.

The distribution of hadrons produced in deeply inelastic electron–proton collisions depends on the azimuthal angle between lepton scattering plane and hadron production plane in the photon-proton centre-of-mass frame. In addition to the well known up-down asymmetry induced by the azimuthal dependence of the Born level subprocess, there is also a non-vanishing left-right asymmetry, provided the incoming electron is polarized. This asymmetry is time-reversal-odd and induced by absorptive corrections to the Born level process. We investigate the numerical magnitude of azimuthal asymmetries in semi-inclusive hadron production at HERA with particular emphasis on a possible determination of the time-reversal-odd asymmetry.

The dominant electroweak double logarithmic corrections to the process $e^+e^-\rightarrow f\bar f$ at high energy are found in all orders of perturbation theory. In contrast to results in simple Yang-Mills theories these corrections do not exponentiate.

The systematic approach to solving the recurrence relations for multi-loop integrals is described. In particular, the criteria of their reducibility is suggested.

Using a perturbative model for diffractive interactions, we derive an expression for the polarized diffractive structure function $g_1^D$ in the high energy limit. This structure function is given by the interference of diffractive amplitudes with polarized and unpolarized exchanges. For the polarized exchange we consider both two-gluon and quark-antiquark amplitudes. The polarized diffractive amplitude receives sizable contributions from non-strongly ordered regions in phase space, resulting in a double logarithmic enhancement at small $x$. The resummation of these double logarithmic terms is outlined. We also discuss the transition from our perturbative expression to the nonperturbative region. A first numerical estimate indicates that the perturbative contribution to the spin asymmetry is substantially larger than the nonperturbative one.

Corrections of $O(\alpha_s^2)$ to the decay of the top quark into a W boson and a bottom quark are calculated. The method is based on an expansion of the top quark propagator for small external momentum, q, as compared to the top quark mass, M_t. The physical point q^2 = M_t^2 is reached through Pad\'e approximations. The described method allows to take effects induced by a finite W boson mass into account. The numerical relevance of the result is discussed. Important cross-checks against recent results for the decay rate $b \to u l \bar\nu$ and the two-loop QED corrections to $\mu$-decay are performed.

Order alpha^2 contribution to the orthopositronium decay rate due to one-photon virtual annihilation is found to be delta Gamma = (alpha/pi)^2 (pi^2 ln(alpha) - 0.8622(9))Gamma_LO.

Small-$x$ DIS is described as the scattering of a partonic fluctuation of the photon off a superposition of target color fields. Diffraction occurs if the emerging partonic state is in a color singlet. Introducing a specific model for the averaging over all relevant color field configurations, both diffractive and inclusive parton distributions at some low scale $Q_0^2$ can be calculated. A conventional DGLAP analysis results in a good description of diffractive and inclusive structure functions at higher values of $Q^2$.

We discuss the program EXP used to automate the successive application of asymptotic expansions to Feynman diagrams. We focus on the generation of the relevant subgraphs and the determination of the topologies for the remaining integrals. Both tasks can be solved by using backtracking-type recursive algorithms. In addition, an application of EXP is presented, where the integrals were calculated using the FORM packages MINCER and MATAD.

Recent results on second order quantum corrections to semileptonic decays of b quarks and positronium spectroscopy are reviewed. Similarities between calculations in these seemingly different problems are demonstrated. Technical aspects of solving systems of recurrence relations, and application of dimensional regularization to bound states are explained.

Two-loop QED corrections to the decay rate of parapositronium (p-Ps) into two photons are presented. We find Gamma(p-Ps –> 2 photons) = 7989.50(2)/microsec. The non-logarithmic O(alpha^2) corrections turn out to be small, contrary to some earlier estimates. We speculate that the so-called ``orthopositronium lifetime puzzle'' will not likely be solved by large QED corrections.

We suggest a method to determine V_ub / V_ts through a comparison of B → X_u l nu_l and B → X_s gamma. The relevant quantity is the spectrum of the light-cone component of the final state hadronic momentum, which in B → X_s gamma is the photon energy while in B → X_u l nu_l this requires a measurement of both hadronic energy and hadronic invariant mass. The non-perturbative contributions at tree level to these distributions are identical and may be cancelled by taking the ratio of the spectra. Radiative corrections to this comparison are discussed to order alpha_s and are combined with the non-perturbative contributions.

The determination of the Fermi coupling constant, G_F, is examined in the light of recently calculated 2-loop QED corrections and planned experiments tomeasure the muon lifetime to a level below 1ppm. The methods used in the calculation of the QED corrections are described in detail. Sources of thedominant theoretical and experimental uncertainties are identified. Finally the incorporation of G_F into analyses using the full electroweak Standard Model is discussed.

The reconstruction of the Higgs potential in the Standard Model or supersymmetric theories demands the measurement of the trilinear Higgs couplings. These couplings affect the multiple production of Higgs bosons at high energy colliders. We present a systematic overview of the cross sections for the production of pairs of (light) neutral Higgs bosons at the LHC. The analysis is carried out for the Standard Model and its minimal supersymmetric extension.

