  The article investigates the possibility that right-handed neutrinos are
Majorana particles embedded in an abelian multiplicative $U(1)_R$ factor, with
the Lagrangian in the new factor being invariant under chiral gauge
transformations. Majorana neutrinos couple to charged and neutral currents,
producing new signatures to (anti)neutrino-electron elastic scattering and an
additional term to coherent scattering of neutrinos on atomic nuclei. The model
is ultraviolet complete and depends on one extra hypercharge correlating the
reactions and providing upper bounds for the new coupling constant.
