Cross-section Calculations

In the program, the variables used in the generation of a $2 \to 2$ process are $\tau$, $y$ and $z = \cos\hat{\theta}$. For a $2 \to 1$ process, the $z$ variable can be integrated out, and need therefore not be generated as part of the hard process, except when the allowed angular range of decays is restricted. In unresolved lepton beams, i.e. when $f_{\mathrm{e}}^{\mathrm{e}}(x) = \delta(x-1)$, the variables $\tau$ and/or $y$ may be integrated out. We will cover all these special cases towards the end of the section, and here concentrate on `standard' $2 \to 2$ and $2 \to 1$ processes.