Verifiable type-III seesaw and dark matter in a gauged $\boldsymbol{U(1)_{\rm B-L}}$ symmetric model

Abstract: We propose a new extension of the Standard Model that incorporates a gauged $U(1){\rm B-L}$ symmetry and the type-III seesaw mechanism to explain neutrino mass generation and provide a viable dark matter (DM) candidate. Unlike the type-I seesaw, the type-III seesaw extension under $U(1){\rm B-L}$ is not automatically anomaly-free. We show that these anomalies can be canceled by introducing additional chiral fermions, which naturally emerge as DM candidates in the model. We thoroughly analyze the DM phenomenology, including relic density, direct and indirect detection prospects, and constraints from current experimental data. Furthermore, we explore the collider signatures of the model, highlighting the enhanced production cross-section of the triplet fermions mediated by the B-L gauge boson, as well as the potential disappearing track signatures. Additionally, we investigate the gravitational wave signals arising from the first-order phase transition during B-L symmetry breaking, offering a complementary cosmological probe of the framework.