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\title{Recent results in hyperon physics from the NA48 and KTeV experiments}
\author{C. Lazzeroni\address{Cavendish Laboratory, University of Cambridge, \\
JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom}\thanks{On behalf of the NA48 and KTeV Collaborations}
}
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\begin{document}
\begin{abstract}
Recent results from the NA48 and KTeV experiments
on neutral hyperon decays are presented.
%\vspace{1pc}
\end{abstract}
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\maketitle
\section{INTRODUCTION}
The NA48 experiment was performed
at the CERN SPS accelerator and used a 400 GeV/c proton beam impinging
on a Be target to produce a neutral beam \cite{na48}.
In 2002, the beam line was modified to increase the $K_S$ and neutral hyperon
intensity while the $K_L$ line was blocked. The target position and
the production angle (-4.2 mrad) were chosen in such a way
that the beam axis passed through
the center of the electromagnetic calorimeter \cite{na481}.
In order to minimize the interaction of the neutral beam with air,
the final collimator was followed by a 90 m long evacuated tank terminated
by a 0.3\% $X_0$ thick kevlar window.
The NA48 detector \cite{na48} was located downstream of this region
in order to collect the products of the particles decaying in the volume
contained by the tank. For a detailed description of the detector and the
trigger, see \cite{na481}. On average, about $1.4 \times 10^4$ $\Xi^0$
per spill, with energy between 70 and 220 GeV, decayed in the
fiducial volume (vertex position bewteen 5 m and 50 m from the target).
In this fiducial volume large numbers of
$\Xi^0 \rightarrow \Lambda \pi^0$ and
$\overline{\Xi^0} \rightarrow \bar{\Lambda} \pi^0$ were recorded:
$N(\Xi^0) = (2.422 \pm 0.003_{stat} \pm 0.018_{syst})\cdot 10^9$,
$N(\overline{\Xi^0}) = (2.254 \pm 0.012_{stat} \pm 0.017_{syst})\cdot 10^8$
and mainly used for normalizating
the various branching ratio measurements.
The accumulated statistics allow high precision
studies of $K_S$ and hyperons.
The KTeV experiment took place at the Tetravon accelerator. The data
analysed here were taken in 1999 during the E799-II configuration
of KTeV \cite{muktev}. An intense 800 GeV/c proton beam was directed onto
a BeO target. After a system of collimators, converters and dipoles,
the surviving neutral beams entered a 65 m long vacuum tank, that
defined the decay region, which began 94 m from the target.
The KTeV detector was located downstream of this region;
for a detailed description of the detector and the
trigger, see \cite{muktev}.
About $3\times 10^8$ $\Xi^0$ decayed in the decay region,
with momentum peaked at 290 GeV/c. The sweeping magnets in the beamline
were designed and operated so that the integrated magnetic field delivered
$\Xi^0$ hyperons polarised (with about 10\% polarization) in the positive
or negative vertical direction. The magnetic field was reversed
regularly so that the net polarization was zero for the data discussed here.
\section{$\Xi^0$ BETA DECAYS}
%\subsection{$\Xi^0 \rightarrow \Sigma e \nu$}
The study of hadron beta decays gives important information on the interplay
between the weak interaction and hadron structure,
determined by the strong interaction.
In this context the $\Xi^{0}$ beta decay allows testing both of
SU(3) symmetry, via its strong analogy with the well-known neutron beta decay,
and of the quark mixing model, via extraction of $V_{us}$
(the sine of the Cabibbo angle).
NA48 collected a sample of 6316
$\Xi^{0}\rightarrow \Sigma^{+} e^{-} \bar{\nu}_{e}$ events
(with the $\Sigma^{+}$ decaying into $p \pi^{0}$)
with energy between 70 and 220
GeV and decay vertex between 5 m and 50 m from the final collimator.
%(see Fig. \ref{ena48}).
With a background of about 2\%, a
value for the branching ratio has been extracted:
$BR(\Xi^{0}\rightarrow \Sigma^{+} e^{-} \bar{\nu}_{e})=
(2.51 \pm 0.03_{stat} \pm 0.09_{syst} ) 10^{-4}$,
where the systematic error is dominated by the trigger
efficiency determination,
the geometrical acceptance and the form factors.
