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Charged lepton mixing via heavy sterile neutrinos
Pseudoscalar meson decay leads to an entangled state of charged leptons
() 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 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 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
with the mass of the neutrino in the intermediate state. Recent results
from TRIUMF, suggest an upper bound for one generation
of a heavy sterile neutrino with mass . We obtain the wavefunctions for
the propagating modes, and discuss the relation between the lepton flavor
violating process and charged lepton mixing,
highlighting that a measurement of such process implies a mixed propagator
. 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
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