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We have studied anomalous four-photon couplings in the $\mu^+\mu^-\rightarrow \mu^+ \gamma\gamma \mu^-$ scattering at a future muon collider. Thecollision energies of 3 TeV, 14 TeV, and 100 TeV are addressed. Bothdifferential and total cross sections versus invariant mass of the outgoingphotons are calculated. The best 95\% C.L. exclusion bounds on anomalouscouplings are obtained to be $g_1 = 2.23 \times 10^{-8}$ TeV$^{-4}$ and $g_2 =4.22 \times 10^{-8}$ TeV$^{-4}$. They correspond to the muon collision energyof 100 TeV. The partial-wave unitary constraints on $g_1$ and $g_2$ areexamined. We have demonstrated that the unitarity is not violated in a regionof the anomalous couplings obtained in the present paper.

Probing anomalous $\gamma\gamma\gamma\gamma$ couplings at a future muon collider