Test of CPT and Lorentz Invariance from Muonium Spectroscopy

Abstract

Following a suggestion of Kostelecký et al. we have evaluated a test of CPT and Lorentz invariance from the microwave spectrosopy of muonium. Precise measurements have been reported for the transition frequencies v ₁₂ and v ₃₄ for ground state muonium in a magnetic field H of 1.7 T, both of which involve principally muon spin flip. These frequencies depend on both the hyperfine interaction and Zeeman effect. Hamiltonian terms beyond the standard model which violate CPT and Lorentz invariance would contribute shifts δv ₁₂ and δv ₃₄. The nonstandard theory indicates that v ₁₂ and v ₃₄ should oscillate with the earth’s sidereal frequency and that δv ₁₂ and δv ₃₄ would be anticorrelated. We find no time dependence in v ₁₂—v ₃₄ at the level of 20 Hz, which is used to set an upper limit on the size of CPT and Lorentz violating parameters.