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\title{Preliminary $\Xi_{c}^{+}$ Lifetime Measurement from SELEX}
\author{U. Akgun (on behaf of the SELEX collaboration)\address[iowa]{Department of Physics and Astronomy,\\
The University of Iowa, Iowa City, IA 52242-1479, USA}}%
\begin{document}
\begin{abstract}
We report the results of a new $\Xi_{c}^{+}$ lifetime measurement from
hadroproduction data taken by the SELEX (E781) experiment. Fermilab charged
hyperon beam ($\Sigma^{-}$, $\pi^{-}$ and $p$) at 600 GeV is used to produce charm
particles in Cu and diamond targets. This measurement was made using decays into the
$\Xi_{c}^{+} \rightarrow \Xi^{-} \pi^{+} \pi^{+}$ , $\Xi_{c}^{+} \rightarrow p^{+} K^{-} \pi^{+}$,
and $\Xi_{c}^{+} \rightarrow \Sigma^{+} K^{-} \pi^{+}$ modes. We used binned maximum likelihood method and $301\pm31$
events yield a lifetime of $430\pm22\pm9$ fs.
\vspace{1pc}
\end{abstract}
% typeset front matter (including abstract)
\maketitle
\section{Introduction and Event Selection}
In this report we present the results of a new $\Xi_{c}^{+}$ lifetime measurement from
hadroproduction data taken by the SELEX (E781) experiment at Fermilab. SELEX
experiment has excellent particle identification capabilities therefore it is
very efficient for studying charm baryons decays. Fermilab charged hyperon
beam ($\Sigma^{-}$, $\pi^{-}$ and $p$) at 600 GeV is used to produce charm
particles in Cu and diamond targets. The details of the three-stage magnetic spectrometer is shown elsewhere \cite{my_thesis}.
High precision vertex detectors provide average proper-time resolution of 20
fs for the charm decays. The system of proportional chambers, drift chambers and silicon strip
detectors measures the momentum with less than $1\%$ resolution. Charged particle identification was done
by a 10 m long Ring-Imaging Cerenkov (RICH) detector that separates $\pi$ from K up to 165 GeV/c.
The charm interactions were selected by a scintillator trigger. The trigger
for charm required at least 4 charged tracks after the targets as indicated by
an interaction counter and at least 2 hits in a scintillator hodoscope after
the second analyzing magnet. It accepted about 1/3 of all inelastic
interactions. Triggered events were further tested in an online computational
filter based on downstream tracking and particle identification
information. The online filter selected events that had evidence of a
secondary vertex from tracks completely reconstructed using the forward PWC
spectrometer and the vertex silicon.
The Monte Carlo generated decays were simulated and embedded
into data events. To separate the charm signal from non-charm background we
optimized the Monte Carlo sample over data sidebands by using the the following tools:
(i) Decay vertex separation significance $L/\sigma$, where L is the spatial separation between the first and the second
vertices,
(ii) The charm baryon was reconstructed as the vector sum of its secondary tracks, the summation vector is extrapolated back
to the primary vertex. Its misdistance with respect to the primary vertex is used,
(iii) The secondary vertex tracks are extrapolated back to the $z_{prim}$. We used the second largest
misdistance with respect to primary vertex,
(iv) Sum of the squared transverse momentum of the secondary particles with respect to
the charm track,
(v) We also required a minimum momentum cut for the $\pi^{+}$, which helps to reject the soft pions that cause high background.
Optimising these variables yield; $157 \pm 21$ $\Xi_{c}^{+} \rightarrow \Xi^{-} \pi^{+} \pi^{+}$ events (see Figure \ref{total_mass}-a),
$98\pm17$ $\Xi_{c}^{+} \rightarrow p^{+} K^{-} \pi^{+}$ events (see Figure \ref{total_mass}-b), and $46\pm11$ $\Xi_{c}^{+} \rightarrow \Sigma^{+} K^{-} \pi^{+}$ events (see Figure \ref{total_mass}-c). The shaded areas in the Figure \ref{total_mass} are estimated reflections from $\Lambda_{c}^{+} \rightarrow \Sigma^{-} \pi^{+} \pi^{+}$ and $\Lambda_{c}^{+} \rightarrow \Sigma^{+} \pi^{-} \pi^{+}$, respectively. The shapes are determined by Monte Carlo simulations and the areas are normalized to the observed number of signal events in $\Lambda_{c}^{+}$ data. We calculated to have 12 $\Lambda_{c}^{+} \rightarrow \Sigma^{-} \pi^{+} \pi^{+}$ events under the $\Xi_{c}^{+} \rightarrow \Xi^{-} \pi^{+} \pi^{+}$ signal, due to misidentification of $\Sigma^{-}$ as $\Xi^{-}$, and 23 $\Lambda_{c}^{+}\rightarrow \Sigma^{+} \pi^{-} \pi^{+}$ events under the signal of $\Xi_{c}^{+} \rightarrow \Sigma^{+} K^{-} \pi^{+}$ decay channel due to misidentification of $\pi^{-}$ as $K^{-}$.
