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{\bf{
CP, CPT Study at Jefferson Laboratory
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\begin{center}
E.P.Solodov, BINP, 11 prospekt Lavrentyeva, Novosibirsk, 630090, Russia
e-mail:solodov@inp.nsk.su
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\section{ Physics Motivation}
%
 $\phi$-meson, as many times discussed (see. \cite{est90}) is a good source of
correlated pairs of neutral kaons because
it decays into correlated $K_S K_L$ pairs 32\% of the time.
By studying the equal decay modes of $K_L$ and $K_S$
quantum mechanics correlation can be seen in 0-8 $K_S$ lifetime region
(c$\tau_S$=2.676cm).
Final states can be the same due to
CP-violating decay of $K_L$ into $\pi^0\pi^0$ or  $\pi^+\pi^-$ with
$2\times10^{-3}$ branching ratio but as for $K_S$ they are main decay modes.
Semileptonic dacays also can be used for
this interferometery, but B($K_S\rightarrow\pi l \nu_l$) is expected at
the level of $5\times 10^{-4}$.

The idea of experiments discussed for $\phi$-factories is in simultanious
detection of $K_S K_L$ decays in $\pi^+\pi^-\pi^0\pi^0$ state and
reconstruction of their decay points with accuracy better than one
$K_S$ decay length.
Due to fully asymmetric final state ($J^{PC}=1^{- -}$) quantum mechanics
prohibits decay of both kaons at the same distance from originated $\phi$
if they have the same decay mode.

In addition to this very exciting quantum mechanics test at macroscopic
distances
this interferometry can be used for a study of direct CP violation in
$K_L$ decays ($\epsilon '/\epsilon$) and for precision CPT tests.
For these purposes one should measure the difference in number of events when
$\pi^+\pi^-$ pair appeares before $\pi^0\pi^0$ ($N_{+-}$)
with those when $\pi^0\pi^0$ pair is first ($N_{00}$).
\\

$$
A(t_{+-}-t_{00})=(N_{+-}-N_{00})/(N_{+-}+N_{00}),
$$

where $t_{+-}, t_{00}$ are times (or decay lengths) from $\phi$ to
decay point of kaon with neutral or charged pions.
\\
This asymmetry integrated over all $K_L$ decay lengths
(less acceptance gives less accuracy) is related as
A=$3\cdot Re(\epsilon ' /\epsilon)$ with direct CP violation parameter.

 The evaluation of this asymmetry in the interference region
$(t_{+-}-t_{00}=1-5~ \tau_S$)
gives an information about imaginary part of $\epsilon ' /\epsilon$ and
CPT conservation.

As it was shown in \cite{est90} with the $10^{11}$ produced $\phi$'s and
reasonable detector acceptance (20\% of $K_L$ decay length, c$\tau_L$=15.49 m
and $\beta=0.22$ in case of $e^+e^-\rightarrow\phi$) the
$\epsilon ' /\epsilon$ value can be measured with about $10^{-4}$
accuracy. DAFNE claimes to have 50\% acceptance for $K_L$ decays with a
4 m diameter of drift chamber.

If photon detector can reconstruct $\pi^0\pi^0$ vertex with accuracy
better $\tau_S$ the interferometry test would give accuracy in CPT test
parameter $\Delta\Phi = \Phi_{+-} - \Phi_{00}$ about 0.1 degree
with a present limit about 1 degree.

By using $K_L$ decay or nuclear interaction in the forward system as a
tag $K_S$ rare decays can be studied, including first observation
of CP violated $K_S\rightarrow\pi^0\pi^0\pi^0$ and
$K_S\rightarrow\pi^+\pi^-\pi^0$
modes, which are predicted at the level of $2\times10^{-9}$.

The electroproduction of $\phi$ at CEBAF also can be a source of
correlated $K_S K_L$ pairs and below some preliminary analysis of
posibility to perform similar experimets is presented.
%
\section{Photon Flux}
%
For estimation the total number of produced $\phi$'s was chosen
$N_{\phi}=10^{11}$.
For a year experimental time $10^7$ s the corresponding $\phi$ production rate
should be $10^4$/s. This rate is equivalent to $3\times10^{33}$ luminosity
of $e^+ e^-$ collider which is a goal for $\phi$-factories.

As an example 2.5 cm of Be taget was chosen (7\% rad.length, 4.6 $g/cm^2$) the
same as was using in RadPhi experiment at CEBAF.

The total hadron production cross section for 4-6 GeV photons is 150
$\mu$b/nucleon and for $\phi$ production it is 0.5 $\mu$b/nucleon.

All together give a flux $7\cdot10^{9}$ photons/s for a $\phi$ rate
of $10^4$/s.

To be able  to reconstruct decay length in terms of life time units with
accuracy better than one $\tau_S$ and for constrained purpose, about 2\%
uncertainty in photon energy is required. Existing tagging system is not
capable to work with this flux but Pestov  counters with 25 ps resolution
could help.

 For that value of photon flux and desired photon energy spread the
coherent bremsstrahlung system, reported by Richard Jones (UConn)
at Bloomington workshop can be used. With 8 GeV initial electrons
it can produce 6 GeV photons with about 2\% energy spread with
intensity about $3\times10^8$ (plus about $2\times10^8$ of 5 and 4 GeV)
For CPT study it should be 20 times more intensive photon beam.
\\

Questions: Is $10^{10}$ flux achievable with tagged photons by 25 ps Pestov
           counters?
           Or by coherent bremsstrahlung system? With higher electron
           energy (16-20 GeV) may be it is posible to get this rate
	for 4-5 GeV photons.
           What is lifetime of the diamond crystal at that intensity?
           What is the physical limit of intensity?
%
\section{$K_S K_L$ 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 \cite{est90}, 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
$\phi\rightarrow\eta '\gamma$.
%
\section{Target and Recoil System}
%
The recoil system should measure the proton momentum and its output
angle with sufficient accuracy
to predict $\phi$ total energy and momentum direction
to be used as a constraint in $K_S K_L$ reconstruction. This determination
should be better than the overall detector resolution to be effectively
used and should be an order of few percent.

