  The spontaneous breaking of the global lepton number, an accidental symmetry
in the Standard Model of particle physics, results in a massless goldstone
boson, the Majoron, which can be taken as a cold dark matter candidate with
properties similar to these of the axion. In this letter, we propose a novel
mass generation mechanism for the Majoron via radiative corrections induced by
the interaction of a tiny lepton-number-violating (LNV) Majorana mass term of
right-handed neutrinos in the canonical seesaw mechanism. We show that this LNV
Majorana mass term not only generates the mass of the Majoron but also leads to
a non-zero initial velocity of the Majoron, which subsequently impacts on the
relic abundance of the Majoron generated in the early universe via the
misalignment mechanism. With the assistance of the Weinberg operator, the same
initial velocity may also generate the lepton asymmetry, which is subsequently
transported into the baryon asymmetry of the universe (BAU) via the weak
sphaleron process. As a result, the neutrino masses, dark matter and the BAU
can be addressed in this concise theoretical framework.
