Searching for heavy leptophilic Z ′: from lepton colliders to gravitational waves

We study the phenomenology of leptophilic Z ′ gauge bosons at the future high-energy e + e − and μ + μ − colliders, as well as at the gravitational wave observatories. The leptophilic Z ′ model, although well-motivated, remains largely unconstrained from current low-energy and collider searches for Z ′ masses above 𝒪 (100 GeV), thus providing a unique opportunity for future lepton colliders. Taking U(1)_L_α-L_β ( α , β = e , μ , τ ) models as concrete examples, we show that future e + e − and μ + μ − colliders with multi-TeV center-of-mass energies provide unprecedented sensitivity to heavy leptophilic Z ′ bosons. Moreover, if these U(1) models are classically scale-invariant, the phase transition at the U(1) symmetry-breaking scale tends to be strongly first-order with ultra-supercooling, and leads to observable stochastic gravitational wave signatures. We find that the future sensitivity of gravitational wave observatories, such as advanced LIGO-VIRGO and Cosmic Explorer, can be complementary to the collider experiments, probing higher Z ′ masses up to 𝒪 (10 4 TeV), while being consistent with naturalness and perturbativity considerations.