Proton proton Interaction

Could we generate pp > H± H± ( MET , 4 jets) with 14 TEV energy process with Insert Double high model by using Geant4.

I’m not sure what the “Insert Double” model is (could you post a reference please?), but this sounds like it’s more of an event generation task where tools like Pythia etc would be needed. Geant4 doesn’t model the primary proton-proton collisions in the LHC beams, but can read in and propagate the particles resulting from these as modelled by, for example, Pythia.