The final-state radiation machinery is always applied in the c.m. frame of the hard scattering, from which normally emerges a pair of evolving partons. Occasionally there may be one evolving parton recoiling against a non-evolving one, as in , where only the gluon evolves in the final state, but where the energy of the photon is modified by the branching activity of the gluon. (With only one evolving parton and nothing else, it would not be possible to conserve energy and momentum when the parton is assigned a mass.) Thus, before the evolution is performed, the parton pair is boosted to their common c.m. frame, and rotated to sit along the axis. After the evolution, the full parton shower is rotated and boosted back to the original frame of the parton pair.
The interpretation of the energy and momentum splitting variable is not unique, and in fact the program allows the possibility to switch between four different alternatives [Ben87a], `local' and `global' definition combined with `constrained' or `unconstrained' evolution. In all four of them, the variable is interpreted as an energy fraction, i.e. and . In the `local' choice of definition, energy fractions are defined in the rest frame of the grandmother, i.e. the mother of parton . The preferred choice is the `global' one, in which energies are always evaluated in the c.m. frame of the hard scattering. The two definitions agree for the branchings of the partons that emerge directly from the hard scattering, since the hard scattering itself is considered to be the `mother' of the first generation of partons. For instance, in the is considered the mother of the and , even though the branching is not handled by the parton-showering machinery. The `local' and `global' definitions diverge for subsequent branchings, where the `global' tends to allow more shower evolution.
In a branching the kinematically allowed range of
, is given by
For `unconstrained' evolution, which is the preferred alternative,
one may start off by assuming the daughters to be massless, so that the
allowed range is