 Two obvious disadvantages of Be taget are: Fermi motion
of nuclei in the Be atom what leads to about 200 MeV additional energy
spread of secondary particles; and recoil proton should go through
condense Be matiarial to be detected in the recoil system. These
DE/DX losses can be minimized by making cylindrical target with small
diameter.

As an alternative to Be target liquid hydrogen can be used. With density
of 0.07 $g/cm^3$ the 70 cm length of $LH_2$ is needed for the same $\phi$ rate
(8\% rad.length).
The transverse dimention can be made relatively smaller, than for
Be taget and no effect from Fermi motion is expected.
%
\section{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.
%
\section{Detector Requirements}
%
Some detector features were discussed at Bloomington Workshop July 14-16,
1997 and were summarized in A. Dzierba letter to participants.
 It was agreed, that detector should be designed employing state-of-art
detector technology. I would suggest to consider 4$\pi$ detector with
equivalent systems to be able to perform complete analysis for all
particles in backward and forward directions
(momentum, energy, angular resolution, particle
ID ...). As it is seen from above, CP,CPT study gives good example about
quality of the detector. It should include:

- good tracking in all directions with momentum measurement to
reconstruct kaon mass and predict the direction and momentum
of another kaon, decaying into photons.

- good segmented 4$\pi$ calorimeter to reconstruct effective kaon mass and
remove background from $K_L \rightarrow\pi^0\pi^0\pi^0$ decay. It should be
able to reconstruct decay point with accuracy better than one $\tau_S$.

- good particle ID. For CP study the main background decay into two
charged pions is $K_L \rightarrow\pi\mu\nu_{\mu}$ decay, when neutrino is soft
and muon can be selected as pion. Boost can give some advantage
compare to colliding beams experiments, when pions and muons are soft and
muon range system cannot be used.

- good timing

Beam line should prevent detector from direct exposition of huge initial flux
of electrons and photons.

The target and recoil proton region should have about 1.5m length surrounded by
cylindrical drift chamber and cylindrical calorimeter covering polar angles
from about 20 to 180 degrees with no holes. This recoil region should be
instrumented with all above systems. Good example with similar dementions
and resolutions is CMD-2 detector. CsI crystals (pure, with good timing)
can be used. (After producing about 10 tons of crystals for KEK, Novosibirsk
can do another similar job for TJNAL)
Recoil proton has 200-700 MeV/c
momentum and also will be clearly seen in the same detector.

But for the trigger one should use fast timing (with DE/DX recognition).
Full hadronic rate is expected at the level of $10^6$ and trigger system
should reduce this rate to about $10^3$ or so to be able to record data.
So fast (scintillators?) counters should be set before DC with amplitude
analysis for DE/DX of protons. (May be after DC? Or crystals are fast enough?)

The forward going system should cover $\pm$20(?) degrees with uniform
acceptance.
One dipole magnet will not give this uniformity, but two in perpendicular
direction could do. Torroidal magnetic spectrometer can also be considered.
By detecting charged particle in forward direction, it should be posibility
to reconstruct decay point in the decay region with accuracy about few cm.

Good segmented calorimeter with excelent spatial resolution is required.
With four detected photons from two neutral pions one should be
able to reconstruct kaon decay point with about 10 cm accuracy or better.
It may be crystal calorimeter or liquid Krypton as in CERN NA48 or
in KEDR detector in Novosibirsk.

For CP study it is not nesessery to select kaons, so Cerenkov counters
are not needed, but muon range system should be used. But Cerenkov
counters will be usefull for identifying charged kaons from other decays.
About 50\% of $\phi$ decays give $K^+ K^-$ pairs and rare decays and
interactions of tagged charged kaons can be studied. CP-violation
in asymmetry in $K^{\pm}\rightarrow\pi^{\pm}\pi^+\pi^-$ rates can be searched.

 The trigger rate should be an order of 1 MHz and with sofisticated
trigger processors the rate should be reduced to about 1 kHz to be able to
record to tapes only interesting events. (Remember we expect
$10^4 \phi$/s.)
%
\section{Conclusion}
%
The continuous electron beam at Jefferson Laboratory can provide
photon beam with necessary intensity for production of $10^4 \phi$/s.
This rate is the same as the goal intensity of $\phi$-factories, which
are under construction in Frascati and Novosibirsk.
The very exiting experiments for CP-CPT study can be performed with
this number of $\phi$-mesons with different experimental approach to
systematic errors.

 Detector, designed for CP-CPT study automaticaly becomes a general
purpose detector with excellent resolutions, particle identification and
sophisticated triggers.

The photon and secondary particles rate proposed for CP-CPT study is not
extremely high. For example LHC-B experiment at CERN plans to work with
much higher rate.

The CP-CPT measurements should be consider as posible program for
a new generation of the detectors in Jefferson Laboratory.
%
\begin{thebibliography}{99}

\bibitem{est90}{ S. Eidelman, E. Solodov, and J. Thompson,
        Nuclear Physics B (Proceedings Supplement) {\bf 24A} (1991) 174.}

\end{thebibliography}
%
\end{document}
