Implications of portal vector-like lepton on associated Higgs production at a multi-TeV muon collider

We have explored a portal vector-like lepton (pVLL) extension of the Standard Model (SM) and studied its implications for Higgs and vector-boson associated production ($hV$, with $~V = Z$-boson or dark photon) at a future muon collider facility. We show that while the $~\mu^+ \mu^- \to hZ~$ production rate remains close to its SM prediction in a wide range of parameter space, the rate for $~\mu^+ \mu^- \to h\gamma_d~$ can be substantially enhanced owing to the non-decoupling nature of the interaction involving the heavy lepton, the muon and the dark photon. We demonstrate that the $h\gamma_d$ production rate can exceed the corresponding $hZ$ rate by a factor of $1$-$100$ within the perturbative unitarity limit, making it a promising channel for probing Higgs interactions and potential new physics effects. Furthermore, this process can also be used to constrain the dark photon mass ($m_{\gamma_d}$) and/or the dark gauge coupling ($g_d$) consistent with the current muon $g-2$ measurements within the pVLL framework. We perform a detailed collider analysis of the $h\gamma_d$ process in the $b\bar{b}~+$ missing energy final state. A $2\sigma$ exclusion limit for $m_{\gamma_d}$ up to $80$ GeV is obtained assuming $~g_d=0.05$, $~\sin\theta_L=4\times10^{-5}$, $~\sin\theta_s=0.05$, for a heavy lepton mass $~\sim 3$ TeV at a $3$ TeV muon collider with an integrated luminosity of $1$ ab$^{-1}$.