Could the muon's shape be attributing to our measurements of the $g$ term for the magnetic moment? I read that the $g$ term in the magnetic moment is being studied carefully these days in muons. I was wondering if the $L$ term was also being studied? I know that electrons have been found to be basically perfect spheres, but I was wondering if a similar study had been done of muons. Also, if the muons did end up being "lumpy" could that cause the offset in what we are measuring for $g$?
 A: Comments along the lines of “the electron is perfectly spherical” are a low-jargon shorthand for describing the continued non-observation of any permanent electric dipole moment for the electron; for example.  Permanent electric dipole moments probe CP-violating physics. The fact that the universe contains more matter than antimatter, and in particular the size of the matter-antimatter excess, suggests that there is new CP-violating physics right around the corner, in terms of experimental sensitivity.  The continued anomaly in the muon’s magnetic moment also suggests that there is new physics just around the corner. Whether those are the same new physics is not obvious; the electric and magnetic dipole moments have different symmetries.
The direct measurement of the muon’s EDM (from the Particle Data Group) is
$$d_\mu < 2\times10^{-6}\,e\,\mathrm{fm}.$$
Compare with the electron EDM limit
$$d_e < 0.11\times10^{-15}\,e\,\mathrm{fm}.$$
This dramatic difference in precision is because electrons are stable and muons aren’t. We can look at moles of electrons all at once for arbitrarily long times, while unstable muons have to be used within a microsecond of coming out of the particle accelerator.
If there were some lepton-universal process that gave a permanent electric dipole moment (“nonspherical shape”) to all the charged leptons, that process would have to be enhanced by a factor of a billion for us to find it in muons before we find it in electrons.