This value is in agreement with the KTeV measurement, based on
625 events: $BR_{KTeV} (\Xi^{0}\rightarrow \Sigma^{+} e^{-} \bar{\nu}_{e})=
(2.54 \pm 0.11_{stat} \pm 0.16_{syst} ) 10^{-4}$\cite{ektev}.
Including the dependence of the form factors on the momentum transfer
and the radiative corrections, the value for
$V_{us}$ extracted
from the branching ratio measurement is:
$V_{us}=0.208\pm{0.006} \ {^{+0.030}_{-0.025}}_{g_{1}/f_{1}}$, in
agreement with the Standard Model expection of $0.2274\pm0.0021$\cite{PDG}.
The systematic error is largely dominated by the error on the ratio
of the form
factors $g_{1}/f_{1}=1.267\pm0.035$ taken from PDG.
Alternatively, a value for $g_{1}/f_{1}$ can be extracted from the
measured branching ratio, using $V_{us} = 0.2257$ \cite{PDG}, giving:
$g_{1}/f_{1}=1.20 \pm 0.04_{br} \pm 0.03_{ext}$,
where the last uncertainty includes contributions from $V_{us}$,
$\Xi^0$ lifetime and form factor $f_2 /f_1$.
The agreement with the prediction for exact SU(3) symmetry
favours SU(3) breaking models that leave $g_1 / f_1$ unchanged.
A sample of 102 $\Xi^0 \rightarrow \Sigma^+ \mu^-
\bar{\nu_{\mu}}$ events was selected,
%The selection criteria for $\Xi^0 \rightarrow \Sigma^+ \mu^-
%\bar{\nu_{\mu}}$ decays was kept as similar as possible
%to $\Xi^0 \rightarrow \Sigma e \nu$,
%except for the requirement applied on the muon
%detector. A sample of 102 events was selected,
with a background of $32 \pm 3.0$ (see
Fig. \ref{muna48}).
Using the electron decay as normalization channel,
the measurement of the muon
branching ratio was extracted:
$BR(\Xi^{0}\rightarrow \Sigma^{+} \mu^{-} \bar{\nu}_{\mu})= (2.2 \pm 0.3_{stat}
\pm 0.2_{syst} ) 10^{-6}$.
This is the largest sample of semi-muonic decays so far collected.
%\begin{figure}[htbp]
%%\includegraphics[width=12cm, height=12cm,scale=1.0,angle=90]{finalmu_fig2.eps}
%\includegraphics[scale=0.4]{sigma_mass.eps}
%\vspace{-0.5cm}
% \caption{Distribution of $p\pi^0$ invariant mass for selected events with negative electron.}
% \label{ena48}
%\end{figure}
\begin{figure}[htbp]
\includegraphics[scale=0.27]{finalmu_fig2.eps}
\vspace{-0.5cm}
\caption{Distribution of $p\pi^0$ invariant mass for selected events with negative muon in NA48. A clear signal for $\Sigma^+$ is visible.}
\label{muna48}
\end{figure}
KTeV collected a sample of 9
$\Xi^{0}\rightarrow \Sigma^{+} \mu^{-} \bar{\nu}_{\mu}$ events
(with the $\Sigma^{+}$ decaying into $p \pi^{0}$), and a sample
of 1139 $\Xi^{0}\rightarrow \Sigma^{+} e^{-} \bar{\nu}_{e}$
for normalization purpose, requiring 2 charged particles (one
being an electron or a muon) and 2 neutral clusters.
The distribution of events that survived the selection is shown in a plot of
$p_t^2$ (the square of the transverse momentum relatve to the beam) of
the $\Sigma^+ \mu^-$ versus the invariant mass of the $p \pi^0$ system
(see Fig. \ref{muktev}). For details on the selection, see \cite{muktev}.
The box is defined by the Monte Carlo simulation to accept 90\% of the
signal events. There are 9 signal events inside the box, clustered
around 1.189 GeV/c$^2$, and 1 event outside.
