Can charged leptons undergo oscillation? Neutrino oscillation is an observed fact while charged lepton oscillation is not. Unlike neutrinos, is it possible for the charged leptons to oscillate, theoretically? In other words, is there anything that forbids the oscillation of charged lepton in principle?
 A: No, lepton oscillation does not happen, because we define e, µ and τ to be the mass eigenstates of the charged leptons. We then define the three neutrinos $\nu_e$, $\nu_\mu$, and $\nu_\tau$ to be the neutrinos corresponding to these three charged leptons.
If we did it the other way around, and defined $\nu_e$, $\nu_\mu$, and $\nu_\tau$ to be the mass eigenstates of the neutrinos, and e, µ and τ, to be the charged lepton states corresponding to these neutrino mass eigenstates, then charged leptons would oscillate, but neutrinos would not. 
Although there's no reason we couldn't define things this way in theory, it would be a bad idea in practice, because generating mass eigenstates of charged leptons is nearly automatic, whereas generating mass eigenstates of neutrinos is quite difficult. 
However, this argument shows that there is symmetry between neutrinos and leptons, and that the only reason that lepton oscillation doesn't happen and neutrino oscillation does is our definitions of e, µ, τ, $\nu_e$, $\nu_\mu$, and $\nu_\tau$.
Why don't the mass eigenstates of the neutrinos correspond to the mass eigenstates of the charged leptons? There's no reason they have to in the Standard Model, and it turns out they don't. 
A: According to https://arxiv.org/pdf/0706.1216.pdf - the answer is most likely yes.  If I read the paper correctly (and I am only an engineer, not a scientist) the reason is the mass difference between the particles.
From the bullet points at the end:
Charged leptons e, µ and τ do not oscillate into each other because they are mass eigenstates. Since in β decays and muon decays the production of µ ± and τ
± is kinematically forbidden, there are no charged lepton oscillations associated with these processes.
