Hunting for heavy $Z^\prime$ with IceCube neutrinos and gravitational waves

In the minimal gauged B-L extension of the Standard Model, we demonstrate that PeV-scale dark matter (DM) and the baryon asymmetry of the Universe (BAU) can be simultaneously explained through the three right-handed neutrinos (RHNs) present in the theory. The DM candidate undergoes decay into light neutrinos, providing an explanation for the observed IceCube events, while the other two RHNs generate the BAU via leptogenesis. The breaking of gauge symmetry gives rise to detectable gravitational waves (GWs) from decaying cosmic strings (CS), making this framework testable at several future GW detectors-despite being beyond the reach of conventional collider experiments due to the extremely weak coupling. The symmetry-breaking scale establishes a connection between particle masses, couplings, and the GW spectrum, offering a unified and predictive scenario.