Single axion-like particles production in the γγ channel at high energy muon colliders

Axion-like particles (ALPs), which are pseudo-scalar particles, appear in various new physics models with the spontaneous global symmetry breaking. The difference between ALPs and axion models is that for the former both masses and couplings of ALPs are free parameters. It appears that the ALPs with masses above 1[Formula: see text]GeV are beyond the reach of low-energy accelerators, existing cosmological and astrophysical constraints, while high-energy colliders provide unique possibilities to explore such particles. With the establishment of the International Muon Collider Collaboration, muon colliders have been widely concerned. In general, ALPs are mainly produced at muon colliders through the [Formula: see text] annihilation and electroweak vector-boson-fusion (VBF) processes. In this paper, we study the prospect of the production of heavy ALPs with mass greater than 10[Formula: see text]GeV via the massless [Formula: see text]-fusion process at the multi-TeV muon collider. Focusing on the couplings of ALPs to the Standard Model gauge bosons, we obtain the excluding and discovering capabilities for ALPs at the 3[Formula: see text]TeV and 10[Formula: see text]TeV muon colliders. Our numerical results suggest that the multi-TeV muon collider may be more sensitive to ALPs with the mass of 35–400[Formula: see text]GeV than LHC, and can provide the possibility to search for ALPs with masses greater than 3[Formula: see text]TeV. In addition, we also discuss the effect of narrow width approximation on the ALP search sensitivity.