Type II Seesaw Leptogenesis in a Majoron background

Abstract: We discuss spontaneous Leptogenesis in the Type II Seesaw model of neutrino masses featuring an electroweak triplet scalar $T$ in a coherent pseudo Nambu-Goldstone boson (pNGB) background. In the "wash-in" scenario the inverse decays of Higgs bosons to $T$ generate a chemical potential for the triplet that is then transmitted to the lepton sector via the leptonic decays of $T$. Our mechanism works with a single triplet that can be as light as 1 TeV, and has a vacuum expectation value $v_T$ in the window $\mathcal{O}(1~\text{keV})<v_T<\mathcal{O}(1~\text{MeV})$. This range of $v_T$ can lead to appreciable decays of the triplet's doubly charged component into both same sign di-leptons and same sign pairs of $W$-bosons, which could potentially allow for an experimental distinction from a recently proposed inflationary Type II Seesaw Affleck-Dine scenario preferring the leptonic mode. In the "singlet-doublet-triplet Majoron" UV-completion of the Type II Seesaw model, the required pNGB is automatically included in the form of the Majoron, that originates from the phase of the lepton number breaking singlet scalar. The coherent motion of the Majoron can furthermore explain the dark matter relic abundance via the kinetic misalignment mechanism. Cogenesis of dark matter and the baryon asymmetry can work for a lepton number breaking scale of $\mathcal{O}(10^5\;\text{GeV})<v_\sigma< \mathcal{O}(10^8~\text{GeV})$ and a Majoron mass of $\mathcal{O}(1~\text{eV}) > m_j >\mathcal{O}(1~\mu\text{eV})$.