Searching for Heavy Leptophilic $Z^{\prime }$: from Lepton Colliders to Gravitational Waves

Abstract

We study the phenomenology of leptophilic $Z^{\prime }$ gauge bosons at the future high-energy $e^{+}{e}^{-}$ and ${\mu }^{+}{\mu }^{-}$ colliders, as well as at the gravitational wave observatories. The leptophilic $Z^{\prime }$ model, although well-motivated, remains largely unconstrained from current low-energy and collider searches for $Z^{\prime }$ masses above $\mathcal{O}(100\mathrm{GeV})$, thus providing a unique opportunity for future lepton colliders. Taking $U(1{)}_{L_{\alpha }-L_{\beta }}(\alpha ,\beta =e,\mu ,\tau )$ models as concrete examples, we show that future $e^{+}{e}^{-}$ and ${\mu }^{+}{\mu }^{-}$ colliders with multi-TeV center-of-mass energies provide unprecedented sensitivity to heavy leptophilic $Z^{\prime }$ 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 $Z^{\prime }$ masses up to $\mathcal{O}(10^4\mathrm{TeV})$, while being consistent with naturalness and perturbativity considerations.

Comments: 43 pages, 19 figures, and 4 tables