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

TL;DR

The paper investigates a portal vector-like lepton (pVLL) extension of the Standard Model that couples to a dark photon $\gamma_d$ and a dark scalar, exploring its impact on Higgs production in association with a vector boson at a future muon collider. It demonstrates that while the SM-like $\mu^+\mu^- \to hZ$ rate remains largely unchanged, the $\mu^+\mu^- \to h\gamma_d$ channel can be dramatically enhanced due to non-decoupling effects in the muon–heavy muon–dark photon vertex, potentially surpassing $hZ$ by factors ranging from 1 to 100 within perturbative unitarity. A detailed collider analysis in the $b\bar{b}$ + missing energy final state shows that a $2\sigma$ exclusion can probe $m_{\gamma_d}$ up to about $80$ GeV at $\sqrt{s}=3$ TeV for representative benchmark parameters, with sensitivity extending to higher energies and luminosities. The work also demonstrates that the $h\gamma_d$ channel provides a complementary probe of dark-photon mass and coupling, and can explore regions compatible with the muon $g-2$ measurement, thereby offering a practical path to test Higgs interactions and dark-sector portals at future muon colliders.

Abstract

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 $~μ^+ μ^- \to hZ~$ production rate remains close to its SM prediction in a wide range of parameter space, the rate for $~μ^+ μ^- \to hγ_d~$ 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 $hγ_d$ 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 ($m_{γ_d}$) 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 $hγ_d$ process in the $b\bar{b}~+$ missing energy final state. A $2σ$ exclusion limit for $m_{γ_d}$ up to $80$ GeV is obtained assuming $~g_d=0.05$, $~\sinθ_L=4\times10^{-5}$, $~\sinθ_s=0.05$, for a heavy lepton mass $~\sim 3$ TeV at a $3$ TeV muon collider with an integrated luminosity of $1$ ab$^{-1}$.

Figures (18)

• Figure 1: Region (coloured) of parameter space allowed by muon $g-2$ measurement at $1\sigma$ level Aliberti:2025beg in the (a) $m_{\gamma_d}-g_d$ plane for $\sin\theta_L = 4 \times 10^{-5}$ and four different $m_{\mu_p}$ values ($1$ TeV, $1.5$ TeV, $2$ TeV and $3$ TeV) and (b) $m_{\mu_p}-m_{\gamma_d}$ plane for two sets of ($g_d, ~\sin\theta_L$).
• Figure 2: Feynman diagrams for associated production of Higgs and a vector boson ($V=Z,\gamma_d$) at muon collider ($\mu^+ \mu^- \to h V$).
• Figure 3: Ratios of cross sections ( $R_i$'s defined in Eq. \ref{['eq:ratio_equations']} ) for different benchmark points at (a) $\sqrt{s}=3$ TeV and (b) $10$ TeV.
• Figure 4: Variation of ratio of cross sections ($R_2$) for the process $\mu^+ \mu^- \to h \gamma_d$ with respect to the SM $hZ$ production rate in $m_{\gamma_d}$--$m_{\mu_{_p}}$ plane assuming $\sqrt{s}=3$ TeV for two different set of ($g_d,~ \sin\theta_L$) and a fixed value of $\sin\theta_s$. (a) The left plot corresponds to $g_d=0.05,~\sin\theta_s = 0.05,~\text{and}~ \sin\theta_L=4 \times 10^{-5}$ and (b) the right plot corresponds to $g_d=0.5,~\sin\theta_s = 0.05,~\text{and}~\sin\theta_L=1.66 \times 10^{-6}$. The region above the dashed (black) line is allowed by the constraint on $\omega_f$ described in Eq. \ref{['eq:perturbative_unitarity_bound']}.
• Figure 5: Variation of ratio of cross sections ($R_2$) for the process $\mu^+ \mu^- \to h \gamma_d$ with respect to the SM $hZ$ production rate in $m_{\gamma_d}$--$m_{\mu_{_p}}$ plane assuming $\sqrt{s}=10$ TeV for two different set of ($g_d,~ \sin\theta_L$) and a fixed value of $\sin\theta_s$. (a) The left plot corresponds to $g_d=0.05,~\sin\theta_s = 0.05,~\text{and}~ \sin\theta_L=4 \times 10^{-5}$ and (b) the right plot corresponds to $g_d=0.5,~\sin\theta_s = 0.05,~\text{and}~\sin\theta_L=1.66 \times 10^{-6}$. The region above the dashed (black) line is allowed by the constraint on $\omega_f$ described in Eq. \ref{['eq:perturbative_unitarity_bound']}.