Wave Packet for Massless Fermions and its Implication to the Superluminal Velocity Statistics of Neutrino

Abstract

Non-dispersive wave packet for massless fermions is formulated on the basis of squeezed coherent states that are put in a form of common eigenfunction for the Hamiltonian and the helicity operator, starting from the Dirac equation. The wave packet thus constructed is demonstrated to propagate at a constant velocity as that of light. This explicit expression of wave packet for the massless fermions can facilitate theoretical analysis of problems where a wave packet is of formal significance. Furthermore, extensive wave packet may result in a superluminal velocity statistics if determined from the time-of-flight measurement, as recently done on muon neutrinos, when a threshold particle flux or energy transfer, which is eventually referred to the propagation of wave packet, to invoke a detection event is assumed.

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