Vector-field spontaneous baryogenesis with Lorentz invariance violation

Abstract: We extend spontaneous baryogenesis by considering the spontaneous breaking of $U(1)_B$ through a complex vector field. This field interacts with baryons and leptons via a vector-current coupling and, by construction, acquires a nonzero vacuum expectation value. Accordingly, the theory also exhibits a spontaneous violation of Lorentz invariance, effectively realizing a Bumblebee model. In this picture, the pseudo-Nambu-Goldstone boson arising from spontaneous breaking of the $U(1)_B$ global symmetry is the global phase of the Bumblebee vector and, in the broken phase, it results minimally coupled with the baryonic current, guaranteeing the violation of the baryon number. Consequently, we assume that the pseudo-Nambu-Goldstone, arising from spontaneous breaking of $U(1)_B$, plays the role of the inflaton, leading to baryogenesis across the entire inflationary stage, up to when the inflaton decays into baryon-antilepton and antibaryon-lepton pairs through a CP-violating interaction that also violates the Lorentz symmetry. Afterwards, we address the issue of flavor oscillations among baryon and lepton fields, including the oscillation probability in the calculation of the baryon asymmetry. Remarkably, our framework predicts a non-null mixing factor even for massless fermions. This mixing acts on the spatial momenta rather than on the masses of the produced fermions, allowing larger values of the coupling constant even guaranteeing the production of light fermions. The net baryon asymmetry results accordingly modified, and may also reproduce the experimental data for allowed values of the coupling constant.