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Work on electroweak precision calculations and event generators for electroweak physics studies at current and future colliders is summarized.

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We present a subtraction scheme for eliminating the ultraviolet, soft, and collinear divergences in the numerical calculation of an arbitrary one-loop QCD amplitude with an arbitrary number of external legs. The subtractions consist of local counter terms in the space of the four-dimensional loop momentum.

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Some methods for the numerical computation of two-loop non-infrared vertices are reviewed. A new method is also proposed and compared to the old ones. Finally, some preliminary results are presented, concerning the evaluation of the fermionic corrections to \(\sin ^2\theta _{\rm eff}^{\rm lept}\) through the described techniques.

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We review the Laporta algorithm for the reduction of scalar integrals to the master integrals and the differential equations technique for their evaluation. We discuss the use of the basis of harmonic polylogarithms for the analytical expression of the results and some generalization of this basis to wider sets of transcendental functions.

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The physics of high-energy collider experiments asks for delicate comparisons between theoretical predictions and experimental data. Signals and potential backgrounds for new physics have to be predicted at sufficient accuracy. The accuracy as well as the computational complexity of the calculations leading to the predictions depend on both the number of external particles in the process analyzed and the order of the quantum corrections, the number of loops, included in the calculation. We present some approaches to problems occurring in these calculations regarding the integration of phase-space and the inclusion of one-loop corrections.

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While the Monte Carlo approach to integration dominates any numerical calculation in particle physics phenomenology, the Quasi-Monte Carlo method, which promises better performance, is restrained to relatively minor applications. One of the reasons is the difficulty in estimating reliably the error when using Quasi-Monte Carlo point sequences. The classical Monte Carlo estimator, that consistently overestimates the error, has been used up to now. We review the situation on the error estimators for classical Monte Carlo and present a new estimator for Quasi-Monte Carlo.

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A joint effort of the network in investigation of a Higgs sector in Standard Model and beyond at high energy colliders is summarized.

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Some of the most interesting Higgs-production processes at future \(e^+e^-\) colliders are of the type \(e^+e^-\to f\bar fH\). We present a calculation of the complete \({\cal O}(\alpha )\) corrections to these processes in the Standard Model for final-state neutrinos and top quarks. Initial-state radiation beyond \({\cal O}(\alpha )\) 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 \(\pm 10 \%\) and will thus be an important part of precise theoretical predictions for future \(e^+e^-\) colliders. Furthermore, an overview is given of a technique for a fast and reliable numerical calculation of multi-leg one-loop integrals. The method is numerically stable also for exceptional momentum configurations and easily allows the introduction of complex masses and the calculation of higher orders in the expansion around \(D=4\).

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We review some recent developments in top quark production and decay at current and future colliders.

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Top flavour-changing neutral interactions with a light quark \(q=u,c\) and a gauge or Higgs boson are very suppressed within the Standard Model (SM), but can reach observable levels in many of its extensions. We review the possible size of the effective vertices \(Ztq\), \(\gamma tq\), \(gtq\) and \(Htq\) in several SM extensions, and discuss the processes in which these interactions might show up at LHC and at a high energy \(e^+ e^-\) linear collider.

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A review of the activity of the European Network “Physics at Colliders” in the area of SUSY particle physics is presented.

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We present a computation of the leading two-loop corrections to the MSSM Higgs boson masses and electroweak symmetry breaking conditions. The computation is performed in the effective potential approach and includes corrections controlled by the third-family Yukawa couplings and the strong gauge coupling. We discuss a renormalisation scheme that avoids unphysically large threshold effects associated with the bottom Yukawa couplings. We also discuss the implementation of our corrections in computer programs that compute the MSSM mass spectrum from a set of unified high-energy boundary conditions.

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Recent studies about the impact of the CP-violating complex parameters in supersymmetry on the decays of third generation squarks and about \(T\)-odd asymmetries in neutralino and chargino production and decay are reviewed. The CP-even branching ratios of the third generation squarks show a pronounced dependence on the phases of \(A_t\), \(A_b\), \(\mu \) and \(M_1\) in a large region of the supersymmetric parameter space. This could have important implications for stop and sbottom searches and the MSSM parameter determination in future collider experiments. We have estimated the expected accuracy in the determination of the parameters by global fits of measured masses, decay branching ratios and production cross sections. We have found that the parameter \(A_t\) can be determined with an error of 2–3 %, whereas the error on \(A_b\) is likely to be of the order of 50–100 %. In addition we have studied CP-odd observables, like asymmetries based on triple product correlations, which are necessary to unambiguously establish CP violation. We have analysed these asymmetries in neutralino and chargino production with subsequent three-body decays at the International Linear Collider with longitudinally polarised beams in the MSSM with complex parameters \(M_1\) and \(\mu \). The asymmetries, which appear already at tree-level because of spin correlation between production and decay, can be as large as 20 % and will therefore be an important tool for the search for CP-violating effects in supersymmetry.

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The Fortran code SDECAY is presented which calculates the decay widths and branching ratios of all supersymmetric particles in the Minimal Supersymmetric Standard Model, including higher order effects. The program incorporates the usual two-body decays of sfermions and gauginos as well as the three-body decay modes of charginos, neutralinos and gluinos. The three-body stop and sbottom decays are implemented as well and even the four-body stop decays are calculated. Moreover, the important loop-induced decays, the QCD corrections to the two-body widths involving strongly interacting particles and the dominant electroweak effects to all processes are evaluated.

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New large colliders will probe scales up to few TeV, indicating the way Nature has chosen to extend the Standard Model. We review alternative scenarios to the traditional Minimal Supersymmetric Standard Model: the little Higgs model, split supersymmetry and extra dimensional models with low energy signals.

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Neutrino physics plays a very important role in understanding several aspects of fundamental physics. In this short review, we revise three different aspects connected to them. Neutrino oscillations at low energy (up to few GeV) offer the possibility to study possible leptonic CP violation whereas at ultra-high energy (\(E_\nu \gt 10^3\) TeV) they could enable to check scenarios of Physics Beyond the Standard Model involving extra-dimensions. On the other hand, \(e^+ e^-\) colliders can help in detecting new heavy Majorana neutrinos suggested by Grand Unified Theories with masses of \({\cal O}(10^2\) GeV).

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We discuss some effects associated to thin defects in extra dimensions. After describing the generation of quantum corrections localized at orbifold fixed points, we show some phenomenological implications of the localized terms and point out to generic problems of field theories in the presence of infinitely thin defects, which signal a breakdown of the low-energy expansion. We discuss possible physical interpretations and ways out of these phenomena. Finally, we examine some of these issues in a deconstructed orbifold, which can be regarded as an ultraviolet completion of these models.