  Understanding the origin of lepton number violation is one of the fundamental
questions in particle physics today. Neutrinoless double beta decay provides a
way in which this violation can be tested. In this article, we derive the form
of hadronic and leptonic matrix elements for all possible long-range mechanisms
of neutrinoless double beta decay. With these, we calculate the numerical
values of the nuclear matrix elements (NME) and phase space factors (PSF) by
making use of the interacting boson model of the nucleus (IBM-2) for NMEs and
of exact Dirac wave functions for the PSFs. We show that:\ (I) lepton number
violation can occur even with zero (or very small) neutrino mass and (II) the
angular correlations of the emitted electrons can distinguish between different
models of non-standard (NS) mechanisms. We set limits on the coupling constants
of some NS models, in particular Left-Right models and SUSY models.
