Uncertainties in constraints from pair production on superluminal neutrinos

Abstract

The use of the vacuum lepton pair production process ( ! e À e þ ), 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.

Use of energy loss mechanisms to constrain Lorentz invariance violations

“…Differential decay rate for two of the dynamical matrix elements reported in Ref. [22] in the case of energy-independent velocity (E = p (1 + η0)). E and E are, respectively, the energies of the incoming and outgoing neutrinos.…”

“…(1)) for the first and second dynamical matrix elements of Ref. [22], respectively. And the standard deviations are 0.34 and 0.15, respectively.…”

“…If the energy loss increases with the amount of Lorentz invariance violation, the observations of high energy particles may be used to place limits on the size of the Lorentz invariant violating parameters (see Refs. [18][19][20][21][22][23][24]). Reactions of this sort include: photon and neutrino splitting (γ → 3γ and ν l → ν l ν l ν l ), photon production by charged leptons and neutrinos (e ± → e ± γ and ν l → ν l γ), and pair production by neutrinos (ν l → ν l e + e − ), which will be the one we will use hereafter when specific information is needed; we refer the reader to Ref.…”

“…Reactions of this sort include: photon and neutrino splitting (γ → 3γ and ν l → ν l ν l ν l ), photon production by charged leptons and neutrinos (e ± → e ± γ and ν l → ν l γ), and pair production by neutrinos (ν l → ν l e + e − ), which will be the one we will use hereafter when specific information is needed; we refer the reader to Ref. [22] for all details about this decay. This latter process is only permitted if the incoming neutrino is superluminal 1 and its energy is above certain threshold.…”

Lorentz Violation Footprints in the Spectrum of High-Energy Cosmic Neutrinos—Deformation of the Spectrum of Superluminal Neutrinos from Electron-Positron Pair Production in Vacuum

“…can produce two new particles when its energy is above a threshold energy E * . This threshold energy is given in terms of the energy scale Λ and the order of the correction n by [18]:…”