### 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 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 () have been used to place a bound on for the muon (see Equation (52) for the
definition of ) [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 of

where in a non-rotating frame with oriented along the earth’s spin axis.
The second muon experiment that yields strong limits is the g-2 experiment [58, 39, 72]. In
this experiment relativistic (or ) 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 for the muon. Lorentz violation changes this evolution equation, and
therefore this type of experiments can bound the mSME. As in the case of the experiments
in Section 5.1, two types of bounds can be placed from the muon experiment. The first is a direct
comparison between the factors for and , which limits the CPT violating
coefficient . Furthermore, an analysis of sidereal variations involving only one of
the at the current sensitivity in [72] could bound the coefficient at the level of
[58].