Stefan Dittmaier

Predictions for all processes e+e− → fermions + γ

The complete matrix elements for e+e− → 4 and e+e− → 4fγy are calculated in the Electroweak Standard Model for polarized massless fermions. The matrix elements for all final states are reduced to a few compact generic functions. Monte Carlo generators for e+e− → 4f and e+e− → 4fγ are constructed. We compare different treatments of the finite widths of the electroweak gauge bosons; in particular, we include a scheme with a complex gauge-boson mass that obeys all Ward identities. The detailed discussion of numerical results comprises integrated cross sections as well as photon-energy distributions for all different final states.

A general approach to photon radiation off fermions

Soft or collinear photon emission potentially poses numerical problems in the phase-space integration of radiative processes. In this paper, a general subtraction formalism is presented that removes such singularities from the integrand of the numerical integration and adds back the analytically integrated contributions that have been subtracted. The method is a generalization of the dipole formalism of Catani and Seymour, which was formulated for NLO QCD processes with massless unpolarized particles. The presented formalism allows for arbitrary mass and helicity configurations in processes with charged fermions and any other neutral particles. Particular attention is paid to the limit of small fermion masses, in which collinear singularities cause potentially large corrections. The actual application and the efficiency of the formalism are demonstrated by the discussion of photonic corrections to the processes , e−γ→e−γ(γ), and .

Application of the background-field method to the electroweak standard model

Abstract Application of the background-field method yields a gauge-invariant effective action for the electroweak Standard Model, from which simple QED-like Ward identities are derived. As a consequence of these Ward identities, the background-field Green functions are shown to possess very desirable theoretical properties. The renormalization of the Standard Model in the background-field formalism is studied. A consistent on-shell renormalization procedure retaining the full gauge symmetry is presented. The structure of the counterterms is shown to greatly simplify compared to the conventional formalism. A complete list of Feynman rules for the Standard Model in the background-field method is given for arbitrary values of a quantum gauge parameter including all counterterms necessary for one-loop calculations.

One-loop Singular Behaviour of QCD and SUSY QCD Amplitudes with Massive Partons

We discuss the structure of infrared and ultraviolet singularities in on-shell QCD and supersymmetric QCD amplitudes at one-loop order. Previous results, valid for massless partons, are extended to the case of massive partons. Using dimensional regularization, we present a general factorization formula that controls both the singular ǫ-poles and the logarithmic contributions that become singular for vanishing masses. We introduce generalized Altarelli–Parisi splitting functions and discuss their relations with the singular terms in the amplitudes. The dependence on the regularization scheme is also considered.

Electroweak radiative corrections to e+e−→WW→4 fermions in double-pole approximation — the RacoonWW approach

Abstract We calculate the complete O (α) electroweak radiative corrections to e + e − →WW→4 f in the electroweak Standard Model in the double-pole approximation. We give analytical results for the non-factorizable virtual corrections and express the factorizable virtual corrections in terms of the known corrections to on-shell W-pair production and W decay. The calculation of the bremsstrahlung corrections, i.e., the processes e + e − →4 fγ in lowest order, is based on the full matrix elements. The matching of soft and collinear singularities between virtual and real corrections is done alternatively in two different ways, namely by using a subtraction method and by applying phase-space slicing. The O (α) corrections as well as higher-order initial-state photon radiation are implemented in the Monte Carlo generator RacoonWW . Numerical results of this program are presented for the W-pair-production cross section, angular and W-invariant-mass distributions at LEP2. We also discuss the intrinsic theoretical uncertainty of our approach.We calculate the complete O(alpha) electroweak radiative corrections to e+e- -->WW -->4f in the electroweak Standard Model in the double-pole approximation. We give analytical results for the non-factorizable virtual corrections and express the factorizable virtual corrections in terms of the known corrections to on-shell W-pair production and W decay. The calculation of the bremsstrahlung corrections, i.e. the processes e+e- -->4f+gamma in lowest order, is based on the full matrix elements. The matching of soft and collinear singularities between virtual and real corrections is done alternatively in two different ways, namely by using a subtraction method and by applying phase-space slicing. The O(alpha) corrections as well as higher-order initial-state photon radiation are implemented in the Monte Carlo generator RACOONWW. Numerical results of this program are presented for the W-pair-production cross section, angular and W-invariant-mass distributions at LEP2. We also discuss the intrinsic theoretical uncertainty of our approach.

Stable calculations for unstable particles: Restoring gauge invariance

We discuss theoretical and phenomenological aspects of the use of boson propagators with energy-dependent widths in predictions for high-energy scattering processes. In general, gauge invariance is violated in such calculations. We discuss several approaches to restore gauge invariance, necessary for a reliable result. The most promising method is the addition of the relevant parts of the fermionic corrections, which fulfills all Ward identities. The numerical difference between this and other approaches is studied. A number of recommendations are given for LEP2 computations.

Four-Fermion Production in Electron-Positron Collisions /

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 Fermion loop scheme for finite width effects in

Abstract We describe the gauge-invariant treatment of the finite-width effects of W and Z bosons in the fermion-loop scheme and its application to the six-fermion (LEP2) processes et-e+ → four fermions, with massless external fermions. The fermion-loop scheme consists in including all fertnionic one-loop corrections in tree-level amplitudes and resumming the self-energies. We give explicit results for the unrenormalized fermionic one-loop contributions to the gauge-boson self-energies and the triple gauge-boson vertices, and perform the renormalization in a gauge invariant way by introducing complex pole positions and running couplings. A simple effective Born prescription is presented, which allows for a relatively straightforward implementation of the fermion-loop scheme in LEP1 and LEP2 processes. We apply this prescription to typical LEP2 processes, i.e. e t- e + → μ t- ν μ u d , e t- e + → s c u d , and e t- e + → e t- ν e r d , and give numerical comparisons with other gauge-invariance-preserving schemes in the energy range of LEP2, NLC and beyond.

e^{+} e^{-}

Abstract Application of the background-field method to QCD and the electroweak Standard Model yields gauge-invariant effective actions giving rise to simple Ward identities. Within this method, we calculate the quantities that have been treated in the literature using the pinch technique. Putting the quantum gauge parameter equal to one, we recover the pinch-technique results as a special case of the background-field method. The one-particle-irreducible Green functions of the background-field method fulfil for arbitrary gauge parameters the desirable theoretical properties that have been noticed within the pinch technique. Therefore the background-field formalism provides a general framework for the direct calculation of well-behaved Green functions. Within this formalism, the pinch technique appears as one of arbitrarily many equivalent possibilities.

annihilation into four fermions

Abstract First numerical results of the Monte Carlo generator RacoonWW for e + e − →WW→4 f (+ γ ) in the electroweak Standard Model are presented. This event generator is the first one that includes O (α) electroweak radiative corrections in the double-pole approximation completely. We briefly describe the strategy of the calculation and give numerical results for total cross sections, including CC03, and various distributions.First numerical results of the Monte Carlo generator RACOONWW for e+e- --> WW --> 4fermions(+gamma) in the electroweak Standard Model are presented. This event generator is the first one that includes O(alpha) electroweak radiative corrections in the double-pole approximation completely. We briefly describe the strategy of the calculation and give numerical results for total cross sections, including CC03, and various distributions.First numerical results of the Monte Carlo generator RACOONWW for e+e- -->WW -->4fermions(+gamma) in the electroweak Standard Model are presented. This event generator is the first one that includes O(alpha) electroweak radiative corrections in the double-pole approximation completely. We briefly describe the strategy of the calculation and give numerical results for total cross sections, including CC03, and various distributions.