A fit to the total $\Xi_{c}^{+}$ mass distribution using a Gaussian for signal and a linear function for background yields $301\pm31$ reconstructed $\Xi_{c}^{+}$ and a Gaussian $\sigma$ of 8.8 $MeV/c^{2}$ (see Figure \ref{total_mass}-d).
\begin{figure}[htb]
\begin{center}
\includegraphics*[width=\linewidth]{Figure1.eps}
\end{center}
\caption{Applied correction functions for $\Xi_{c}^{+} \rightarrow \Xi^{-} \pi^{+} \pi^{+}$ (top),
$\Xi_{c}^{+} \rightarrow \Sigma^{+} K^{-} \pi^{+}$ (middle), and $\Xi_{c}^{+} \rightarrow p^{+} K^{-} \pi^{+}$ (bottom)}
\label{total_CF}
\end{figure}
\begin{figure*}[htb]
\begin{center}
\includegraphics*[width=14cm]{Figure2.eps}
\end{center}
\caption{a) $\Xi_{c}^{+} \rightarrow \Xi^{-} \pi^{+} \pi^{+}$ mass
distribution after the cuts. The shaded area is the estimated reflection
from $\Lambda_{c}^{+} \rightarrow \Sigma^{-} \pi^{+} \pi^{+}$ decay
channel.
b) $\Xi_{c}^{+} \rightarrow p^{+} K^{-} \pi^{+}$ mass distribution after
the cuts.
c) $\Xi_{c}^{+} \rightarrow \Sigma^{+} K^{-} \pi^{+}$ mass distribution
after the cuts. The shaded area is the estimated reflection from
$\Lambda_{c}^{+} \rightarrow \Sigma^{+} \pi^{-} \pi^{+}$decay channel.
d) Total mass distribution, the gaussian fit yields $301\pm31$
$\Xi_{c}^{+}$ events. }
\label{total_mass}
\end{figure*}
\section{Analysis Technique}
The average longitudinal error, $\sigma_{z}$, on the primary and the secondary vertices for $\Xi_{c}^{+} \rightarrow \Xi^{-} \pi^{+} \pi^{+}$ sample are 358 $\mu m$ and 539 $\mu m$ respectively, which gives combined error of 647 $\mu m$. In $\Xi_{c}^{+} \rightarrow \Xi^{-} \pi^{+} \pi^{+}$ signal region the average momentum is 213 $GeV/c$, corresponding to a time resolution of 25 $fs$, about $5 \%$ of the $\tau_{\Xi_{c}^{+}}$.
Since the bin-smearing effects are small we used binned maximum likelihood fitting technique to determine the $\Xi_{c}^{+}$ lifetime. This fit was applied to a reduced proper time distribution;
{\scriptsize
\begin{equation}
t' = t - t_{min} = \frac{L-N\sigma_{L}}{\beta\gamma c}
\label{reduced_proper_time}
\end{equation}
}
Where, N is the significance of the detachment cut which has been adopted.
A correction function, f(t'), is applied to all data to take into account the
factors dependent on the detector resolution and systematic effects. The
correction function is obtained from bin by bin ratio of simulated events'
reduced proper time distributions before and after the reconstruction code (see Figure \ref{total_CF}). The reflection events from
$\Lambda_{c}^{+}$ decays are taken into account and the $\Lambda_{c}^{+}$ lifetime,
$\tau_{\Lambda_{c}^{+}}$, is set to 200 $fs$ \cite{PDG04}.
The probability density was performed by the function;
{\scriptsize
\begin{equation}
P(t')=N_{s}(1-(m+n)S(t')f(t')+mB(t')+nR(t'))
\label{density_function}
\end{equation}
}
Where;
{\scriptsize
\begin{equation}
S(t') = \frac{e^{-t'/\tau_{\Xi_{c}^{+}}}}{\tau_{\Xi_{c}^{+}}}
\label{signal}
\end{equation}
}
{\scriptsize
\begin{equation}
B(t') = e^{-t'/\tau_{Bckg}} \frac{\alpha}{\tau_{Bckg}} + (1-\alpha) \frac{C}{t'_{max}}
\label{background}
\end{equation}
}
and
{\scriptsize
\begin{equation}
R(t') = \frac{e^{-t'/\tau_{\Lambda_{c}^{+}}}}{\tau_{\Lambda_{c}^{+}}}
\label{reflection}
\end{equation}
}
$N_{s}$ is the total number of events having a mass $\pm 20$ $MeV/c^{2}$ around the mean mass of the signal peak. $\tau_{\Xi_{c}^{+}}$, $\tau_{Bckg}$,and $\tau_{\Lambda_{c}^{+}}$ are the lifetimes of $\Xi_{c}^{+}$, background events, and reflection ($\Lambda_{c}^{+}$) events, respectively. The reduced proper time distribution of the sibeband events are fitted to exponential plus a constant term, C. $\alpha$ is the ratio of exponential within this background fit. The variables m and n are the percentages of the background and reflection events under the signal, respectively. f(t') is the corresponding correction function.
