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\begin{document}

\title{ Rare Kaon Decays From NA48 }

\author{ Sven A. Schmidt }

\address{ Institut f\"ur Physik, Johannes Gutenberg-Universit\"at Mainz, \\
	55099 Mainz, Germany, sven.schmidt@cern.ch }


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\maketitle

\abstracts{ In an analysis of 1999 and part of 1998 NA48 data 1397
$K_L \to \pi^0 \gamma \gamma$ candidates above a background of
approximately 30 events have been found. From this a preliminary
branching ratio of BR($K_L \to \pi^0 \gamma \gamma, a_v = -0.45) =
(1.51\pm0.05_{\mbox{stat}}\pm0.20_{\mbox{sys}})\cdot10^{-6}$ has been
determined. A clear signal for a diphoton mass $m_{\gamma\gamma} <
240~\mbox{MeV/c}^2$ has been observed. From a special high intensity
$K_S$ run a signal of 149 $K_S \to \gamma \gamma$ events above
background has been found, yielding a branching ratio of
BR($K_S \to \gamma \gamma) =
(2.6\pm0.4_{\mbox{stat}}\pm0.2_{\mbox{sys}})\cdot10^{-6}$. }


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\section{ The Decay $K_L\to \pi^0 \gamma\gamma$ }

The decay $K_L\to \pi^0 \gamma\gamma$ is of considerable theoretical
interest. In the framework of chiral pertubation theory a calculation
to the order $p^4$ predicts\cite{Eck87} a branching ratio of
approximately $0.68\cdot 10^{-6}$. While the first measurements agreed
with the theoretical prediction with respect to the invariant diphoton
mass spectrum, significantly higher branching ratios were observed by
NA31 $((1.7 \pm 0.3 ) \cdot 10^{-6})$\cite{Bar90}$^,$\cite{Bar92} and
E731 $((1.86 \pm 0.6 ) \cdot 10^{-6})$\cite{Pap91}.

Consideration of the next to leading order $p^6$ and vector meson
dominance contributions improve the agreement between experiment and
theory\cite{Coh93}$^,$\cite{dAm97}.
In case of non-vanishing vector meson exchange the invariant diphoton
mass spectrum is significantly enhanced for in the lower mass regions
(Fig. \ref{fig:pi0gg}a).

\begin{figure}[htb]
	\centering
	\epsfxsize=\textwidth
	\epsfbox{schmidt.pi0gg_result2.eps}
	\caption{ 
	a)~Theoretical predictions for the invariant diphoton mass for
	$K_L \to \pi^0 \gamma \gamma$.
	b)~Invariant diphoton mass for $K_L \to \pi^0 \gamma \gamma$ 
	candidates.
	c)~Signal for lower diphoton mass region
	($m_{\gamma\gamma} < 240$~MeV/c$^2$).
	\label{fig:pi0gg}
	}
\end{figure}

The $\pi^0 \gamma \gamma$ channel and its normalization channel $K_L
\to \pi^0\pi^0$ were both triggered by the standard
$\epsilon'/\epsilon$ neutral trigger. Significant background channels
are $K_L \to \pi^0\pi^0$ and $K_L \to \pi^0\pi^0\pi^0$ with lost
and/or overlapping clusters in the electromagnetic
calorimeter. Background from $K_L \to \pi^0\pi^0$ is suppressed by
rejecting events with a $\chi^2$ of less than 100 for a $2\pi^0$
hypothesis. $3\pi^0$ events with lost/overlapping photons are rejected
by cuts against misreconstructed $z$-vertices, combinatorial kaon/pion
vertex differences, and cluster widths.

From part of 1998 and the full sample of 1999 NA48\cite{Fan99} data
1397 candidates have been found above a very low background of about
30 events. To determine the acceptance, a Monte Carlo simulation with
an effective vector coupling of $a_v = -0.45$ has been used to obtain
the preliminary branching ratio of BR($K_L \to \pi^0 \gamma \gamma,
a_v = -0.45) =
(1.51\pm0.05_{\mbox{stat}}\pm0.20_{\mbox{sys}})\cdot10^{-6}$. The
signal in the invariant mass region below 240~MeV/c$^2$ gives clear
evidence for a contribution beyond the order of $p^4$ (Figure
\ref{fig:pi0gg}c).

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\section{ The Decay $K_S \to \gamma\gamma$ }

Similar to $K_L \to \pi^0 \gamma \gamma$, the decay
$K_S\to\gamma\gamma$ is important for understanding and testing chiral
pertubation theory. A previous measurement by NA31 has found a
branching ratio of $(2.4\pm 0.9)\cdot 10^{-6}\,\,$\cite{Bar95}. Theory
predicts a branching ratio of $2.25\cdot 10^{-6}$ with an error of
less than 10\%$\,\,$\cite{dAm86}.

From a dedicated high intensity $K_S$ run in 1999 a new measurement of
the branching ratio with approximately four times the statistics of
the NA31 sample is possible. The analysis addresses background from
$K_L\to\gamma\gamma$, $K_S\to\pi^0\pi^0$, and $\Lambda\to
n\pi^0$. After background subtraction a signal of 149 $K_S \to
\gamma\gamma$ candidates remains, giving a branching ratio of BR($K_S
\to \gamma \gamma) =
(2.6\pm0.4_{\mbox{stat}}\pm0.2_{\mbox{sys}})\cdot10^{-6}$$\,\,$\cite{Lai00}.


\begin{thebibliography}{99}

\bibitem{Eck87} G.~Ecker, A.~Pich, E.~de Rafael, 
	\Journal{\PLB}{189}{363}{1987}.
\bibitem{Bar90} G.~Barr {\it et al}, \Journal{\PLB}{242}{523}{1990}.
\bibitem{Bar92} G.~Barr {\it et al}, \Journal{\PLB}{284}{440}{1992}.
\bibitem{Pap91} V.~Papadimitriou {\it et al}, \Journal{\PRD}{44}{573}{1991}.
\bibitem{Coh93} A.~Cohen, G.~Ecker, A.~Pich, \Journal{\PLB}{304}{347}{1993}.
\bibitem{dAm97} G.~D'Ambrosio, J.~Portoles, \Journal{\NPB}{492}{417}{1997}.
\bibitem{Fan99} V.~Fanti {\it et al}, \Journal{\PLB}{465}{335}{1999}.

\bibitem{Bar95} G.~Barr {\it et al}, \Journal{PLB}{351}{579}{1995}.
\bibitem{dAm86} G.~D'Ambrosio, D.~Espriu, \Journal{PLB}{175}{237}{1986}.
\bibitem{Lai00} A.~Lai {\it et al}, submitted to {\it Phys. Lett.} B,
preprint CERN-EP-2000-122.

\end{thebibliography}

\end{document}

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