Regeneration

The crucial point for all above can be nuclear interaction of kaons with the target nuclei. This is the main difference of target experiments with colliding beams ones.

The total nuclear cross section for 2-3 GeV kaons is about 20 mb/nucleon including about 1 mb/nucleon (should be checked) regeneration of $K_L$ into $K_S$. For average pass of kaon through half of the target length the total hadronic interaction rate for $3\cdot10^3$ kaons is 15/s (88/s ?!! should be checked!) what should be compared with 50/s of usefull $K_S K_L$ pair rate. But only about 3/s (17/s ?!!) are $\Sigma\pi$ or $\Lambda\pi$ which can give similar signature as kaon decay. But they can be rejected by missing mass analysis and looking for recoil proton. So nuclear interaction wont give too much background to correlated kaon pairs.

More complicated with regeneration. The above cross section gives 0.7/s of regenerated $K_L$ compare with 0.1/s of usefull CP decays. The regenerated $K_S$ has different angular and momentum distribution than original $K_S$ or $K_L$ and constrained fit for $\pi^+\pi^-\pi^0\pi^0$ final state could remove most of them.

Question: how many? There is approved by INTASS grand for study of this effect in KLOE drift chamber (Frascati(J.Franzini)-Novosibirsk(E.Solodov)), where regeneration is smaller, but still 100 times higher than signal from direct CP violation.

It should be mentioned, that regeneration itself will not give an asymmetry, because in final state one has $K_S K_S$. Regeneration reduces sensitivity of the asymmetry measurement (10% for KLOE, 7 times for CEBAF?!). But if one rejects regenerated events by constrained fit, it becomes dangerous, because constrained fit can remove more $\pi^+\pi^-$ than $\pi^0\pi^0$ due to better resolution and immediately gives asymmetry. It should be under control at the level of $10^{-3}$ or better.

For the new CEBAF detector it may be reasonable to consider 10 times shorter target with 10 times more photon flux ($10^{11}$/s !). Or it may be a compromize - shorter target - longer running time.

The $LH_2$ target has some advantage. Because $K_S$ decay length is shorter, than target length, the regeneration (and nuclear interactions) is not integrated over full length of the target as for Be case. It could give factor of 2-3 in signal/background ratio.

We should think how to reduce this background.

Also regeneration can bring us a new interesting physics. The coherent fraction of regenerated $K_S$'s (it is a question how many?) will interfere with original $K_S$'s and in general should be canceled. Or it may give another interesting effects.

Note: Numbers of this sections are very preliminary and because of importance should be carefully checked.