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

We have studied anomalous four-photon couplings in the $\mu^+\mu^- \rightarrow \mu^+ \gamma\gamma \mu^-$ scattering at a future muon collider. The collision energies of 3 TeV, 14 TeV, and 100 TeV are addressed. Both differential and total cross sections versus invariant mass of the outgoing photons are calculated. The best 95\% C.L. exclusion bounds on anomalous couplings 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 energy of 100 TeV. The partial-wave unitary constraints on $g_1$ and $g_2$ are examined. We have demonstrated that the unitarity is not violated in a region of the anomalous couplings obtained in the present paper.