## How to maintain CPT invariance in Kaon oscillations

Hey,

I'm trying to get my head around neutral Kaon oscillations. As far as I understand it neutral Kaons can change between $K^0$ and $\overline{K^0}$ as they propagate. Going through the quantum mechanics of this implies that this oscillation must be facilitated by a mass difference between the $K^0$ and $\overline{K^0}$ in a $\cos(\Delta m t)$ term.

But I thought a mass difference between any particle and its antiparticle implies CPT violation.

As far as I know CPT is not known to be violated so my question is: How do Kaon Oscillations maintain CPT invariance?

Thanks in advance for any help :D

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 Mentor The K0 and K0bar are not mass eigenstates.
 Blog Entries: 1 Recognitions: Science Advisor Consider the Hamiltonian across the K0 and K0-bar states. CPT says the masses of these states are equal: $$\left(\begin{array}{cc}M&0\\0&M\end{array}\right)$$ But the weak interaction adds a perturbation that turns K0 into K0-bar: $$\left(\begin{array}{cc}M&ε\\ε&M\end{array}\right)$$ As V50 says, K0 and K0-bar are no longer the eigenstates, and the originally degenerate mass eigenvalues have been split into two unequal eigenvalues.

## How to maintain CPT invariance in Kaon oscillations

Thanks! That makes sense.

So I guess the $\Delta m$ refers to the difference in mass of the modified states coupling to the weak interaction (a superposition of K0 and K0-bar)?

 Mentor No, those "particles" are the weak eigenstates. The mass eigenstates are called K1 and K2. Neglecting CP violation, K1 is the short-living KS and K2 is the "long"-living KL. CP violation introduces another, but small mixing in this system - KS has some small component of K2 and KL has a small component of K1.
 Thanks. I think I understand that. Am I right in thinking that if there was no CP violation the mass eigenstates would have the same mass and therefore there would be no kaon oscillations?
 Mentor Without CP violation, the mass eigenstates would be identical to K_S and K_L, but those would remain a mixture of the weak eigenstates.

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