We investigate some consequences if neutrinoless double beta decays of nuclei are dominated by short range interactions. To illustrate our results, we assume that such decays proceed mainly through short range interactions involving two-W-bosons exchanges and confine ourselves to only include new scalars without new gauge interactions for SM fermions. For the neutrino mass problem we propose to solve it by adopting that the active light neutrinos have predominantly Dirac masses and the small Majorana masses induced by the new scalars render them pseudo(quasi)-Dirac particles. This particular aspect of neutrinos may be detectable in the next generation of neutrino oscillation experiments and/or neutrino telescopes. If so this opens a new connection between neutrinoless double beta decays and neutrino physics. We also noted the new physics signals such as high charged scalar states that can be explored in hadron colliders. In particular, we find that a high energy e^- e^- collider will be very useful in testing the origin of lepton number violation which complements neutrinoless double decays studies.
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