Louis Lello, Daniel Boyanovsky
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 oscillations 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. The mixed $\mu -e$ propagator cannot be completely diagonalized by a unitary (or bi unitary) transformation as a consequence of the different spinor structure between the kinetic and mass terms. Mixing angle(s) are GIM suppressed and are \emph{momentum and chirality dependent}. The negative chirality mixing angle near the muon mass shell is $\theta_L(M^2_\mu) \propto G_F \sum U_{\mu j} m^2_j U^*_{j e}$ with $m_j$ the mass of the neutrino in the intermediate state. Recent results from TRIUMF suggest an upper bound $\theta_L(M^2_\mu) < 10^{-14}\,\Big(M_S/\mathrm{100}\,MeV\Big)^2$ 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 $\mu \rightarrow e\gamma$ with charged lepton mixing, highlighting that a measurement of such process implies a mixed propagator $\mu, e$ and suggest further contributions to this process as a consequence of mixing with momentum dependent mixing angles.
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http://arxiv.org/abs/1212.4167
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