Probing Invisible Decay of $Z^\prime$ at Muon Collider with Topological Data Analysis and Machine Learning

We explore the use of topological data analysis (TDA) combined with machine learning for discriminating standard model backgrounds from the invisible decay of the $Z^\prime$ boson associated with monophoton emission at a 3 TeV muon collider. Reconstructed events are mapped into a six-dimensional kinematic space and aggregated into bags of events, from which persistent homology is used to extract Betti number distributions. Within the Multiple Instance Learning paradigm, classifiers trained on these topological descriptors demonstrate significantly improved classification accuracy compared to the conventional ML approaches based on event-wise kinematic inputs. We also draw exclusion contours at 95\% CL in the $(m_{Z^\prime}, m_χ)$ parameter space, highlighting the potential of topological features to extend the discovery reach of future collider experiments.