The initial-state radiation algorithm reconstructs one shower initiator in each beam. (If initial-state radiation is not included, the initiator is nothing but the incoming parton to the hard interaction.) Together the two initiators delineate an interaction subsystem, which contains all the partons that participate in the initial-state showers, in the hard interaction, and in the final-state showers. Left behind are two beam remnants which, to first approximation, just sail through, unaffected by the hard process. (The issue of additional interactions is covered in the next section.)
A description of the beam-remnant structure contains a few components. First, given the flavour content of a (colour-singlet) beam particle, and the flavour and colour of the initiator parton, it is possible to reconstruct the flavour and colour of the beam remnant. Sometimes the remnant may be represented by just a single parton or diquark, but often the remnant has to be subdivided into two separate objects. In the latter case it is necessary to share the remnant energy and momentum between the two. Due to Fermi motion inside hadron beams, the initiator parton may have a `primordial ' transverse momentum motion, which has to be compensated by the beam remnant. If the remnant is subdivided, there may also be a relative transverse momentum. In the end, total energy and momentum has to be conserved. To first approximation, this is ensured within each remnant separately, but some final global adjustments are necessary to compensate for the primordial and any effective beam-remnant mass.