Whether can the decision of the orthopositronium problem to stimulate   studying the problem of a dark matter in the Universe?
  The nature of a dark matter in the Universe can be connected with realization of the (plus/minus) Planck mass in final state of the beta-plus-decay of the nuclei Na-22, Ga-68, etc. and in a gravitational field of sufficient force. This hypothesis (the topological quantum transition - a generalized "displacement current") follows out of the phenomenological model that has explained the anomalies of the orthopositronium, forming in substance by the beta-decay positrons. Vacuumlike state of substance of the positive mass (Gliner, 1965) is structured in this model (the "microstructure" of vacuum) as the long-range "atom" with the Planck mass in the limited macroscopic "volume" of space-time. Accordingly, the negative mass C-field (Hoyle & Narlikar, 1964) plays the role of a compensating field. 
B.M.Levin, V.I.Sokolov