Parity Violation

Experimentally it is found that weak interactions violate the parity symmetry. The typical experience consists in the study of the angular distribution of the emitted electrons related to the direction of the spin of the nucleous in the $\beta$ decay:

$$Co^{60} \rightarrow Ni^{*60} + e^{-} +\bar{\nu}_{e}$$ (69)

If

$$\cos \theta = \frac{\vec{p}_{e}\cdot \vec{J}}{\mid \vec{p}_{e}\mid J}$$ (70)

measures the mentioned angle, the angular distribution of $e^{-}$ is

$$W_{e}(\theta) = 1 + \alpha \cos \theta$$ (71)

Now, if parity were preserved the probability of a phenomenon and that of its specular image should be identical. In the present case, the image of the disintegration of $Co^{60}$ with the electron towards the backward hemisphere, as defined by the spin of the nucleous, is the disintegration of the $Co^{60}$ with the electrom emitted towards the forward hemisphere. It should be noticed that the spin, being an axial vector, does not change under the parity operation and therefore

$$\cos \theta \stackrel{P}{\rightarrow} - \cos \theta$$ (72)

indicating that the conservation of $P$ symmetry would imply

$$\alpha \equiv 0$$ (73)

Nevertheless, the result of the experiment provides the value

$$\alpha_{exp} = - 0.4$$ (74)

showing that the laws governing the weak interactions are not invariant under parity transformations.

This result makes it necessary to include in the phenomenological Lagrangian some pseudoscalar terms. So the $(V-A)$ interaction results carrying implicitly the condition of ``leftists" of the neutrinos (they only present left chirality).