What is the meaning of 'CP violation' in the Cronin and Fitch experiment?

[Y Y Kim]

Below are the statements in the "David Griffiths, Introduction to Elementary Particles 2nd Edition, 147~148 p.":

Evidently, the long-lived neutral kaon is not a perfect eigenstate of CP after all, but contains a small admixture of K1. The coefficient epsilon is a measure of nature's departure from perfect CP invariance.

I am confused, because I don't think above statements alone can prove the CP violation. We can think the observation of two pions-decay in the long-lived neutral kaon is merely the result of 'K1 impurity' in the long-lived neutral kaon. Hence, there is no CP violation in above sentences.

Instead, I think the most important point of the experiment is that in spite of the impurity's effect, Cronin and Fitch could observe K2's decay into two pions. If K2 decayed into two pions, then it would reveal the CP violation.

Therefore, I cannot understand why the sentence "The coefficient epsilon is a measure of nature's departure from perfect CP invariance." is in the Griffiths' textbook. Is really the fact that long-lived neutral kaon is mixed state of the CP eigenstates evidence of the CP violation?

 

[Vanadium 50]

Consider charge conservation. A physical particle cannot be a mix of charged and neutral states. If CP is conserved, a physical particle cannot be a mix of CP even and CP odd states. Yet the K0L is. Therefore, CP is not conserved.

 

[Y Y Kim]

Thank you!

But, we can write K0 as K0=(K1+K2)/sqrt(2). This is a mixed state of CP even and CP odd states.
What is the problem?
Furthermore, I learned that conserved quantity is 'expectation value', so it seems to be no problem because K0's parity expectation value is 1/2*1+1/2*(-1)=0.

 

[Vanadium 50]

Do you agree with my argument on charge? If not, we need to get that straight.
If you do, what is different with CP?

 

[Y Y Kim]

Yes I agree with your argument on charge. But actually I think I didn't understand the relation between a conserved quantity and mixed state.
Also, I am confused because I cannot find 'a mixed state of charged and neutral states' as you said, but can find 'a mixed state of CP even and CP odd states'.

 

[Vanadium 50]

That's because CP is not conserved.

We don't see mixed states of different charges because charge is conserved.
We do see states of mixed CP because CP isn't conserved.

 

[vanhees71]

With the charge superselection rule it's not that simple. Of course, from charge conservation you can conclude that if you don't have a superposition of states with different charges, then there won't develop such a state later, because charge is conserved. You also have to argue that there cannot be a superposition of states with different charge number to begin with, i.e., why such a state cannot be prepared in the first place.

There are proofs in the literature. One uses locality and electromagnetic local gauge symmetry:

F. Strocchi, A. S. Wightman, Proof of the charge superselection rule in local relativistic quantum field theory
J. Math. Phys. 15, 2198 (1974); https://doi.org/10.1063/1.1666601

 

[Vanadium 50]

I don't think the OP's problem is that we haven't included enough complications yet.

Because charge is conserved we can't write down a (physical) state that is part Q=-1 and part Q=+1. If CP were conserved, you could not write down a state that is part part CP=-1 and part CP=+1. But since we do see such states, we know CP is not conserved - just as if we saw a particle that spontaneously changed its charge we would know charge wasn't conserved.

 

[vanhees71]

Of course, we can write down such a state. The question is, whether it occurs in Nature and if it doesn't, why not. A conservation law is not sufficient for such a superselection rule. E.g., of course you can have a superposition of different angular-momentum states, i.e., of different $J$ although angular momentum is conserved (for a closed system). There's a superselection rule forbidding to superimpose integer and half-integer angular-momentum states though, because a rotation around $2 \pi$ should only give a common phase factor for all states, i.e., you need an additional physical constraint to impose a superselection rule. In the case of the charge superselection rule the constraint comes from em. gauge invariance as shown in the quoted paper.

All this has nothing to do with CP violation by the weak interaction. CP is not conserved due to the weak interaction, and the CP eigenstates (K-long and K-short) of the neutral kaons are not the flavor eigenstates the weak interaction couples to, i.e., the weak interaction couples K-long and K-short, i.e., even if you prepare a K-long (by just observing them from a sufficiently large distance from their source) you'll find some of them decaying into only two pions, which was how CP violation was first observed by Cronin and Fitch.

 

[Vanadium 50]

Of course, we can write down such a state.

Which is why I said "physical".

But again, I don't think the OP's problem is that we haven't added enough complications. I want him to think about what it means for something to be conserved, and to compare withe examples he (hopefully) already knows, in a context where he finds the traditional explanation unsatisfactory.

Cronin and Fitch.

And Jim Christianson and Rene Turlay.

 

[vanhees71]

Which is why I said "physical".

You can write down many "states", but that doesn't imply that they are "physical". According to the quoted paper by Strocchi and Wightman there's indeed a charge superselection rule, because of local em. gauge invariance, and that's the theoretical explanation for the empirical evidence that such "states" are not realized in nature, but of course you are right in saying that this has nothing to do with CP violation. Perhaps we should open another thread about the "charge superselection rule"?