Tri-photon at muon collider: a new process to probe the anomalous quartic gauge couplings

The muon collider has recently received a great deal of attention because of its ability to achieve both high energy and high luminosity. It plays as a gauge boson collider because the vector boson scattering (VBS) becomes the dominant production topology for Standard Model processes starting from a few TeV of collision energy. In this paper, we propose that the process of ${\mu }^{+}{\mu }^{-}$ annihilation into tri-photon is also very sensitive to the search of anomalous quartic gauge couplings (aQGCs). We investigate the projected constraints on the transverse operators contributing to aQGCs through ${\mu }^{+}{\mu }^{-}\to Z^{\ast }\mathrm{/}{\gamma }^{\ast }\to \gamma \gamma \gamma$ at muon colliders. For the muon collider with $\sqrt{s}=3$ TeV and $\mathcal{L}=1{\mathrm{a}\mathrm{b}}^{-1}$, the expected constraints are about two orders of magnitude stronger than those at the 13 TeV LHC.