Approximations for W-Pair Production at Linear-Collider Energies

We determine the accuracy of various approximations to the O(alpha) corrections for on-shell W-pair production. While an approximation based on the universal corrections arising from initial-state radiation, from the running of alpha, and from corrections proportional to m_t^2 fails in the Linear-Collider energy range, a high-energy approximation improved by the exact universal corrections is sufficiently good above about 500GeV. These results indicate that in Monte Carlo event generators for off-shell W-pair production the incorporation of the universal corrections is not sufficient and more corrections should be included.Comment: 7 pages, late

Gauge-Boson Production in Electron-Photon Collisions

We summarize results for the processes $e^-\gamma \to \nu W^-, e^-Z, e^-\gamma$ within the electroweak Standard Model. We discuss the essential features of the corresponding lowest-order cross-sections and present numerical results for the unpolarized cross-sections including the complete $O(\alpha)$ virtual, soft-photonic, and hard-photonic corrections. While at low energies the weak corrections are dominated by the leading universal corrections, at high energies we find large, non-universal corrections, which arise from vertex and box diagrams involving non-Abelian gauge couplings.Comment: 7 pages + 5 figures appended as ps-files (uuencoded), latex, CERN-TH. 6980/9

Reduction schemes for one-loop tensor integrals

We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e+ e- -> 4 fermions. The described methods for 3-point and 4-point integrals are, in particular, applicable in the case where the conventional Passarino-Veltman reduction breaks down owing to the appearance of Gram determinants in the denominator. One method consists of different variants for expanding tensor coefficients about limits of vanishing Gram determinants or other kinematical determinants, thereby reducing all tensor coefficients to the usual scalar integrals. In a second method a specific tensor coefficient with a logarithmic integrand is evaluated numerically, and the remaining coefficients as well as the standard scalar integral are algebraically derived from this coefficient. For 5-point tensor integrals, we give explicit formulas that reduce the corresponding tensor coefficients to coefficients of 4-point integrals with tensor rank reduced by one. Similar formulas are provided for 6-point functions, and the generalization to functions with more internal propagators is straightforward. All the presented methods are also applicable if infrared (soft or collinear) divergences are treated in dimensional regularization or if mass parameters (for unstable particles) become complex.Comment: 55 pages, latex, some references updated and few comments added, version to appear in Nucl. Phys.

Techniques for one-loop tensor integrals in many-particle processes

We briefly sketch the methods for a numerically stable evaluation of tensor one-loop integrals that have been used in the calculation of the complete electroweak one-loop corrections to \Pep\Pem\to4 fermions. In particular, the improvement of the new methods over the conventional Passarino--Veltman reduction is illustrated for some 4-point integrals in the delicate limits of small Gram (and other kinematical) determinants.Comment: 5 pages, latex, 2 postscript figures, to appear in the proceedings of the "7th International Symposium on Radiative Corrections (RADCOR2005)", Shonan Village, 200

Which Bosonic Loop Corrections are Tested in Electroweak Precision Measurements?

The nature of the electroweak bosonic loop corrections to which current precision experiments are sensitive is explored. The set of effective parameters \De x, \De y, and \eps, which quantify SU(2) violation in an effective Lagrangian, is shown to be particularly useful for this purpose. The standard bosonic corrections are sizable only in the parameter \De y, while \De x and \eps are sufficiently well approximated by the pure fermion-loop prediction. By analyzing the contributions to \De y it is shown that the bosonic loop corrections resolved by the present precision data are induced by the change in energy scale between the low-energy process muon decay and the energy scale of the LEP1 observables. If the (theoretical value of the) leptonic width of the W boson is used as input parameter instead of the Fermi constant \GF, no further bosonic loop corrections are necessary for compatibility between theory and experiment.Comment: 15 pages, latex, 6 uuencoded postscript figures, talk presented by G. Weiglein at The Second German-Polish Symposium, New Ideas in the Theory of Fundamental Interactions, Zakopane, September 199

Electroweak corrections to e+ e- -> f anti-f H

Some of the most interesting Higgs-production processes at future e+ e- colliders are of the type e+ e- -> f anti-f H. We present a calculation of the complete O(alpha) corrections to these processes in the Standard Model for final-state neutrinos and top quarks. Initial-state radiation beyond O(alpha) at the leading-logarithmic level as well as QCD corrections are also included. The electroweak corrections turn out to be sizable and reach the order of +/-10% and will thus be an important part of precise theoretical predictions for future e+ e- colliders.Comment: 4 pages, LaTeX, 4 postscript figures, talk given at Loops and Legs 2004, 7th DESY Workshop on Elementary Particle Theory, Zinnowitz, German