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

Abstract

Abstract 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 $$ \mathcal{O} $$ O (100 GeV), thus providing a unique opportunity for future lepton colliders. Taking $$ \textrm{U}{(1)}_{L_{\alpha }-{L}_{\beta }} $$ 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 $$ \mathcal{O} $$ O (104 TeV), while being consistent with naturalness and perturbativity considerations.