Probing anomalous Zγγγ couplings at a future muon collider

The sensitivity to anomalous quartic gauge couplings (AQGCs) of the γγγ Z interaction is studied in the μ⁺μ⁻ → μ⁺γγ μ⁻ scattering at a future muon collider with unpolarized beams. The anomalous γγγ Z vertex is described by two couplings, ζ₁ and ζ₂. The differential and total cross sections are calculated for the center-of-mass energies of 3 TeV, 14 TeV, and 100 TeV. For these values of the collision energy the $95%$ C.L. exclusion regions for AQGCs are obtained depending on the systematic error. In particular, for the 14 TeV muon collider with the integrated luminosity $L = 20$ ab⁻¹ the best sensitivities are derived to be ζ₁ = 3.1 × 10⁻⁵ TeV⁻⁴ and ζ₂ = 6.5 × 10⁻⁵ TeV⁻⁴. These constraints are three orders of magnitude stronger than the bounds obtained for the 27 TeV HE-LHC with $L = 15$ ab⁻¹. At the 100 TeV muon collider with $L = 1000$ ab⁻¹ AQGCs can be probed up to (1.64 ÷ 3.4) × 10⁻⁸ TeV⁻⁴. The partial-wave unitarity constraints on couplings ζ₁, ζ₂ are evaluated. It is shown that the unitarity is not violated in the region of the AQGCs examined in the present paper.