Non-Standard Neutrino Propagation and Pion Decay

Motivated by the findings of the OPERA experiment, we discuss the hypothesis that neutrino propagation does not obey Einstein special relativity. Under a minimal set of modifications of the standard model Lagrangian, we consider the implications of non standard neutrino propagation on the description of neutrino interactions and, specifically, on the pion decay processes. We show that all the different dispersion relations which have been proposed so far to explain OPERA results, imply huge departures from the standard expectations. The decay channel $\pi^+ \to e^+ \nu_{\rm e}$ becomes significantly larger than in the standard scenario, and may even dominate over $\pi^+ \to \mu^+ \nu_{\rm \mu}$. Moreover, the spectral distribution of neutrinos produced in the decay processes and the probability that a pion decays in flight in neutrinos show large deviations from the standard results.