Gutierrez-Rodriguez, A.Cetinkaya, V.Koksal, M.Gurkanli, E.Ari, V.Hernandez-Ruiz, M. A.2026-04-252026-04-2520252190-5444https://doi.org/10.1140/epjp/s13360-025-06400-2https://hdl.handle.net/11486/8456In the post-LHC era, the muon collider represents a frontier project capable of providing high-energy and high-luminosity leptonic collisions among future lepton-lepton particle accelerators. In addition, it provides significantly cleaner final states than those produced in hadron collisions. With this expectation in mind, in this article, we research the sensitivity of the anomalous neutral gauge boson couplings Z gamma gamma gamma, ZZ gamma gamma, and ZZZ gamma defined by dimension-8 operators, through the mu+mu-->mu+mu-Z gamma signal, with the Z-boson decaying to a neutrino pair. The projections at the future muon collider with a center-of-mass energy of s=10 TeV, integrated luminosity of L=10ab-1, and systematic uncertainties of delta sys=0%,3%,5%, give an expected sensitivity on the anomalous fT,j/Lambda 4 couplings at 95% confidence level of the order of O(10-3-10-1)TeV-4. Compared with the research of the ATLAS and CMS Collaborations on the anomalous quartic gauge couplings, we find that the high-luminosity future muon collider could have better sensitivity.eninfo:eu-repo/semantics/closedAccess#BAŞV!Article140510.1140/epjp/s13360-025-06400-22-s2.0-105006808063N/AWOS:001498100200005Q2