Exploring Leptogenesis, WIMP Dark Matter, and Gravitational Waves in an extended Scalar Framework

Abstract

We explore an extension of the Type-I seesaw framework in which a scalar mediator $\Phi$ connects the Standard Model (SM) to a dark sector consisting of right-handed neutrinos or RHNs ($N_i$) and a complex scalar $S$. The interactions are governed by a phenomenologically viable ${\mathcal{Z}}_4\times CP$ symmetry, allowing a dimension-5 effective operator involving the SM lepton doublet, Higgs, RHNs, and $\Phi$. Once $\Phi$ acquires a vacuum expectation value, its couplings to the SM and RHNs affect the standard leptogenesis through $N_i$ decay, while electroweak symmetry breaking (EWSB) subsequently induces neutrino masses through the same structure. Furthermore, a $\Phi$-portal interaction induces a vacuum expectation value for real (imaginary) component of $S$ opening additional annihilation channels for its imaginary (real) component, identified as dark matter (DM) in the GeV-TeV mass range (excluded in the simplest scalar singlet DM scenario). The spontaneous breaking of the associated discrete symmetry can lead to domain wall formation, whose required early annihilation may generate observable gravitational wave signals, providing a way to ideate the symmetry-breaking scale and its connection to neutrino mass, baryogenesis, and dark matter.

27 pages, 13 figures, 4 tables