%In all background modes the two charged particle originate from a single
%vertex, so a cut at $P_T > 0.018$ GeV/c$^2$ was applied, where $P_T$
%is the square of the total transverse momentum of the 2 charged particles
%relative to a line from the target to the vertex.
The background, evaluated using Monte Carlo simulation and data with
wrong sign assignements for tracks, was found to be negligible
inside the signal box; 54 background events were subtracted from the
normalization channel. Using these samples, the ratio of the decay rates
is measured to be
$\Gamma( \Xi^{0}\rightarrow \Sigma^{+} \mu^{-} \bar{\nu}_{\mu}) /
\Gamma ( \Xi^{0}\rightarrow \Sigma^{+} e^{-} \bar{\nu}_{e} ) = (1.8^{+0.7}_{-0.5} (stat) \pm 0.2 (syst)) \times 10^{-2}$.
The systematic uncertainties receive contributions from the statistics in
the normalization mode, the ratio of acceptances, and the muon
identification efficiency. Using the value $Br(\Xi^{0}\rightarrow \Sigma^{+} e^{-} \bar{\nu}_{e})=(2.7\pm 0.4) \times 10^{-4}$ \cite{pdg04},
the branching ratio for
the muon semileptonic decay is found to be:
$Br( \Xi^{0}\rightarrow \Sigma^{+} \mu^{-} \bar{\nu}_{\mu})= (4.7^{+2.0}_{-1.4}
(stat) \pm 0.8 (syst) ) \times 10^{-6}$,
where the systematic error also includes the contribution
from the uncertainty of the electron beta decay.
\begin{figure}[htbp]
\includegraphics[scale=0.32]{ktev_fig02.eps}
\vspace{-0.5cm}
\caption{Distribution of $p\pi^0$ invariant mass for selected events with negative muon in KTeV.}
\label{muktev}
\end{figure}
\section{ASYMMETRY IN RADIATIVE DECAYS}
The weak radiative hyperon decays are quite accessible experimentaly,
in terms of the branching ratio and the asymmetry of the baryon emission
with respect to the initial spin. However, despite their simplicity, there
are theoretical difficulties in explaining these decays, mainly because
predictions using the quark model do not match predictions from an analysis
at the hadron level\cite{review}.
Hara theorem proved that the asymmetry is zero in the SU(3) limit for
$\Xi^-$ and $\Sigma^+$ decays, assuming CP invariance and
U-spin symmetry\cite{hara}.
An estimate, based on single quark $s \rightarrow d$ transitions and that
takes into account SU(3) breaking, predicts a modest positive
asymmetry\cite{vasanti}.
However, the only asymmetry been accurately measured so far
is $-0.76 \pm 0.08$
for $\Sigma^+ \rightarrow p \gamma$\cite{foucher}.
To constrain the theoretical models, it is important to measure accurately
the parameters of weak radiative decays for all hyperons.
In the decay $\Xi^0 \rightarrow \Lambda \pi^0$,
the proton angular distribution with respect to the $\Xi^0$ direction
in the $\Lambda$ rest frame can be written as $dN / d cos \Theta_{\Lambda} =
N_0 (1+\alpha_{\Xi}
\alpha_{\Lambda} cos \Theta_{\Lambda})$, where $\alpha_{\Xi}$ is the
weak decay asymmetry and $\alpha_{\Lambda}=0.642$ is the $\Lambda$
weak decay asymmetry. A similar formula is valid for $\Xi^0 \rightarrow
\Lambda \gamma$, where the sign minus can be understood in terms of
fundamental angular momentum considerations\cite{PDG}:
$dN / d cos \Theta_{\Lambda} =
N_0 (1- \alpha_{\Xi}
\alpha_{\Lambda} cos \Theta_{\Lambda})$.
This can be extended to the $\Xi^0 \rightarrow \Sigma^0 \gamma$ decay,
considering the angles $\Theta_{\Xi \Lambda}$ of the $\Lambda$ direction
with respect to the $\Xi$ direction in the $\Sigma$ rest frame, and
$\Theta_{\Sigma p}$ of the proton direction
with respect to the $\Sigma$ direction in the $\Lambda$ rest frame:
$d^2 N / d cos \Theta_{\Xi \Lambda} d cos \Theta_{\Sigma p} =
N_0 (1 + \alpha_{\Xi}
\alpha_{\Lambda} cos \Theta_{\Xi \Lambda} cos \Theta_{\Sigma p} ) =
N_0 (1+ \alpha_{\Xi} \alpha_{\Lambda} x $.
