The LHCb Collaboration recently gave an update on testing lepton flavour universality with $B^+ rightarrow K^+ ell^+ ell^-$, in which a 3.1 standard deviations from the standard model prediction was observed. The g-2 experiment also reports a 3.3 standard deviations from the standard model on muon anomalous magnetic moment measurement. These deviations could be explained by introducing new particles including leptoquarks. In this paper, we show the possibility to search for heavy spin-1 leptoquarks at a future TeV scale muon collider by performing studies from three channels: 1) same flavour final states with either two bottom or two light quarks, 2) different flavour quark final states, and 3) a so-called VXS process representing the scattering between a vector boson and a leptoquark to probe the coupling between leptoquark and tau lepton. We conclude that a 3 TeV muon collider with $3~{ab^{-1}}$ of integrated luminosity is already sufficient to cover the leptoquark parameter space in order to explain the LHCb lepton flavour universality anomaly.
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