Majoron-Driven Leptogenesis in Gauged $U(1)_{L_{\mu}-L_{\tau}}$ Model

We propose a novel leptogenesis scenario in the gauged $U(1)_{L_{\mu}-L_{\tau}}$ model. Achieving successful leptogenesis in the $U(1)_{L_{\mu}-L_{\tau}}$ symmetric phase is challenging due to the absence of a CP phase, caused by restriction from the gauge symmetry. To overcome this issue, we introduce an additional global symmetry, $U(1)_{B-L}$, and a scalar field $\Phi$ responsible for breaking this symmetry. Through the kinetic misalignment mechanism, the majoron field associated with $U(1)_{B-L}$ symmetry breaking has a kinetic motion in the early universe. Subsequently, time-dependent majoron field background induces the background CP phase dynamically, leading to successful leptogenesis in the $U(1)_{L_{\mu}-L_{\tau}}$ symmetric phase. Furthermore, majoron itself serves as a dark matter candidate in this scenario. As one of the phenomenological applications, we consider the model that can also explain the muon $g-2$ anomaly.