The weird behaviours of the weak force

The Wu experiment

💼 Case: a sample of $^{60}\rm Co$ in a magnetic solenoid cooled to $0.01\,\rm K$ as to avoid thermal fluctuations such that all the spins are aligned

We then study beta decay

$$ ^{60}\rm Co \to ^{60} \rm Ni ^* +e^-+\overline \nu _e $$
Where we measure if the electron emissions have a preferred direction

⚽ Goal: find which direction the electron go if parity is violated or conserved

1️⃣ Parity is conserved

Applying the parity operation (ie $z\to -z$) we get:
- Momentum vector change sign $\vec p \to -\vec p$
- Total angular momentum doesn't change $\vec J \to \vec J$
🗒️Note: to apply the “parity operation” physically we simply change the setup of the solenoid reversing the spin of $^{60} \rm Co$

💎 Conclusion: if parity is conserved we expect the electrons to go equally in both directions of the axis

2️⃣ Parity not conserved

This is simply the opposite of the above thus

💎 Conclusion: we expect that there is a bias towards one direction

🗒️ Note: the diagram shows the setup for both 1️⃣ and 2️⃣

🟰 Experimental result

Parity is not conserved‼️

The weak interaction and handedness

The result above is explained by handedness ie the weak interaction only couples to left-handed fermions and right-handed antifermion

💼 Case: Consider mass-less neutrinos (this is a bas example as neutrinos have mass and their handedness is miss understood)

The neutrinos can have spin $\pm \frac 12 \hbar$
On the figure positive and negative helicity for left right respectively

Helicity: the spin projection along its direction of motion (divided by its maximal possible value)

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For our massless particles this corresponds to right-handed and left-handed states (chirality)

💎 Conclusion: handedness is what causes the parity $P$ violation in the weak interaction

🗒️ Note: experimentally we expect to create left handed neutrinos but this doesn't happen

$P$ and $C$ violations

The charge conjugation $C$ is also violated in the weak interaction. Lets show this

💼 Case: decay of a polarised muon ${\mu^{-} \to e^- + \overline \nu_e + \nu_\mu}$, muon is in rest frame

🗒️ Note: the arrows represent the spins

Now applying the $C$ operation we get

$$ \begin{matrix} e^-\to e^+ & \overline \nu_e\to \nu _e \\ \nu _\mu \to \overline \nu _\mu & \mu^-\to \mu ^+ \end{matrix} $$
From the second figure we see that this creates right handed neutrinos thus

💎 Conclusion: $C$ is violated