Right- and Left-Handed Neutrinos?

Neutrinos are lepton family partners to the electron, muon, and tau particles of the Standard Model of Leptons and Quarks. Each neutrino is thought to be distinct, the electron neutrino being different from the muon neutrino, for example. We now know, however, that each lepton family neutrino type has a very small mass and is actually a linear combination of three fundamental neutrino states: ν₁, ν₂, and ν₃.

For the weak interaction, there is the left-handed doublet state | ν_L, e_L> and the two right-handed singlet states | ν_R > and | e_R >, with the consequence that the right-handed states interact with the Z⁰ boson but do not participate in the weak interaction mediated by the W⁺ and W ^– bosons. The left-handed doublet interacts with all three weak bosons. Must one resort solely to the explanation “that is how Nature behaves,” or is there another fundamental reason for left-handed doublet and right-handed singlet states?

Answer

No. The weak interaction is associated with the SU(2)-weak part of the Standard Model gauge group that operates in the unitary plane a plane with two complex axes. That is, particle fundamental lepton and quark states are defined in this unitary plane. All rotations in the normal unitary plane involve only left-handed doublets and right-handed singlets, dictated solely by the mathematics of the geometrical transformation. Mathematicians call these transformations right and left screw operations. So the physical property of left-handed doublet states for the weak interaction is dictated by the mathematical property of rotations in the unitary plane. Nature simply “knows” the mathematics!

The antiparticle eigenstates are in the conjugate unitary plane, which is gauge-equivalent (not equivalent) to the normal unitary plane, so the energy values of particles and antiparticles are the same, but all other properties are opposites. In this conjugate unitary plane the mathematics dictates right-handed doublets and left-handed singlets. The existence of two gauge equivalent but different 2-D complex spaces conjugate to one another dictates that the universe has both particles and antiparticles. Why there exist so many more particles than antiparticles in our present universe remains to be resolved.