Microwave Spectroscopy of the Muonium $2S_{1/2}-2P_{3/2}$ Fine Structure Interval

We report a microwave spectroscopy measurement of the muonium $2S_{1/2}-2P_{3/2}$ fine structure transition, yielding a transition frequency of $9871.0 \pm 7.0~\mathrm{MHz}$, in agreement with state-of-the-art QED predictions within one standard deviation. In combination with the recent Lamb shift result, the $2P_{1/2}-2P_{3/2}$ splitting is determined, improving the spectroscopic characterization of the $n=2$ manifold in muonium. These results provide a stringent test of bound-state QED in a purely leptonic system and establish a path toward future searches for Lorentz violation and muon-specific new physics.