Neutral Scalar Signatures at a Muon Collider in the $Z_3$ symmetric Three Higgs Doublet Model

Abstract

Extending the scalar sector of the Standard Model is a well-motivated approach to exploring physics beyond the Standard Model. In this work, we investigate the phenomenology of the Three Higgs Doublet Model at a future muon collider. The scalar spectrum of the 3HDM comprises three CP-even Higgs bosons, two CP-odd Higgs bosons, and a pair of charged Higgs states. Focusing on Higgs pair production via muon-antimuon annihilation, we study the production and decay of neutral scalar states through the process $\mu^+\mu^- \to \phi_i \phi_j$, assuming a mass hierarchy in which the SM-like CP-even Higgs is the lightest state. We analyze several benchmark scenarios leading to $b\bar{b}b\bar{b}$ and $b\bar{b}t\bar{t}$ final states, and perform a cut-and-count analysis at a center-of-mass energy of $\sqrt{s}=3$ TeV. Our results demonstrate that a future muon collider provides a sensitive and promising environment to probe extended Higgs sectors, with neutral scalar states in the mass range of $200-400$ GeV being discoverable with $5\sigma$ significance for integrated luminosities of $\mathcal{O}(1-4 \ \mathrm{ab}^{-1})$.