From the 2002 data, NA48 selected $\sim 4\times 10^6$ $\Xi^0 \rightarrow
\Lambda \pi^0$, $\sim 52600$ $\Xi^0 \rightarrow \Lambda \gamma$ and
$\sim 15600$ $\Xi^0 \rightarrow \Sigma^0 \gamma$ events.
The background is respectively 0.1\% (mainly from $\Xi^0 \rightarrow
\Sigma^0 \gamma$), 0.7\% (mainly from $\Xi^0 \rightarrow \Lambda \pi^0$,
fake $\Lambda$s
and fragments of 2 events overlapping in time), and 3\%
(mainly from $\Xi^0 \rightarrow \Lambda \pi^0$).
From these samples, measurements of the decay asymmetries were obtained
from the respective distributions of $cos \Theta$ (or $x$); the
obtained values are shown in Table\ref{asym}, together with
the previous measurements to which they all agree. In all cases,
the NA48 measurements represent a significant improvement in precision.
The major sources of systematic uncertainties come from the acceptance
correction and the trigger efficiency.
\begin{table}[htb]
\caption{Preliminary NA48 measurements of asymmetries for weak $\Xi^0$ decays,
compared to the previous ones from literature.}
\label{asym}
%\newcommand{\m}{\hphantom{$-$}}
%\newcommand{\cc}[1]{\multicolumn{1}{c}{#1}}
%\renewcommand{\tabcolsep}{2pc} % enlarge column spacing
%\renewcommand{\arraystretch}{1.2} % enlarge line spacing
\begin{tabular}{@{}ll}
\hline
$\alpha_{\Xi} \alpha_{\Lambda} (\Lambda \pi^0)$ & $-0.282 \pm 0.003_{stat}
\pm 0.028_{syst}$\\
PDG & $-0.264 \pm 0.013$ \\
\hline
$\alpha_{\Xi} \alpha_{\Lambda} (\Lambda \gamma)$ & $-0.439 \pm 0.013_{stat}
\pm 0.038_{syst}$ \\
NA48(1999)\cite{oldasym} & $-0.50 \pm 0.13$ \\
\hline
$\alpha_{\Xi} \alpha_{\Lambda} (\Sigma \gamma)$ & $-0.438 \pm 0.020_{stat}
\pm 0.041_{syst}$ \\
KTeV\cite{ktevasym} & $-0.40 \pm 0.06$\\
\hline
\end{tabular}
\end{table}
\section{$\Xi^0$ LIFETIME}
Several experiments in the 1960s and 1970s performed measurements
of the $\Xi^0$
lifetime, yielding a world average, based on an integrated data
sample of less than 8000
events, of $\Gamma(\Xi^0) = (2.90 \pm 0.09) \times 10^{-10} s $ \cite{PDG}.
In the last 30 years or so, no new measurements have been published.
The $\Xi^0$ lifetime is an important input to other
$\Xi^0$-related parameters,
like $V_{us}$ from hyperon beta decays, and
is also theoretically interesting.
When assuming the full validity of
the $\Delta I = 1/2$
rule in hadronic weak decays, the decay matrix elements of
the neutral and charged
$\Xi \rightarrow \Lambda \pi$ should simply be connected by
$M(\Xi^0 \rightarrow \Lambda
\pi^0) = M(\Xi^- \rightarrow \Lambda \pi^-) / \sqrt{2}$ because of
isospin arguments.
Taking into account the slightly different masses of the
particles involved, as well as
the rare decays to other final states\cite{PDG}, the lifetimes
should follow the relation
$\Gamma(\Xi^0) / \Gamma(\Xi^-) \approx 2.031$. The comparison
of measured lifetimes
is a good test for $\Delta I = 1/2$ violating effects.
