Each incoming beam particle may leave behind a beam remnant, which does not take part in the initial-state radiation or hard scattering process. If nothing else, the remnants need be reconstructed and connected to the rest of the event. In hadron-hadron collisions, the composite nature of the two incoming beam particles implies the additional possibility that several parton pairs undergo separate hard or semi-hard scatterings, `multiple interactions'. This may give a non-negligible contribution to the `underlying event' structure, and thus to the total multiplicity. Finally, in high-luminosity colliders, it is possible to have several collisions between beam particles in one and the same beam crossing, i.e. pile-up events, which further act to build up the general particle production activity that is to be observed by detectors. These three aspects are described in turn, with emphasis on the middle one, that of multiple interactions within a single hadron-hadron collision.
Work is ongoing to improve the theoretical framework for multiple interactions. PYTHIA therefore contains two partly separate approaches to this physics, which also leads to two partly separate descriptions of beam remnants. We will refer to these as the ``old model'' and the ``new model''. The old model, based on [Sjö87a], is available as a backup solution while the new new one is being developed, and for backward reference and comparisons. Furthermore, the new model is only being developed for hadron-hadron collisions. Several of the key multiple interactions aspects are common between the old and new models, such as the generation of kinematics of the multiple (semi)hard interactions and the impact-parameter picture, while other aspects are addressed in a more or less similar spirit, such as the desire to reduce the string length relative to naïve expectations. The new model [Sjö03a] attempts a more sophisticated description of correlations in flavour, colour, longitudinal and (primordial) transverse momenta between the beam remnants and the shower initiators than offered by the old one, and also introduces some other improvements. Therefore the current section starts with a description of the old model, and thereafter outlines where the new model differs.