Majorana Majoron and the Baryon Asymmetry of the Universe

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.