The subprocesses 297-301 give the production of a pair of Higgses via the -channel exchange of a or a state.
Note that Higgs pair production is still possible through subprocess 141, as part of the decay of a generic combination of . Thus it can be used to simulate and for associated neutral Higgs production. The fact that we here make use of the can easily be discounted, either by letting the relevant couplings vanish, or by the option MSTP(44)=4.
Similarly the decay allows the production of a pair of charged Higgs particles. This process is especially important in colliders. The coupling of the to is determined by the charge alone (neglecting loop effects), while the coupling is regulated by PARU(142), and that of the by PARU(143). The piece can be switched off, e.g. by MSTP(44)=4. An ordinary , i.e. particle code 23, cannot be made to decay into a Higgs pair, however.
The advantage of the explicit pair production processes is the correct implementation of the pair threshold.