This is the first part of a report submitted to Compaq (formerly DEC) on the parallelization of the symbolic manipulation program FORM on cluster architectures using message passing libraries.

After an introduction to the sequential version of FORM and the mechanisms behind it we report on the status of our ongoing project of its parallelization. An analysis of the parallel platforms used is given and the structure of a parallel prototype of FORM is explained.

After a short introduction to the mechanisms behind the sequential version of the symbolic manipulation program FORM we report on the status of the project of its parallelization on a variety of computer architectures and show first results, which indicate a significant speedup.

The production of photons accompanied by jets in large-$Q^2$ deep inelastic $ep$ scattering is calculated in next-to-leading order. We describe how to consistently include contributions from quark-to-photon fragmentation and give numerical results relevant for HERA experiments.

We calculate the contributions of the axial current to top quark pair production in e+ e- annihilation at threshold. The QCD dynamics is taken into account by solving the Lippmann-Schwinger equation for the P wave production using the QCD potential up to two loops. We demonstrate that the dependence of the total and differential cross section on the polarization of the e+ and e- beams allows for an independent extraction of the axial current induced cross section.

u decay rate > The order alpha_s^2 contribution to the inclusive semileptonic decay width

of a b quark \Gamma( b -> X_u e \overline{\nu}_e ) is calculated
 analytically for zero mass u quarks.

The partial decay rate of the $Z$ boson into bottom quarks constitutes an important decay channel. This is mainly due to the virtual presence of the top quark in the loop diagrams giving rise to correction factors which are quadratic in the top quark mass. At one- and two-loop order it turned out that the leading term in the heavy-top expansion leads to very good approximations to the exact result. In this work the non-singlet diagrams at O(\alpha_s^2 G_F M_t^2) are considered.

We propose to use events with radiated photons in e^+e^- collisions to measure the total cross section of e^+ e^- \to hadrons as a function of the center of mass energy. The Monte Carlo simulation for the collider DAPHNE shows that a competitive accuracy can be achieved with this method.

The harmonic polylogarithms (hpl's) are introduced. They are a generalization of Nielsen's polylogarithms, satisfying a product algebra (the product of two hpl's is in turn a combination of hpl's) and forming a set closed under the transformation of the arguments \( x=1/z \) and \( x=(1-t)/(1+t) \). The coefficients of their expansions and their Mellin transforms are harmonic sums.

In this talk the recent results on perturbative QCD corrections to the hadronic decay rate of the tau lepton are presented. We discuss the structure of perturbation theory series of the leading mass correction. On the base of this analysis the numerical value of the strange quark mass is extracted.

We investigate the reaction $e p \to e PS X$ where PS denotes a pseudoscalar meson $\pi^0, \eta, \eta'$, or $\eta_c$ and X either a proton or resonance or continuum states into which the proton can go by diffractive excitation. At high energies photon and odderon exchange contribute to the reaction. The photon exchange contribution is evaluated exactly using data for the total virtual photon-proton absorption cross section. The odderon exchange contribution is calculated in nonperturbative QCD, using functional integral techniques and the model of the stochastic vacuum. For the proton we assume a quark-diquark structure as suggested by the small odderon amplitude in $pp$ and $p \bar{p}$ forward scattering. We show that odderon exchange leads to a much larger inelastic than elastic PS production cross section. Observation of our reaction at HERA would establish the soft odderon as an exchange object on an equal footing with the soft pomeron and would give us valuable insight into both the nucleon structure and the mechanism of high energy diffractive scattering.

We present a calculation of the O(m alpha^7 ln(alpha)^2) corrections to positronium energy levels. The result is used to estimate the current uncertainty in theoretical predictions of the positronium spectrum.

The problem of our understanding of the spin structure of the nucleon has been with us since the publication of the EMC measurements of the polarised structure function of the proton in 1987. In this talk a review of the results presented in Working Group 6 at this workshop is given.

We present an analytic calculation of the O(m alpha^6) recoil and radiative recoil corrections to energy levels of positronium nS states and their hyperfine splitting. A complete analytic formula valid to O(m alpha^6) is given for the spectrum of S states. Technical aspects of the calculation are discussed in detail. Theoretical predictions are given for various energy intervals and compared with experimental results.

To establish the Higgs mechanism sui generis experimentally, the self-energy potential of the Higgs field must be reconstructed. This task requires the measurement of the trilinear and quadrilinear self-couplings, as predicted, for instance, in the Standard Model or in supersymmetric theories. The couplings can be probed in multiple Higgs production at high-luminosity e+e- linear colliders. Complementing earlier studies to develop a coherent picture of the trilinear couplings, we have analyzed the production of pairs of neutral Higgs bosons in all relevant channels of double Higgs-strahlung, associated multiple Higgs production and WW/ZZ fusion to Higgs pairs.

Recent progress in the calculation of multi-loop, multi-scale diagrams is reviewed. Expansion techniques combined with new developments in Computer algebra allow to evaluate the R ratio for massive quarks up to order $\alpha_s^2$ and, partly, even $\alpha_s^3$. Similar techniques can be applied to Higgs- or Z-boson decays and mixed QCD and electroweak interactions.