The PYTHIA machinery to handle and processes is fairly sophisticated and generic. The same cannot be said about the generation of hard-scattering processes with more than two final-state particles. The number of phase-space variables is larger, and it is therefore more difficult to find and transform away all possible peaks in the cross section by a suitably biased choice of phase-space points. In addition, matrix-element expressions for processes are typically fairly lengthy. Therefore PYTHIA only contains a very limited number of and processes, and almost each process is a special case of its own. It is therefore less interesting to discuss details, and we only give a very generic overview.
If the Higgs mass is not light, interactions among longitudinal and gauge bosons are of interest. In the program, processes such as and ones such as are included. The former are for use when the still is reasonably narrow, such that a resonance description is applicable, while the latter are intended for high energies, where different contributions have to be added up. Since the program does not contain or distributions inside hadrons, the basic hard scattering has to be convoluted with the and branchings, to yield effective and processes. However, it is possible to integrate out the scattering angles of the quarks analytically, as well as one energy-sharing variable [Cha85]. Only after an event has been accepted are these other kinematical variables selected. This involves further choices of random variables, according to a separate selection loop.
In total, it is therefore only necessary to introduce one additional
variable in the basic phase-space selection, which is chosen to be
, the squared invariant mass of the full or
process, while is used for the squared invariant
mass of the inner or process. The variable
is coupled to the full process, since parton-distribution weights
have to be given for the original quarks at
. The variable is
related to the inner process, and thus not needed for the
processes. The selection of the
done after , but before has been chosen. To improve the
efficiency, the selection is made according to a weighted phase space
of the form
For a light the effective approximation above breaks down,
and it is necessary to include the full structure of the
fusion) matrix elements.
The , and variables are here retained, and selected
according to standard procedures. The Higgs mass is represented by the
choice; normally the is so narrow that the
distribution effectively collapses to a function. In addition,
the three-body final-state phase space is rewritten as