Massive particles are the basic problem of the twistor program. The twistorialization of massive particles does not seem to be a problem in TGD framework thanks to the possibility to interpret them as massless particles in 8-D sense but the situation has been unsatisfactory for virtual particles (see this).
The ideas possibly allowing to circumvent this problem emerged from a totally unexpected direction (the finding of Martin Grusenick described in previous posting). The TGD inspired explanation of the results together with quantum classical correspondence (see this) led to the proposal that Einstein tensor in space-time regions where the energy density vanishes describes the presence of virtual particles assignable to the exchange of momentum between massive objects. This identification is consistent with Einstein's equations in zero energy ontology and leads to a proposal for a concrete geometric identification of virtual particles in TGD framework.
The basic idea is following. In TGD gauge bosons are identified as wormhole contacts with positive energy fermion and negative energy antifermion at the opposite light-like throats of the contact. The observation is that even if the fermions are on mass shell particles, the sum of their momenta has a continuum of values so that interpretation as a virtual boson makes sense. Free fermions do not correspond to single light-like throat but if the interaction region involves a pair of parallel space-time sheets with distance of order CP2 length of order 104 Planck lengths, the CP2 extremal describing fermion has a high probably to touch the second space-time sheet so that topological sum giving rise to second light-like throat is formed. This throat has spherical topology and carries purely bosonic quantum numbers. If on mass shell state with opposite energy is in question, the situation reduces to that for bosons. One can also formulate conditions guaranteing that no new momentum degrees of freedom appear in loops integrals. Since only on mass shell throats are involved one can apply TGD based twistorial description also to virtual particles without any further assumptions.
The detailed explanation of the idea is given by this short article. The reader interested in background can study the chapter Twistors, N=4 Super-Conformal Symmetry, and Quantum TGD of "Towards M-Matrix".