Spontaneous breaking of baryon number, baryogenesis and the bajoron

We explore the spontaneous breaking of global baryon number for baryogenesis. We introduce a model with three majorana fermions and a complex scalar carrying baryon number charge. After symmetry breaking, the baryon asymmetry is generated below the electroweak scale via the decays of one of the majorana fermions. The main focus of the paper is the phenomenology of the Nambu--Goldstone boson of $U(1)_B$, which we call the bajoron. With small sources of explicit baryon number violation, the bajoron acquires a small mass and is generally very long-lived. The model avoids proton decay, satisfies cosmological constraints, and offers interesting collider phenomenology for the Large Hadron Collider. These long-lived particles tied to baryogenesis strongly support the development of far-detector experiments such as MATHUSLA, FASER, SHiP, and others.