Let us introduce a force that has opposite charges on left and right handed particles, due to quantum anomalies electrons cannot feel such a force. But neutrinos on the other hand seem to need such a force. The equations of motion of particles allow for forces that act either equally between opposite spins, Vector forces, and ones that act oppositely between opposite spins, Axial forces. So we may introduce a axial force between neutrinos. Noticing that beta decay produces both an electron and an anti-neutrino, we may see, that a W particle would hold both charges of
both the vector electric force and neutrino axial forces. The W particles (V-A) vector-axial nature first noted by Enrico Fermi, is then derived from the combination of forces on electron and neutrinos. That the Weak force has a (V-A) nature was completely unexpected and was discovered after experimenters noticed that electrons emitted by decaying cobalt-60 held in an magnetic field only spun in the left handed direction. The weak force was from then on described as left handed (V-A) force, but no clear mechanism for arrived at for explaining why the weak force left handed.
In fact under the symmetry of special relativity, left handedness doesn't remain left handed, you may over take a particle spinning in a left handed manner compared with its direction of motion, looking backwards you would see a right handed spinning particle. Thus relativity needs a right handed force as well a left handed force, and right handed as well as left handed neutrinos. In addition, it has been proved by L.M. Slad, that a axial force is need in addition to a left and right handed weak force, in order to give a definite handedness to the fields, that survives relativistic transformations. Having an axial force allows a neutrino to reverse its direction without reversing its handedness, it merely emitted a spin-1 axi-photon after the reversal. It is this axi-photon that carries the fifth force. The symmetry of the axial force allows left and right handed neutrino andleft and right handed W particles the carriers of the weak force to have different masses. This is possible because an axial force is created by gauge invariance (Adams1, Section 2), whenever a particle has its mass described by as a Majorana mass, with different masses for left and right handed particles. The asymmetry noticed at low energy, that neutrinos are light and left handed and that the weak force has a mass and is left handed, then required another symmetry that of the axial force. We thus have 3 reasons for believing in an axial force.
1. That gauge invariance is possible for neutrinos with Majorana mass. Implies an axial force.
2. That the weak force handedness is compatible with relativity. Implies an axial force.
3. That the weak force is V-A, may be retrodicted from an axial force between neutrinos.
I have been investigated the axial force for some five years now, and have blogged about it frequently at my previous blog site and written several papers for it. I managed to use the axial force to defend causality if neutrinos happened to travel faster than light. This I now regret as the OPERA experiment that saw faster than light neutrinos, turned out to be incorrect. The Axial force works whatever the speed of neutrinos are, both normal masses or tachyonic masses is fine to the axial force.
I have found that the axial force could be quite strong maybe as strong as a sixtieth of the strength of the electromagnetic force and still not be noticed. The reason is that neutrinos so very light, that the slightest forces on them causes them to move very quickly, as large measurement distances, bigger than 5 nanometers in air, and much less in solids the axial force is completely screened by the motions of background neutrinos. This makes the axial force a chameleon force, hidden from normal experiments, and explains why it has not be detected by other experiments. For my next article I will write of a experiment that might detect an axial force, and hope I can get experimentalists to try performing it.