Uncertainties in constraints from pair production on superluminal neutrinos

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 1 order of magnitude in the results for the pair production decay width, are used to show the uncertainties on these constraints.

Figure 1

Value of the terminal energy $E_n$ (approximate final energy of a neutrino with initial energy higher than $E_n$) for the cases $n=1$ (left panel) and $n=2$ (right panel) as a function of the high-energy scale $\Lambda$ written in terms of the Planck energy $E_P$. The curves show the differences with respect to the matrix element used in the calculation and with different distances of propagation, typical of galactic or extragalactic neutrinos.

Figure 2

Value of the terminal energy $E_0$ (approximate final energy of a neutrino with initial energy higher than $E_0$) for different distances of propagation, as a function of the degree of superluminality in the neutrino speed.