Superluminal Neutrinos at OPERA Confront Pion Decay Kinematics

TL;DR

The paper argues that Lorentz invariance violation cannot easily explain OPERA's superluminal neutrino results without conflicting with pion decay kinematics and cosmic ray data, setting very tight bounds on neutrino velocity deviations.

Contribution

It demonstrates that the level of Lorentz invariance violation needed for superluminal neutrinos conflicts with established pion decay and cosmic ray observations, providing stringent bounds.

Findings

OPERA's superluminal neutrino velocity limit: < 4×10^{-6}

Cosmic ray data constrains neutrino velocity deviation: < 10^{-12}

VLI explanation conflicts with pion decay kinematics

Abstract

Violation of Lorentz invariance (VLI) has been suggested as an explanation of the superluminal velocities of muon neutrinos reported by OPERA. In this note we show that the amount of VLI required to explain this result poses severe difficulties with the kinematics of the pion decay, extending its lifetime and reducing the momentum carried away by the neutrinos. We show that the OPERA experiment limits $\alpha = (v_\nu - c)/c < 4 \times 10^{-6}$. We then take recourse to cosmic ray data on the spectrum of muons and neutrinos generated in the earth's atmosphere to provide a stronger bound on VLI: $(v-c)/c < 10^{-12}$.