  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.
