Multi-Messenger Signatures of Flavor-Aligned Hidden Sectors and Cosmic Strings in Tau-Dominated EFTs

Abstract: Hints of lepton-flavor-dependent couplings in light hidden-sector extensions of the Standard Model motivate effective descriptions in which portal interactions are non-universal across charged leptons. We construct a minimal effective field theory (EFT) in which a flavor-dependent coupling hierarchy gτ ≫ gμ ∼ gₑ arises from spontaneous breaking of an approximate SU(3)ℓ × U(1) flavor symmetry. We show that radiative corrections associated with the charged-lepton Yukawa structure generically select a vacuum alignment dominated by the tau flavor direction, although the resulting hierarchy is not unique without additional ultraviolet input.If the flavor symmetry is gauged, the theory admits topologically stable cosmic string solutions associated with the breaking pattern SU(3)ℓ × U(1) → U(1)³/ℤ₃. We characterize the resulting defect network and its associated gravitational-wave (GW) spectrum in the Nambu–Goto approximation. We further discuss how flavor-dependent couplings to neutrinos could induce, in principle, correlated signatures between stochastic GW backgrounds and directional flavor variations in high-energy neutrino fluxes. These correlations depend on model-dependent assumptions regarding flavor gauge structure and defect–matter couplings. We provide falsifiable conditions under which such a scenario would be excluded by next-generation GW (LISA, SKA) and neutrino (IceCube-Gen2) observatories.