The decay scheme

In the beginning of the decay treatment, either one or two resonances may be present, the former represented by processes such as $\mathrm{q}\overline{\mathrm{q}}' \to \mathrm{W}^+$ and $\mathrm{q}\mathrm{g}\to \mathrm{W}^+ \mathrm{q}'$, the latter by $\mathrm{q}\overline{\mathrm{q}}\to \mathrm{W}^+ \mathrm{W}^-$. If the latter is the case, the decay of the two resonances is considered in parallel (unlike PYDECY, where one particle at a time is made to decay).

First the decay channel of each resonance is selected according to the relative weights $H_R^{(f)}$, as described above, evaluated at the actual mass of the resonance, rather than at the nominal one. Threshold factors are therefore fully taken into account, with channels automatically switched off below the threshold. Normally the masses of the decay products are well-defined, but e.g. in decays like $\mathrm{h}^0 \to \mathrm{W}^+ \mathrm{W}^-$ it is also necessary to select the decay product masses. This is done according to two Breit-Wigners of the type in eq. (), multiplied by the threshold factor, which depends on both masses.

Next the decay angles of the resonance are selected isotropically in its rest frame. Normally the full range of decay angles is available, but in $2 \to 1$ processes the decay angles of the original resonance may be restrained by user cuts, e.g. on the $p_{\perp}$ of the decay products. Based on the angles, the four-momenta of the decay products are constructed and boosted to the correct frame. As a rule, matrix elements are given with quark and lepton masses assumed vanishing. Therefore the four-momentum vectors constructed at this stage are actually massless for all quarks and leptons.

The matrix elements may now be evaluated. For a process such as $\mathrm{q}\overline{\mathrm{q}}\to \mathrm{W}^+ \mathrm{W}^- \to \mathrm{e}^+ \nu_{\mathrm{e}} \mu^- \overline{\nu}_{\mu}$, the matrix element is a function of the four-momenta of the two incoming fermions and of the four outgoing ones. An upper limit for the event weight can be constructed from the cross section for the basic process $\mathrm{q}\overline{\mathrm{q}}\to \mathrm{W}^+ \mathrm{W}^-$, as already used to select the two $\mathrm{W}$ momenta. If the weighting fails, new resonance decay angles are picked and the procedure is iterated until acceptance.

Based on the accepted set of angles, the correct decay product four-momenta are constructed, including previously neglected fermion masses. Quarks and, optionally, leptons are allowed to radiate, using the standard final-state showering machinery, with maximum virtuality given by the resonance mass.

In some decays new resonances are produced, and these are then subsequently allowed to decay. Normally only one resonance pair is considered at a time, with the possibility of full correlations. In a few cases triplets can also appear, but such configurations currently are considered without inclusion of correlations. Also note that, in a process like $\mathrm{q}\overline{\mathrm{q}}\to \mathrm{Z}^0 \mathrm{h}^0 \to \mathrm{Z}^0 \mathrm{W}^+ \mathrm{W}^- \to 6$ fermions, the spinless nature of the $\mathrm{h}^0$ ensures that the $\mathrm{W}^{\pm}$ decays are decoupled from that of the $\mathrm{Z}^0$ (but not from each other).