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\title{Results on $\epsilon'/\epsilon$ and Rare $K_L$ Decays from  KTeV}

\author{Michael Arenton}

\address{Physics Dept., University of Virginia, Charlottesville, VA 22904}

 

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\maketitle

\abstracts{ Results from the KTeV experiment at Fermilab on measurement
of $\epsilon'/\epsilon$ and rare $K_L$ decays are summarized.
}

\section{Introduction}

  This paper summarizes  some of the more recent results on the measurement
of the direct CP violation parameter  $\epsilon'/\epsilon$ and 
rare $K_L$ decays obtained by the KTeV experiment at Fermilab. KTeV
uses a new large acceptance, high resolution and high rate spectrometer to
achieve a highly significant measurement of $\epsilon'/\epsilon$.
 The experimental sensitivity to many rare $K_L$
decay modes was substantially extended
, reaching the necessary levels to observe or place interesting
limits on a number of rare processes and make high statistics measurements of
other modes previously only observed with small event samples.


\section{Measurement of  $\epsilon'/\epsilon$}

 The direct CP violation parameter  $\epsilon'/\epsilon$ is measured from 
 the double ratio of the decay
rates of $K_L$ and $K_S$ into $\pi^+\pi^-$ and $\pi^0\pi^0$ pairs:

$$
  {
     { \Gamma(K_L\to \pi^+\pi^-)/\Gamma(K_S\to \pi^+\pi^-) }
            \over
     { \Gamma(K_L\to \pi^0\pi^0)/\Gamma(K_S\to \pi^0\pi^0) }
  }
  \approx 1 + 6{\rm Re}\left(\epsilon'/\epsilon  \right)
$$

 KTeV has published~ \cite{epe} a measurement based on 20\%
 of the data taken in
the 1996/1997 runs. The signals were extracted with a background level
of about 0.09\% for the $\pi^+\pi^-$ mode and 1.2\% or better for the
$\pi^0\pi^0$ mode.  The resulting samples contained $8.6\times10^5$ and
$1.4\times10^6$ events of the neutral mode in the vacuum and regenerator
beams respectively, and $2.6\times10^6$ and $4.5\times10^6$ in the
charged mode.  A detailed Monte Carlo simulation, which was calibrated
with other high statistics K decay modes, was used to correct for the
different acceptance of $K_L$ and $K_S$ decays.  The final fit for
 $\epsilon'/\epsilon$ was done ``blind'', hiding the result until all
corrections had been evalulated. The result is
$ {\rm Re}\left(\epsilon'/\epsilon  \right)  = 
[28.0 \pm 3.0(stat) \pm
 2.8(syst)] \times 10^{-4}$. 

The additional $5\times$ data sample taken in 1997 is currently being
intensively analysed. Several of the systematic uncertainties appear
to be under better control.  Additionally a further $2\times$ more
data was taken in a run in 1999.

\section{Rare decays}

KTeV has for many rare $K_L$ decay modes made either first measurements,
new measurements with greatly increased statistics, or substantially
more sensitive upper limits on branching fractions. New measurements
have been made of the decays $e^+e^-\gamma\gamma$~\cite{pm_thesis}, $\mu^+\mu^-\gamma\gamma$~\cite{satoshi}
$e^+e^-e^+e^-$, $e^+e^-\mu^+\mu^-$~\cite{eemm}, 
$\pi^0 \rightarrow e^+e^-$,~\cite{edz} and $\pi^+\pi^-e^+e^-$, among others.
Upper limits have been set on $\pi^0e^+e^-$~\cite{p0ee},
and $\pi^0\mu^+\mu^-$~\cite{p0mm},
 and $\pi^0\nu\overline{\nu}$~\cite{p0nnD}~\cite{p0nngg}.
  A high statistics study of $\mu^+\mu^-\gamma$ has
been performed~\cite{breese_thesis}
, and a very high statistics study of $e^+e^-\gamma$ is
in progress.  
A particularly interesting result is the observation of an indirect CP
violating effect in the mode $\pi^+\pi^-e^+e^-$, where an asymmetry in the
distribution of the angle $\phi$ between the planes defined by the 
$\pi^+\pi^-$ and $e^+e^-$ pairs of $[13.6\pm2.5(stat)\pm1.2(syst)]\%$ was
observed, consistent with theoretical expectations.~\cite{ppee}
This asymmetry arises from interference of inner-bremsstrahlung and direct
emission amplitudes. There is also expected to be a smaller amplitude
cooresponding to the $K_L$ charge radius. Continuing analysis of the angular
distributions of this decay may lead to an interesting measurement of the
 $K_L$  charge radius. Additional data taken in 1999 will increase rare
decay sensitivities by factors of 2 to 2.5 for various modes.

\section*{Acknowledgments}
This work was supported by the U.S. Department of Energy, the National
Science Foundation, and the Ministry of Education and Science of Japan.


\begin{thebibliography}{99}

\bibitem{epe}A. Alavi-Harati {\it et al} \Journal{\PRL}{83}{22}{1999}.

\bibitem{pm_thesis}P. Mikelson, Ph.D. dissertation, University of Colorado, 1999.


\bibitem{satoshi}A. Alavi-Harati \it{et.al.},hep-ex/0001005, Phys.Rev. D. in press.

\bibitem{eemm}A. Lath, talk given at DPF 99, UCLA, Los Angeles, January 1999.

\bibitem{edz}A. Alavi-Harati \it{et.al.}, \Journal{\PRL}{83}{922}{1999}

\bibitem{p0ee}A. Alavi-Harati \it{et.al.}, hep-ex/0009030., submitted to
Phys. Rev. Lett.

\bibitem{p0mm}A. Alavi-Harati \it{et.al.}, \Journal{\PRL}{84}{5279}{2000}

\bibitem{p0nnD}A. Alavi-Harati \it{et.al.}, \Journal{\PRD}{61}{072006}{2000}

\bibitem{p0nngg}J. Adams  \it{et.al.}, \Journal{\PLB}{447}{240}{1999} 

\bibitem{breese_thesis}G.B. Quinn, Ph.D. dissertation, University of Chicago, 2000.

\bibitem{ppee}A. Alavi-Harati \it{et.al.}, \Journal{\PRL}{84}{408}{2000}

\end{thebibliography}

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