State of mixed-helicities for massless neutrino

Spin 1/2 massless neutrino obeys the Majorana equation, and its helicity is a constant of motion.By using the squeezed coherent states,we derived the explicit representation of the common eigenstates of helicity operator and Hamiltonian for neutrinos, which, however, are non-normalizable per se.The packet waves thereupon constructed preserve the helicity,but are no more the eigenstate of energy.It is proved that for the wave packet of equally-mixed helicities, the propagation velocity vanishes.This is a scenario without correspondence in either the classical world or the massless Bosons.If such a wave packet of mixed helicities represents a neutrino-antineutrino pair,this may provide a reasonable candidate for dark matter.