Probing the $R_{K^{(*)}}$ Anomaly at a Muon Collider

The LHCb measurements of the $mu / e$ ratio in $B to K ell ell$ decays $(R_{K^{}})$ indicate a deficit with respect to the Standard Model prediction, supporting earlier hints of lepton universality violation observed in the $R_{K^{(*)}}$ ratio. Possible explanations of these $B$-physics anomalies include heavy $Z$ bosons or leptoquarks mediating $b to s mu^+ mu^- $. We note that a muon collider can directly measure this process via $mu^+ mu^- to b bar s$ and can shed light on the lepton non-universality scenario. Investigating currently discussed center-of-mass energies $sqrt{s} = 3$, 6 and 10 TeV, we show that the parameter space of $Z$ and $S_3$ leptoquark solutions to the $R_{K^{(*)}}$ anomalies can be mostly covered. Effective operators explaining the anomalies can be probed with the muon collider setup $sqrt{s} = 6~{rm TeV}$ and integrated luminosity $L = 4~{rm ab^{-1}}$.