Muonium Hamiltonian

Abstract. Following a suggestion of Kostelecky 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 U12 and 1/34 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 <5 12 and <5 34. The nonstandard theory indicates that P12 and 34 should oscillate with the earth s sidereal frequency and that 5v 2 and <5 34 would be anticorrelated. We find no time dependence in m2 — vza at the level of 20 Hz, which is used to set an upper limit on the size of CPT and Lorentz violating parameters. 

The conversion of muonium (y+e ) to its antiatom antimuonium (y e+) would be an example of a muon number violating process,2 and like neutrinoless double beta decay would involve ALe=2. The M-M system also bears some relation to the K°-K7r system, since the neutral atoms M and M are degenerate in the absence of an interaction which couples them. In Table III a four-Fermion Hamiltonian term coupling M and M is postulated, and the probability that M formed at time t=0 will decay from the M mode is given. Present experimental limits22 23 for the coupling constant G are indicated and are larger than the Fermi constant Gp. 

The spin Hamiltonian for muonium in a magnetic field is given by... 

Recent zero-field studies of the free in longitudinal fields have revealed new and unique information on spin glass and other systems but here we concentrate on muonium and muonium-like states in zero magnetic field. In this case, precession is not observed in the classical sense of the word but rather a modulation of the muon polarization with time. This can be most easily understood in the case of muonium itself in terms of the isotropic Hamiltonian of Equation 30. As noted above, muonium is formed via the "capture" of an electron from the stopping medium. Since the fi is longitudinally polarizedl"3 (a ) but the captured e" is not (Qg or Pq), muonium forms initially in two spin states, defined by A> = lV°e> = I 1 1> and B> = I o /3e> = 1//2 10> +... 

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