A hypothesis on neutrino helicity

Abstract

It is firmly established by experimental results that neutrinos are almost 100\% longitudinally polarized and left-handed. It is also confirmed by neutrino oscillation experiments that neutrinos have tiny but non-zero masses. Since their masses are non-zero the neutrinos cannot be strictly described by pure helicity states which coincide with the chirality eigenstates. On the other hand, it is generally assumed that ultrarelativistic massive fermions can be described well enough by the Weyl equations. This assumption obviously explains why the neutrinos are almost 100\% longitudinally polarized. We discuss the validity of this assumption and show that the assumption is fallacious for a fermion with a general spin orientation. For instance, a fermion with a transverse polarization (relative to its momentum) cannot be described by one of the Weyl equations even in the ultrarelativistic limit. Hence, the fact that neutrinos are almost completely longitudinally polarized cannot be explained in the basis of relativistic quantum mechanics or quantum field theory. As a solution to this problem, we propose a new hypothesis according to which neutrinos are strictly described by pure helicity states although they are not massless.