Pseudoscalar meson decay leads to an entangled state of charged leptons
($\mu,e$) and massive neutrinos. Tracing out the neutrino degrees of freedom
leads to a reduced density matrix for the charged leptons whose off-diagonal
elements reveal \emph{charged lepton oscillations}. Although these decohere on
unobservably small time scales $ \lesssim 10^{-23} s $ they indicate charged
lepton \emph{mixing} as a result of common intermediate states. The charged
lepton self energy up to one loop features flavor off-diagonal terms
responsible for charged lepton mixing: a dominant ``short distance''
contribution with $W$ bosons and massive neutrinos in the intermediate state,
and a subdominant ``large distance'' contribution with pseudoscalar mesons and
massive neutrinos in the intermediate state. Mixing angle(s) are GIM
suppressed, and are \emph{momentum and chirality dependent}. The difference of
negative chirality mixing angles near the muon and electron mass shells is
$\theta_L(M^2_\mu) -\theta_L(M^2_e)\propto G_F \sum U_{\mu j} m^2_j U^*_{j e}$
with $m_j$ the mass of the neutrino in the intermediate state. Recent results
from TRIUMF, suggest an upper bound $\theta_L(p^2\simeq M^2_\mu)-\theta_L(p^2
\simeq M^2_e) < 10^{-14}\,\Big(M_S/\mathrm{100}\,MeV\Big)^2$ for one generation
of a heavy sterile neutrino with mass $M_S$. We obtain the wavefunctions for
the propagating modes, and discuss the relation between the lepton flavor
violating process $\mu \rightarrow e\gamma$ and charged lepton mixing,
highlighting that a measurement of such process implies a mixed propagator
$\mu, e$. Furthermore writing flavor diagonal vertices in terms of mass
eigenstates yields novel interactions suggesting further contributions to
lepton flavor violating process as a consequence of momentum and chirality
dependent mixing angles.Comment: 26 pages, 5 fig