Triple Higgs Production at Muon Colliders in the Higgs Triplet Model

The production of three Higgs bosons provides a unique opportunity to probe both the trilinear and quartic Higgs couplings within the Standard Model and beyond. In this study, we investigate triple Higgs production in the Higgs Triplet Model via photon fusion, $\gamma \gamma \to h^0 h^0 h^0$, allowing us to explore the contributions from singly and doubly charged Higgs bosons and their couplings to CP-even scalars. We analyze the total cross sections and kinematic distributions, comparing our results with the corresponding SM predictions. Our calculations utilize an Automated One-Loop Calculator to evaluate the numerical amplitudes for the $2 \to 3$ process. For the collider simulations, we develop a Monte Carlo phase-space integrator to predict outcomes for a future muon collider, covering a center-of-mass energy range from 2 TeV to 10 TeV.