  The use of the vacuum lepton pair production process ($\nu \to \nu e^- e^+
$), a viable reaction for superluminal neutrinos, to put constraints on Lorentz
violations requires a dynamical framework. Different choices of dynamical
matrix elements and modified dispersion relations for neutrinos, leading to
numerical factors differing by one order of magnitude in the results for the
pair production decay width, are used to show the uncertainties on these
constraints.
