Charged lepton mixing via heavy sterile neutrinos

TL;DR

This paper explores how heavy sterile neutrinos induce charged lepton mixing through quantum entanglement and loop effects, revealing momentum-dependent mixing angles and potential implications for lepton flavor violation experiments.

Contribution

It introduces a detailed theoretical framework for charged lepton mixing mediated by heavy sterile neutrinos, including momentum and chirality dependence, and connects it to observable lepton flavor violation processes.

Findings

Charged lepton mixing angles are GIM suppressed and momentum-dependent.

Heavy sterile neutrinos can induce measurable lepton flavor violation.

Upper bounds on mixing angles are derived from experimental data.

Abstract

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.