The behavior of the background events in the signal region is assumed to be
the same with the sideband region events. For $\Xi_{c}^{+} \rightarrow \Xi^{-} \pi^{+} \pi^{+}$ decay channel, since the
reflection events are localized on left side of the mass peak, we chose the
sideband region from 2.50 $GeV/c^{2}$ to 2.54 $GeV/c^{2}$, away from the effects of the possible reflection events.
For $\Xi_{c}^{+} \rightarrow p^{+} K^{-} \pi^{+}$ decay channel, two symmetric
sideband regions, from 2.424 $GeV/c^{2}$ to 2.444 $GeV/c^{2}$ and from 2.484 $GeV/c^{2}$ to 2.504 $GeV/c^{2}$ are chosen.
For $\Xi_{c}^{+} \rightarrow \Sigma^{+} K^{-} \pi^{+}$ decay channel the
reflection is distributed all over the mass region, so we cannot find a
sideband region that is not contaminated by the possible reflection. The events from two symmetric mass regions,
from 2.434 $GeV/c^{2}$ to 2.454 $GeV/c^{2}$ and from 2.494 $GeV/c^{2}$ to 2.514 $GeV/c^{2}$ are chosen as sideband events.
Finally, the Maximum Likelihood Function is the Landau probability of finding $s_{i}$ events in $i^{th}$
reduced proper time bin while we are expecting $P_{i}$ events for all of the bins.
{\scriptsize
\begin{equation}
L = \Pi_{i=1}^{i=nbins} \frac{P_{i}^{s_{i}}e^{P_{i}}}{s_{i}!}
\label{maximum_likelihood}
\end{equation}
}
Where nbin is 40; total number of reduced proper time bins. Since we have three independent
data sets, we analyzed them separately, and took the weighted average, the total lifetime for $\Xi_{c}^{+}$
is found to be $430\pm22$ $fs$.
\begin{table}[htb]
\caption{Lifetimes and event numbers of different decay channels.}
\label{tab:lifetimes}
\begin{tabular}{@{}lll}
\hline
$\Xi_{c}^{+}$ Decay Channel & Event Number & Lifetime (fs)\\
\hline
$\Xi^{-} \pi^{+} \pi^{+}$ & $157 \pm 21$ & $420 \pm 28$ \\
$\Sigma^{+} K^{-} \pi^{+}$ & $46 \pm 11$ & $465 \pm 76$ \\
$p^{+} K^{-} \pi^{+}$ & $98 \pm 17$ & $429 \pm 39$ \\
\hline
Total & $301 \pm 31$ & $430 \pm 22$ \\
\hline
\end{tabular}
\end{table}
\section{Systematic Errors}
The systematic study has been done by using Monte Carlo simulations and
$157\pm21$ events from $\Xi_{c}^{+} \rightarrow \Xi^{-} \pi^{+} \pi^{+}$ decay.
%The items which contribute to the sytematical errors are:
The bin size selection of the reduced proper time distribution contributes 4
$fs$ to systematics. The $X_{f}$ distribution for our data gives $3.6 \pm 0.7$ as $X_{f}$ power. We
produced the MC samples with different $X_{f}$ powers and measured lifetime
with the correction functions coming from these samples.
The systematical error contribution from $X_{f}$ power selection is 7 $fs$.
The Correction Function is fitted to different powers of polynomials, this
variation yields 4 $fs$ systematical errors to our measurement.
The systematical errors due to the selection of the sidebands, and choosing
different $t_{max}$ values of reduced proper time distributions
are negligible. Adding these contributions in quadrature gives a total systematic uncertainty
of 9 $fs$.
The Monte Carlo corrected, sideband subtracted reduced proper time
distribution of the signal events, and lifetime fit are shown in Figure\ref{result}.
\section{Summary}
\label{summary}
This report presents SELEX's preliminary measurement of the $\Xi_{c}^{+}$ lifetime using three different decay modes,
with a combined sample of $301\pm31$ events. We used binned maximum likelihood method and measured the lifetime
to be $430 \pm 22 \pm 9$ fs, where the first error is statistical and the
second is systematical. Our measurement systematical and statistical uncertainities are better than those of the world average.
This measurement give a ratio $\tau_{\Xi_{c}^{+}}$/$\tau_{\Lambda_{c}^{+}} = 2.15 \pm 0.1$, using the $\Lambda_{c}^{+}$ lifetime of PDG ($200 \pm 6 fs$).
\begin{figure}[htb]
\begin{center}
\includegraphics*[width=\linewidth]{Figure3.eps}
\end{center}
\caption{Corrected, sideband subtracted reduced proper time distribution for the $301\pm31$ events. The fit line shows the measured $\Xi_{c}^{+}$ lifetime, 430 fs.}
\label{result}
\end{figure}
\begin{thebibliography}{}
\bibitem{my_thesis} U. Akgun, Ph.D. thesis, The University of Iowa, 2003.
\bibitem{PDG04} Particle Data Group, S. Eidelman{\sl et al.}, Physics Letters B, 592, 2004.
\end{thebibliography}
\end{document}