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

Abstract

We have explore a portal vector-like lepton (pVLL) extension of the Standard Model (SM) and study 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. We also examine the role of the pVLL state in the context of dark matter (DM) phenomenology and identify regions of parameter space consistent with the observed relic abundance by extending the simplified setup with a viable DM candidate. The $h\gamma_d$ production can also be used to constrain the dark photon mass ($m_{\gamma_d}$) and/or the dark gauge coupling ($g_d$) consistent with various constraints including 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$^{-1}$.