P. De Causmaecker

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.

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: (V). The process e+e− → μ+μ−γγ

Abstract We calculate the helicity amplitudes and the cross section for the process e + e − → μ + μ − γγ in the high-energy limit. The resulting expressions are presented in a form which allows an easy numerical evaluation. They are also valid for the kinematical configuration where one or two photons are emitted in directions nearly parallel to any lepton direction.

Four-jet production in e+e− annihilation☆

Abstract For e + e − → qqgg and e + e − → qqqq, we find simple xpressions for the helicity amplitudes, from which the cross section for e + e − → four jets is readily obtained.

Multiple bremsstrahlung in gauge theories at high energies: (VI). The process e+e− → e+e−γγ

Abstract We calculate the helicity amplitudes and the cross section for the process e+e− → e+e−γγ in the high-energy limit. The resulting expressions are presented in a form which allows an easy numerical evaluation. We also present the cross section for configurations where one or two photons are emitted nearly parallel to an incoming or outgoing lepton.

Learning agents for the multi-mode project scheduling problem

Intelligent optimization refers to the promising technique of integrating learning mechanisms into (meta-)heuristic search. In this paper, we use multi-agent reinforcement learning for building high-quality solutions for the multi-mode resource-constrained project scheduling problem (MRCPSP). We use a network of distributed reinforcement learning agents that cooperate to jointly learn a well-performing constructive heuristic. Each agent, being responsible for one activity, uses two simple learning devices, called learning automata, that learn to select a successor activity order and a mode, respectively. By coupling the reward signals for both learning tasks, we can clearly show the advantage of using reinforcement learning in search. We present some comparative results, to show that our method can compete with the best performing algorithms for the MRCPSP, yet using only simple learning schemes without the burden of complex fine-tuning.

Exact and heuristic methods for placing ships in locks

The ship placement problem constitutes a daily challenge for planners in tide river harbours. In essence, it entails positioning a set of ships into as few lock chambers as possible while satisfying a number of general and specific placement constraints. These constraints make the ship placement problem different from traditional 2D bin packing. A mathematical formulation for the problem is presented. In addition, a decomposition model is developed which allows for computing optimal solutions in a reasonable time. A multi-order best fit heuristic for the ship placement problem is introduced, and its performance is compared with that of the left-right-left-back heuristic. Experiments on simulated and real-life instances show that the multi-order best fit heuristic beats the other heuristics by a landslide, while maintaining comparable calculation times. Finally, the new heuristic’s optimality gap is small, while it clearly outperforms the exact approach with respect to calculation time.