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5.7 Muon experiments

Muon experiments provide another window into the lepton sector of the mSME. As discussed in Section 4.3, if the mSME coefficients are to be small then there must be some small energy scale suppressing the Lorentz violating coefficients. There are only a few available small scales, namely particle masses or a symmetry breaking scale. If we assume the scale is particle mass, then muon based experiments would have a signal at least 2 10 larger than equivalent electron experiments due to the larger mass of the muon. The trade-off, of course, is that muons are unstable so experiments are intrinsically more difficult.

There are two primary experiments that give constraints on the muon sector. First, spin transitions in muonium (m+e -) have been used to place a bound on ~b J for the muon (see Equation (52View Equation) for the definition of ~ bJ[149]. Even though muonium is a muon-electron system, the muon sector of the mSME can be isolated by placing the muonium in a strong magnetic field and looking for a particular frequency resonance that corresponds to muon spin flips. The sidereal variation of this transition frequency is then tracked yielding a limit on ~bJ of

| | ||~bJ||< 5× 10 -22mm, (73)
where J = X, Y in a non-rotating frame with Z oriented along the earth’s spin axis.

The second muon experiment that yields strong limits is the m -/m+ g-2 experiment [58Jump To The Next Citation Point3972Jump To The Next Citation Point]. In this experiment relativistic - m (or + m) are injected into a storage ring and allowed to decay. The deposit rate of the decay products along the detector is sensitive to the evolution of the spin of the muon, which in turn is a function of g - 2 for the muon. Lorentz violation changes this evolution equation, and therefore this type of g - 2 experiments can bound the mSME. As in the case of the g - 2 experiments in Section 5.1, two types of bounds can be placed from the muon g - 2 experiment. The first is a direct comparison between the g- 2 factors for - m and + m, which limits the CPT violating coefficient bZ < 10-22 GeV. Furthermore, an analysis of sidereal variations involving only one of the m- /m+ at the current sensitivity in [72] could bound the ~bJ coefficient at the level of 10- 25 GeV [58].

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