  A general Lorentz--invariant parameterization for the long-range part of the
$0\nu\beta\beta$ decay rate is derived. Combined with the short range part this
general parameterization in terms of effective $B-L$ violating couplings will
allow it to extract the $0\nu\beta\beta$ limits on arbitrary lepton number
violating theories. Several new nuclear matrix elements appear in the general
formalism compared to the standard neutrino mass mechanism. Some of these new
matrix elements have never been considered before and are calculated within
pn-QRPA. Using these, limits on lepton number violating parameters are derived
from experimental data on $^{76}$Ge.
