Starting from the hard interaction, initial- and final-state radiation corrections may be added. This is normally done by making use of the parton-shower language -- only for the process does PYTHIA offer a matrix-element option (described in section ). The algorithms used to generate initial- and final-state showers are rather different, and are therefore described separately below, starting with the conceptually easier final-state one. Before that, some common elements are introduced.
The main references for final-state showers is [Ben87a,Nor01] and for initial-state ones [Sjö85,Miu99].