OPERA Collaboration have observed phase speed of neutrino wave function, while advanced time displacement is mainly due to finite life time of pion

TL;DR

The paper suggests that OPERA's neutrino velocity measurements may reflect the phase speed of the neutrino wave function, with finite pion lifetime causing an observed advanced time displacement of about 100ns.

Contribution

It proposes that OPERA's measurements are of the neutrino wave function's phase speed and highlights the impact of pion decay on observed timing.

Findings

OPERA may have measured neutrino wave function's phase speed.

Finite pion lifetime causes a 100ns advanced time displacement.

Waveform deformation due to pion decay explains timing anomalies.

Abstract

First we call the attention that velocity defined by ratio between some intervals of space and time respectively is sometimes ambiguous, in the framework of quantum theory. Velocity in general is not possible to be well defined as some generator of certain space-time symmetry operation. Then in section 3 by analyzing the OPERA experiment we show that the OPERA Collaboration may have measured the phase speed of the neutrino wave function. Employing a very (maybe too) simple model which is just a reproduction from Brillouin's classical book, we demonstrate the phase velocity and group velocity. These are just a qualitative illustration rather than aiming to quantitively explain the OPERA data. However, how to rigorously define the phase containing the particle production ordering information as a space-time distribution observable in QFT needs more investigations. Due to the finite life time of the pions (w.r.t. its flying time in the 1 km long tunnel) which decay to the muon neutrinos, the wave form for neutrinos recorded by OPERA is deformed from that of the proton. Such an effect is estimated to lead to an advanced time displacement of the order of 100ns, which coincides with the measured. Such an effect can only be significant when measuring phase speed and the recorded neutrino events per extraction of proton smaller than one, as the OPERA case.