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Kaon oscillations

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A pi- is sent onto a target producing neutral K mesons and ^ hyperons. Consider the component of the resulting K beam with momentum of p = 10GeV. What is the ratio between K1o and K2o at the production point and at l=10m from the production point? Assume no CP violation.

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The K1^(0) and K2^(0) states which have CP eigenvalues of 1 and -1 and are mass eigenstates are:

|K1^(0)> = 1/sqrt(2) [|K^(0)> - |K^(0)-bar>]

|K2^(0)> = 1/sqrt(2) [|K^(0)> + |K^(0)-bar>]

This means that a K^(0) particle that is produced can be written as the superposition

|K^(0)> = 1/sqrt(2) [|K1^(0)> + |K2^(0)>]

Now the collisions with the target will also lead to the production of the anti particles, the K^(0)-bar, which is the superposition:

|K^(0)-bar> = 1/sqrt(2) [|K2^(0)> - |K1^(0)>]

Since the production of the K-mesons is an incoherent process, you have a statistical mixture of both superpositions. In each of these superpositions, you have ...

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