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\def\st{\scriptstyle}
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\def\mco{\multicolumn}
\def\epp{\epsilon^{\prime}}
\def\vep{\varepsilon}
\def\ra{\rightarrow}
\def\ppg{\pi^+\pi^-\gamma}
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\newcommand{\eoe}{\mbox{${\em Re}(\epsilon^{~\prime}/\epsilon)$}~}
\newcommand{\epsi}{\mbox{$\epsilon$}~}
\newcommand{\epsip}{\mbox{$\epsilon^{~\prime}$}~}
\newcommand{\kkbar}{\rm{K}^{\scriptstyle 0}{\overline{K}^{_{\scriptstyle 0}}}}

\newcommand{\kzbar}{\rm{\overline{K}^{_{\scriptstyle 0}}}}

\newcommand{\kz} {\rm K^{\scriptstyle 0}}
\newcommand{\kl} {\rm K_{\scriptstyle L}}
\newcommand{\ks} {\rm K_{\scriptstyle S}}
\newcommand{\pz}{{\rm\pi^{\scriptstyle 0}}}
\hyphenation{ex-ploi-ting}
\hyphenation{va-ria-tions}
\hyphenation{ac-compli-shed}

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\begin{document}

\title{UPDATE ON THE \eoe MEASUREMENT FROM NA48}

\author{Patrizia CENCI}

\address{Istituto Nazionale di Fisica Nucleare, Perugia, Italy.}

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\maketitle\abstracts{ The NA48 experiment at CERN has been designed 
to reach an ultimate error of $2\times10^{-4}$ on the measurement 
of the direct CP violation parameter \eoe . \\
The most recent preliminary result from NA48 is
$\eoe = (12.2 \ \pm \ 4.9) \times 10^{-4}$,
based on the analysis of the data collected in 1998.
}

\section{The NA48 experimental technique}
The measurement of the direct CP violation parameter 
\eoe is accomplished in the NA48 experiment
by counting the number of events in each of the four decay modes 
$K_L,K_S \rightarrow \pi^0\pi^0,\pi^+\pi^-$
and computing the double ratio $R$:
\begin{displaymath}
R = \frac{ \Gamma(K_L \ra \pi^0\pi^0) }{ \Gamma(K_S \ra \pi^0\pi^0) } 
\cdot \frac{ \Gamma(K_S \ra \pi^+ \pi^-) }{ \Gamma(K_L \ra \pi^+ \pi^-) }
\simeq 1 - 6 \, \eoe
\end{displaymath}

A few million of CP--violating $K_L \ra \pi^0 \pi^0$ decays, 
the rarest among the four relevant processes, 
are collected to achieve the ultimate precision
of $2 \times 10^{-4}$ on the $\eoe$ measurement.

The systematics uncertainty is controlled at high accuracy
by exploiting cancellations of effects which contribute 
symmetrically to the different components of the double ratio $R$.
Detection efficiencies and rate dependent effects due 
to beam intensity variations and accidental activity in the detector
are minimized by collecting the data
simultaneously in the four decay channels.

The $\ks$ and $\kl$ beams are produced concurrently, 
and coincide in space at the position of the detector.
A proton tagger is installed upstream of the $\ks$ target
to distinguish $\ks$ from $\kl$. 
The choice of the production angles makes 
the $\kl$ and $\ks$ momentum spectra similar
in the range 70--170~GeV of accepted kaon energy.
Only those decays occurring in the same fiducial volume
are used to compute $R$.
A counter is installed in the $\ks$ beam line
to define the beginning of the decay region, whose length is
3.5 units of $\ks$ lifetime.
The longitudinal position distributions of the decay vertex 
are made equal for $\kl$ and $\ks$ by applying 
an event--weighting procedure. In this way,
the acceptance correction, due to the large difference
in average decay leghts, is small, 
at the price of a 35$\%$ loss in event statistics. 
The definition of the beginning of the fiducial decay region 
is used to set the neutral energy scale. 
Background effects are reduced by a suitable detector performance.
The $R$ calculation is done in kaon energy bins, 
in order to be insensitive to beam spectra differences.
The corrections finally applied to $R$
are due to several systematics effects: 
$\ks$ and $\kl$ misidentification by proton tagging; 
trigger inefficiency; 
background subtraction; acceptance correction; energy scale; 
accidental activity. Each effect is not larger than a few per mill,
as shown in tab.~\ref{result} .
%
\begin{table}
\centering
\caption{ \it Corrections applied to $R$
and systematics uncertainties (1998 data; units = $10^{-4}$).
}
\vskip 0.1 in
{\small
\begin{tabular}{|l|c|}
\hline
Mistagging probability  & {$~+1 \pm ~8$} \\
Tagging inefficiency  & {$~~- \pm ~3$} \\
Charged trigger  & {$~-1 \pm 11$} \\
Neutral background  & {$~-7 \pm ~2$} \\
Charged background  & {$+19 \pm ~3$} \\
Beam scattering  & {$-10 \pm ~3$} \\
Acceptance & {$+31 \pm ~9$} \\
Neutral scale & {$~~- \pm 10$} \\
Charged vertex  & {$~+2 \pm ~2$} \\
Accidental activity & {$~+2 \pm 12$} \\
\hline
Total correction and systematics on $R$ & $ +37 \pm 24$ \\
\hline
\end{tabular}
}
\label{result}
\end{table}
%
\section{The \eoe analysis in NA48}
%
NA48 has been taking physics data for the \eoe measurement 
since 1997. The analysis of the data collected in 1997,
corresponding to $0.49 \times 10^{6}$ reconstructed
$K_L \rightarrow \pi^0 \pi^0$, leads to the published result:
%~\cite{na48}:
\begin{center}
$ \eoe = (18.5 \pm 4.5(stat) \pm 5.8(syst)) \times 10^{-4} = (18.5 \pm 7.3) \times 10^{-4} $.
\end{center}

In the 1998 run, the improvements in charged trigger and data 
aquisition systems allowed to take data at a beam intensity
of $\sim 1.4\ \times\ 10^{12}$ $ppp$ on the $\kl$ target. 
The preliminary result for the duble ratio $R$,
based on $1.14 \times 10^{6}$ reconstructed $K_L \rightarrow \pi^0 \pi^0$, is:
$R = 0.99267 \pm 0.00173(stat.) \pm 0.00238(syst.)$, 
where the first error is the statistical fluctuation in the event 
samples and the second error comes from the uncertainties listed 
in tab.~\ref{result} .
The preliminary result for the direct CP violating parameter \eoe
using 1998 data is: 
\begin{center}
$\eoe = (12.2 \ \pm \ 2.9(stat) \pm 4.0(syst)) \times 10^{-4} = (12.2 \ \pm \ 4.9) \times 10^{-4}$ . 
\end{center}
This value, combined with the pubblished 1997 measurement, 
leads to: 
\begin{center}
$\eoe = (14.0 \pm 4.3) \times 10^{-4}$ .
\end{center}

A highly efficient run took place in 1999, with $\sim 2 \times 10^{6}$
$K_L \rightarrow \pi^0 \pi^0$ reconstructed events. 
The data analysis is well advanced.

The present result on \eoe from NA48 confirms the occurrence of
direct CP violation in the decays of neutral kaons in two pions.
The NA48 data taking for the \eoe physics program will continue
until the year 2001.

\end{document}

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