Using the previous
measured lifetimes \cite{PDG},
%for $\gamma{\Xi^-) = (1.639 \pm 0.015) \times 10^{-10} \ s$\cite{PDG},
the experimental value of the ratio is $1.77 \pm 0.06$.
\begin{figure}[htbp]
\includegraphics[scale=0.35]{C_etau.eps}
\vspace{-0.5cm}
\caption{Distribution
of $\Xi^0$ energy versus $\Xi^0$ lifetime in units of PDG lifetime.}
\label{life}
\end{figure}
From a sample of $\sim 258000$ $\Xi^0 \rightarrow \Lambda \pi^0$ events
collected in
NA48 with a minimum bias trigger, the $\Xi^0$ lifetime has been measured
for decays that occur outside the final collimator. The distribution
of $\Xi^0$ energy versus $\Xi^0$ lifetime in units of PDG lifetime
is shown in Fig. \ref{life} for collected events; the contour indicates
the events used for the lifetime measurements. Distributions of lifetime
for data and Monte Carlo events (simulated with the PDG lifetime) were
produced and their ratio was fitted in 10 energy bins of 10 GeV each,
from 75 GeV to 175 GeV. The distribution of the ratio, summed over all
energy bins, is shown in Fig. \ref{fit}.
The distribution of the fit results, expressed as relative
deviations from the PDG measurement, is flat
in bins of $\Xi^0$ energy.
The preliminary value obtained is $\tau (\Xi^0) / \tau_{PDG} =
1.0626 \pm 0.0044_{stat} \pm 0.0043_{syst}$ which corresponds to
a lifetime of $\tau (\Xi^0) = (3.082 \pm 0.013_{stat} \pm 0.012_{syst})
\times 10^{-10} \ s$.
Using the measured value for $\Gamma(\Xi^-) = (1.639 \pm 0.015) \times 10^{-10} \ s$\cite{PDG}, the ratio of the neutral over charged lifetime is found
to be $1.880 \pm 0.020$.
\begin{figure}[htbp]
\includegraphics[scale=0.35]{C_fit_Sum.eps}
\vspace{-0.5cm}
\caption{Ratio of lifetimes for data and Monte Carlo events
(simulated with the PDG lifetime)
as a function of $\Xi^0$ lifetime.}
\label{fit}
\end{figure}
\section{CONCLUSIONS}
Recent results from the NA48 and KTeV experiments
on neutral hyperon decays have been presented.
Preliminary measurements have been summarised for the $\Xi^0$ muon-beta
decay for both experiments; preliminary values from NA48 for the
$\Xi^0$ lifetime and for weak decay
asymmetries in various decay channels have been shown.
\begin{thebibliography}{9}
\bibitem{na48} J.~R.~Batley et al., Phys.Lett. B 544 (2002) 97.
\bibitem{na481} NA48/1 Status Report SPSC/M670, CERN/SPSC 2001-029 (2001).
\bibitem{muktev} A.~Alavi-Harati, hep-ex/0504055, 2005.
\bibitem{ektev} A.~Alavi-Harati, hep-ex/0105016, 2001.
\bibitem{PDG} Particle Data Group, Journal of Physics G 33 (2006).
\bibitem{pdg04} Review of Particle Physics, Phys. Lett. B 592 (2004).
\bibitem{review} J.~Lach, P.~Zenczykowski, Int. Jour. Mod. Phys. A 10 (1995).\\
P.~Zenczykowski, Phys. Rev. D 62 (2000).
P.~Zenczykowski, Proceedings of BEACH 2006 Conference, Lancaster, UK (2006).
\bibitem{oldasym} J.~R.~Batley et al., Phys.Lett. B 584 (2004).
\bibitem{ktevasym} A.~Alavi-Harati, Phys. Rev. Lett. 86 (2001).
\bibitem{hara} Y.~Hara, Phys. Rev. Lett. 12 (1964).
\bibitem{vasanti} N.~vasanti, Phys. Rev. D 13 (1976).
\bibitem{foucher} M.~Foucher et al., Phys. Rev. Lett. 68 (1992).
\end{thebibliography}
\end{document}