Helicity - Experiment proving CP violation

[vertices]

Please look at the attach file.

If we take case a) it proves the C and P are independly violated (neutrinos are left handed)

The component of spin along the direction of motion is:

-1 for the photon (bosons can have spin + or - 1)
-1/2 for the neutrino (fermions can have spin + or - 1/2)

So the total spin along the direction of motion is -3/2 which by the conservation of AM equals the spin of initial electron (the 'reactant' if you will). But this electron can only have a spin of + 1/2 or - 1/2, not -3/2 (or +3/2)!

Can someone explain what I am not managing to understand. Thanks:)

 

[humanino]

Hi

Can someone explain what I am not managing to understand.

I can try, but I am not sure what you do not understand !

So the total spin along the direction of motion is -3/2 which by the conservation of AM equals the spin of initial electron (the 'reactant' if you will). But this electron can only have a spin of + 1/2 or - 1/2, not -3/2 (or +3/2)!

Let me try to clarify a little bit. Let us consider the decay axis (horizontal in the plot) to be oriented from left to right for definiteness.

Case (a) : initially electron has +1/2, finally photon has +1 and neutrino has -1/2
Case (b) : initially electron has -1/2, finally photon has -1 and neutrino has +1/2

In both cases, the total AM in the final state (photon + neutrino) equals what was originally carried by the electron. Those two possibilities are what AM conservation allows.

Since no neutrino can be right handed, we do not observe (b) in Nature. Neutrinos are always left-handed. Anti-neutrinos are always right-handed. From these facts, we see that indeed, C and P are separately broken, maximally, but the combination CP is respected. CP violation is not maximal at all, it does occur in neutral Kaon system for instance, but it is a minute effect.

 

[vertices]

thanks humanino :)

I was being really, really silly. I was thinking that the bold arrows represent the helicity vector (it must be a vector, right?) rather than the spins.

BTW, what do you mean by "maximal" in:

"CP violation is not maximal at all, it does occur in neutral Kaon system for instance, but it is a minute effect."

 

[humanino]

I was thinking that the bold arrows represent the helicity vector (it must be a vector, right?) rather than the spins.

Oh, I'm not going into the difference between spin and helicity
Helicity is the projection of the spin on the momentum axis.
For massless particles, the spin projection on any axis can only take + or - the spin value.
But helicity and spin are different things for massive particles.

BTW, what do you mean by "maximal" in:

"CP violation is not maximal at all, it does occur in neutral Kaon system for instance, but it is a minute effect."

Parity is maximally violated by weak interactions in the sens that you have only left-handed neutrinos. If there were a small difference between the weak interactions of left-handed and right-handed neutrinos, parity would only be slightly violated.

Another way to say it : take a process involving a left-handed neutrino, say this process occurs 1000 times per second in your experiment. Now take the mirror image of your experiment. If parity where slightly violated, you could find out it occurs 997 times per second. But parity is maximally violated in the sens that the process with the right-handed neutrino does not occur at all, even once in a billion years.

 

[vertices]

I see, thanks for clearing that up.