Space-time evolution of heavy sterile neutrinos in cascade decays

Heavy sterile-like neutrinos may be produced resonantly from the decay of pseudoscalar mesons and may decay into several different channels in a cascade $\Phi \rightarrow L^\alpha \nu_h;\nu_h\rightarrow \{X\}$. In general these are rare events with displaced vertices. We provide a non-perturbative and manifestly unitary framework that describes the cascade decay and yields the space-time evolution of the probabilities for sterile neutrinos, final states and the total number of events at a far detector. The results are general, valid for Dirac or Majorana neutrinos and only input the total decay rates and branching ratios for the production and decay channels. We apply the general results to two examples of "visible" decay: i) $K^+\rightarrow e^+ \nu_h\rightarrow (e^+) e^+ e^- \nu_e$ via a standard model charged current vertex and ii) the radiative decay $K^+\rightarrow \mu^+ \nu_h \rightarrow (\mu^+) \nu_a \gamma$. For this latter cascade process we find substantial corrections to previous assessments within the parameter space argued to solve the anomalous excess of electron-like events at MiniBooNE. These large corrections may help relieve the tension with recent experimental bounds on radiative decays of heavy sterile neutrinos.Comment: 22 pages, 7 fig

Charged lepton mixing via heavy sterile neutrinos

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