  We study the systematical one-loop decomposition of the dimension-7
long-range $0\nu\beta\beta$ decay operators. We find that there are 3 genuine
one-loop topologies and 8 diagrams. The procedure to determine the SM quantum
number assignments for both internal and external fields is presented. The
Majorana neutrino mass in long-range $0\nu\beta\beta$ models is discussed. We
also present a one-loop $0\nu\beta\beta$ decay model which produces Majorana
neutrino mass at three-loop level. The phenomenological predictions for light
neutrino mass and $0\nu\beta\beta$ decay half-life time including both mass
mechanism and long-range contribution are studied.
