Raymond Gastmans

Single bremsstrahlung processes in gauge theories

Abstract We find that, for QED and for SU( N ) gauge theories, single hard bremsstrahlung cross sections are remarkably simple in the ultrarelativistic limit. They can be written as a product of two factors: one factor is connected with the lowest order, elastic process, and the second one is related to the infrared factor which describes soft quantum emission. We present explicit formulae for various processes.

Multiple bremsstrahlung in gauge theories at high energies (I). General formalism for quantum electrodynamics

Multiple bremsstrahlung is studied on the level of tree diagrams for gauge theories. At high energies and in most of the kinematic region, the fermion mass can be neglected. In this case, it is natural to introduce helicity states for both fermions and gauge particles. Our general formalism is given in detail for quantum electrodynamics. In particular, it is expedient to use photon polarization vectors which depend on the fermion helicities. In this way, extensive cancellations between Feynman diagrams are accomplished automatically.

Multiple bremsstrahlung in gauge theories at high energies (II). Single bremsstrahlung

We calculate the helicity amplitudes for the QED processes e+e−→γγγ, μ+μ−γ, and e+e−γ, in the limit of vanishing fermion masses. This is done by introducing explicit polarization vectors for the radiated photons. With the same technique, we also calculate these processes taking into account Z0 exchange. Finally, we present the unpolarized cross sections in which mass terms are retained to describe the radiation of photons in directions parallel to those of the fermions.

Conformal invariance in quantum gravity

Abstract Trace anomalies in a conformal invariant theory do not arise when its conformal invariance in four dimensions is extended to an arbitrary number n of space-time dimensions: the theory can be made finite in any order of perturbation theory by conformal invariant counterterms in n dimensions. Such an extension of conformal invariance is possible provided one works in the framework of spontaneously broken conformal invariance. This is shown explicitly by working out several examples at the one-loop level and by examining the Ward identities which lead to a general proof. We speculate upon possible consequences of these results on the nature of gravitation and other fundamental interactions.

Dimensional regularization of the infrared problem

Abstract It is shown with a simple example, the scattering of an electron in an external field, how the dimensional regularization technique can be used to handle the infrared divergences associated with real and virtual radiative corrections. It is found that the dimensionality of space-time serves as a cut-off for ultraviolet and infrared divergences, thus completely avoiding the introduction of a fictitious photon mass.

Multiple Bremsstrahlung in Gauge Theories at High-energies. 3. Finite Mass Effects in Collinear Photon Bremsstrahlung

Abstract We present a method for calculating the various spin amplitudes for QED processes in which an arbitrary number of photons is radiated in directions nearly parallel to the fermion directions. This is accomplished by introducing explicit polarization vectors for the photons and by working in the high energy limit, where finite mass effects are treated in leading order.

Helicity Amplitudes for Massless QED

Abstract The introduction of helicity states, for both fermions and photons, is shown to lead to simple expressions for QED amplitudes, in which an arbitrary number of photons are radiated, provided that the fermion masses can be neglected. As an example, the results are given for the process e + e − →4 γ .

Multiple Bremsstrahlung in Gauge Theories at High-Energies. 4. The Process e+ e- ---> gamma gamma gamma gamma

Abstract We calculate the helicity amplitude and the cross section for the process e + e − → 4 γ in the high-energy limit. The resulting expressions are presented in a form which allows an easy numerical evaluation. They are valid for the kinematical configurations where at most two photons are emitted in directions nearly parallel to the lepton directions.

Production of heavy quarkonia from gluons

Abstract By introducing, in a covariant way, explicit polarization vectors for the gluons, we calculate the various helicity amplitudes for the processes g + g →( 2S+1 L J )+ g , with L = S or P . In this way, we obtain simple formulae for the cross sections of these processes, which, in the framework of the perturbative QCD, are related to the hadroproduction of heavy quarkonia.

Hard photon corrections for e+e− → γγ

Abstract The differential cross section for e + e − → γγ is calculated to order α 3 for the case of e + e − colliding beam experiments. Special attention is given to hard photon corrections. For a specific experimental set-up, detailed numerical results are presented. It is found that the radiative corrections can be quite large in the forward direction.