$K_S K_L$ Pair Rate

The rate of $10^4$/s of $\phi$ is taken. It should be mentioned, that the total hadronic rate in this case will be an order of $3\times10^6$. The $K_S K_L$ pair rate from $\phi$ decays is $3\times10^3$. Few types of experiments can be set:

1. Tagged $K_S$. With the near 100% detection efficiency of $K_L$ (by decay in flight and by nuclear interaction in the forward calorimeter) and with constrained from initial $\phi$ energy and momentum this rate can be used for study of rare decays of $K_S$: $K_S\rightarrow\gamma\gamma$ and CP-violation decays $K_S\rightarrow\pi^0\pi^0\pi^0, \pi^+\pi^-\pi^0$ predicted at the level of $2\times10^{-9}$. With $10^7$ s of running time proposed $K_S K_L$ pair rate gives 60 events of that kind.

2. Direct CP violation studies. To have reasonable acceptance for detection of $K_L$ decays in flight with full reconstruction and event selection seems to be difficult experimentally - detector becomes too long: $\gamma\beta\ c\tau_L$ = 100 m. So I do not propose to perform measurement of $\epsilon '/\epsilon$.

3. For the interferometry only about 8-10 $K_S$ decay lenghts are needed. With 3 GeV/c kaon momenta the $K_S$ decay length is $\gamma\beta\ c\tau_S$ = 15cm, so about 1.2-1.5 m decay volume is needed.

In this case usefull rate will be $3\cdot10^3\times 10\cdot\tau_S /\tau_L\times$ (detector acceptance). Assuming 4$\pi$ detector it gives about 50 detected $K_S K_L$ pairs/s. But only 0.2% of them are with $\pi^+\pi^-\pi^0\pi^0$ final state. So, CP rate is 0.1/s. With $10^7$ running time $10^6$ such events can be expected, what can give few$\times10^{-3}$ accuracy in the asymmetry. For the CPT test the most sensitive region is $\Delta t= 1-4~\tau_S$, where intensity is dropping down due to QM. But remain number of events could be enough for CPT test at the level $\Delta\Phi < 0.1^{0}$.

All above estimations were performed in [1], where other $\phi$ decay physics was discussed and which could be performed at CEBAF with less photon flux. It includes radiative and other rare decays of $\phi$ as well as $\eta ,\eta '$ decays when $\phi$ can be considered as source of tagged (with photon) $\eta$ and $\eta '$ via $\phi\rightarrow\eta\gamma$ or $\phi\rightarrow\eta '\gamma$.