Tests of the standard model and its hypothetical extensions require precise theoretical predictions for processes involving massive, unstable particles. It is well-known that ordinary weak-coupling perturbation theory breaks down due to intermediate singular propagators. Various pragmatic approaches have been developed to deal with this difficulty. In this paper we construct an effective field theory for resonant processes utilizing the hierarchy of scales between the mass of the unstable particle, M, and its width, Gamma. The effective theory allows calculations to be systematically arranged into a series in g^2 and Gamma/M, and preserves gauge invariance in every step. We demonstrate the applicability of this method by calculating explicitly the inclusive line shape of a scalar resonance in an abelian gauge-Yukawa model at next-to-leading order in Gamma/M and the weak couplings. We also discuss the extension to next-to-next-to-leading order and compute an interesting subset of these corrections.

We present a study of the effective action approach to incorporate higher-order effects in e^+e^- -> n fermions. In its minimal version, the effective action approach is found to exhibit problems with unitarity and high-energy behaviour. We identify the origin of these problems by investigating the zero-mode solutions of the Ward Identities. A numerical analysis of the importance of the zero-mode solutions is presented for four-fermion production processes.

An important unresolved question in strong interaction physics concerns the parameterization of power-suppressed long-distance effects to hard processes that do not admit an operator product expansion (OPE). Recently Bauer et al. have developed an effective field theory framework that allows one to formulate the problem of soft-collinear factorization in terms of fields and operators. We extend the formulation of soft-collinear effective theory, previously worked out to leading order, to second order in a power series in the inverse of the hard scale. We give the effective Lagrangian and the expansion of “currents” that produce collinear particles in heavy quark decay. This is the first step towards a theory of power corrections to hard processes where the OPE cannot be used. We apply this framework to heavy-to-light meson transition form factors at large recoil energy.

We analyze the structure of higher-order radiative corrections for processes with unstable particles. By subsequently integrating out the various scales that are induced by the presence of unstable particles we obtain a hierarchy of effective field theories. In the effective field theory framework the separation of physically different effects is achieved naturally. In particular, we automatically obtain a separation of factorizable and non-factorizable corrections to all orders in perturbation theory. At one loop this treatment is equivalent to the double-pole approximation (DPA) but generalizes to higher orders and, at least in principle, to beyond the DPA. It is known that one-loop non-factorizable corrections to invariant mass distributions are suppressed at high energy. We study the mechanism of this suppression and obtain estimates of higher-order non-factorizable corrections at high energy.

We propose a novel procedure for handling processes that involve unstable intermediate particles. By using gauge-invariant effective Lagrangians it is possible to perform a gauge-invariant resummation of (arbitrary) self-energy effects. For instance, gauge-invariant tree-level amplitudes can be constructed with the decay widths of the unstable particles properly included in the propagators. In these tree-level amplitudes modified vertices are used, which contain extra gauge-restoring terms prescribed by the effective Lagrangians. We discuss the treatment of the phenomenologically important unstable particles, like the top quark, the W- and Z-bosons, and the Higgs boson, and derive the relevant modified Feynman rules explicitly.

The bremsstrahlung spectrum of photons accompanying W pair production depends on the decay width of the unstable W bosons. The dependence arises from the interference between emission at different stages of the production and decay process. We present a quantitative discussion of this effect, and consider the implications for measurements at LEP2 and LC energies.

This report summarises the results of the four-fermion working group of the LEP2-MC workshop, held at CERN from 1999 to 2000. Recent developments in the calculation of four-fermion processes in electron-positron collisions at LEP-2 centre-of-mass energies are presented, concentrating on predictions for four main reactions: W-pair production, visible photons in four-fermion events, single-W production and Z-pair production. Based on a comparison of results derived within different approaches, theoretical uncertainties on these predictions are established.

The activities of the QCD working group concentrated on improving the understanding and Monte Carlo simulation of multi-jet final states due to hard QCD processes at LEP, i.e. quark-antiquark plus multi-gluon and/or secondary quark production, with particular emphasis on four-jet final states and b-quark mass effects. Specific topics covered are: relevant developments in the main event generators PYTHIA, HERWIG and ARIADNE; the new multi-jet generator APACIC++; description and tuning of inclusive (all-flavour) jet rates; quark mass effects in the three- and four-jet rates; mass, higher-order and hadronization effects in four-jet angular and shape distributions; b-quark fragmentation and gluon splitting into b-quarks.

We demonstrate that the results of the complete first order calculation of the non-factorizable QED corrections to the single-inclusive cross-sections for $e^+e^- \to W^+W^- \to 4$ fermions could be very well reproduced by a simple physically motivated ansatz. The latter allows to take into account effectively the screening role of the non-Coulomb radiative mechanisms by introducing a dampening factor in front of the width-dependent part of the known first-order Coulomb correction, the so-called screened-Coulomb ansatz.

We present the radiative corrections to off-shell $W$-pair production, as calculated within the double-pole approximation.

We calculate the one-loop non-factorizable QCD corrections to the production and decay of pairs of top quarks at various collider experiments. These non-factorizable corrections interconnect the different production and decay stages of the off-shell top-pair production processes. This in particular affects the invariant-mass distributions of the off-shell top quarks, resulting in a shift of the maximum of the distorted Breit–Wigner distributions. Although the non-factorizable corrections can be large, the actual shift in the mass as determined from the peak position of the corrected Breit–Wigner line-shape is below 100MeV.

Radiative corrections to processes that involve the production and subsequent decay of unstable particles are complex due to various theoretical and practical problems. The so-called double-pole approximation offers a way out of these problems. This method is applied to the reaction e+e− → W+W− → 4 fermions, which allows us to address all the key issues of dealing with unstable particles, like gauge invariance, interactions between different stages of the reaction, and overlapping resonances. Within the double-pole approximation the complete O(α) electroweak corrections are evaluated for this off-shell W-pair production process. Examples of the effect of these corrections on a number of distributions are presented. These comprise mass and angular distributions as well as the photon-energy spectrum.

In this letter it is shown how final-state QED corrections to the production of a pair of resonances can distort the line shape of such a resonance in a sizeable way. This effect depends on the definition of the line shape and can reach up to 30%, depending on the final state. The mechanism is first displayed for a particular case of ZZ production, for which an exact and approximate treatment can be given. The approximate method is then applied to W-pair production. In addition some simple rules of thumb are given for accurately estimating the characteristic distortion effects, like the mass shift and peak reduction.

In this paper we study the non-factorizable QED corrections to W-pair-mediated (charged-current) four-fermion production in electron-positron collisions. A brief account of the obtained analytical results is given. They turn out to be different from the ones published in the literature. Numerical results are presented, in particular the effects on the W line-shape. These effects are of the order of a per cent. The validity of the presented calculations starts a few widths above the W-pair threshold. Applying the same methods to ZZ- or ZH-mediated four-fermion production, the non-factorizable O(α) corrections to the Z or H line-shape vanish.

In this paper we present two methods to evaluate non-factorizable corrections to pair-production of unstable particles. The methods are illustrated in detail for W-pair-mediated four-fermion production. The results are valid a few widths above threshold, but not at threshold. One method uses the decomposition of n-point scalar functions for virtual and real photons, and can therefore be generalized to more complicated final states than four fermions. The other technique is an elaboration on a method known from the literature and serves as a useful check. Applications to other processes than W-pair production are briefly mentioned.