ar X iv : h ep - p h / 97 08 44 5 v 1 2 4 A ug 1 99 7 Concerning the Differences Between Zero Mass Dirac and Majorana Neutrinos

That a Majorana neutrino theory is different from a Dirac neutrino theory (even in the zero mass limit) is proved in two sentences. Fermion Statistics For the reactions (Dirac) e + e − → ν ¯ ν and (Majorana) e + e − → νν wherein the two final particles are presumed to have opposite helicity, in the Dirac case the neutrino and anti-neutrino are different particles so that Ψ Dirac (p 1 , λ 1 ; ¯ p 2 , ¯ λ 2) (in momentum-helicity) has no particular particle anti-particle exchange symmetry, while in the Majorana case the two neutrinos are identical fermion particles with an exchange anti-symmetric wave function in the center of mass frame[1] Thus, for the Dirac case with a fixed angle of scattering, the probability of having a left helicity neutrino can and does differ from the probability for having a right helicity anti-neutrino dσ dΩ Dirac ν Lef t = dσ dΩ Dirac ¯ ν Right (in general) (2) and for the Majorana case with a fixed angle of scattering, the probability of having a left helicity neutrino is identical to the probability of having a right helicity neutrino dσ dΩ M ajorana ν Lef t = dσ dΩ M ajorana ν Right. (3) This non-perturbative difference (transcending particular parity violating Lagrangian models) between the Dirac and Majorana cases is true even in the zero mass limit. We disclaim responsibility for work purporting to describe more than one Majorana fermion without employing a properly anti-symmetric neutrino wave function. Finally, we have greatly benefited by reading recent debates[2-6].