Proof that L L

One can also show that [21,22]:

Replacing the kinetic term in Lagrangian (4) using eq.(9) and in the interaction term using eq.(8) one gets:

The charged-current coupling constant in eq.(10) is seen to be a factor larger than in eq.(7) the two Lagrangians are thus different.

The numerical value is determined in the standard-model gauge theory by considering only neutral-current (for ) and electromagnetic (for ) reactions of the electron, i.e. without reference to neutrino properties. One numerically different coupling constant in the two otherwise identical Lagrangians eq.(7) and eq.(10) is a difference which persists to the phenomenological level (i.e. the application of Feynman rules). In other words: if the neutrino is a Majorana particle and its gauge interactions are the one of the standard model, charged-current reactions of the neutrino would have a factor 2 larger cross section than observed. If we assume the strict validity of the standard model