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\begin{document}

\title{Charm Identification using Silicon Detectors in a Neutrino Experiment} 
\vspace*{-0.3cm}
\author{M. Ellis\dag\ and F.J.P. Soler\ddag \footnote[3]{Corresponding author: 
p.soler@rl.ac.uk} }
\address{\dag\ Rutherford Appleton Laboratory, Chilton, Didcot, 
Oxfordshire OX11 0QX, UK}
\address{\ddag\ University of Glasgow, Department of Physics and Astronomy,
Glasgow G12 8QQ, UK and Rutherford Appleton Laboratory, Chilton, Didcot, 
Oxfordshire OX11 0QX, UK}
\vspace*{-0.3cm}
\begin{abstract}
A target consisting of four passive layers of boron carbide and five
layers of silicon microstrip detectors (NOMAD--STAR) with a total surface of 1.14~m$^2$
was installed inside the NOMAD neutrino oscillation experiment at the CERN SPS. 
A sample of 45 charm mesons (with 22 background) was obtained from about 11,500 $\nu_\mu$ charged current
interaction in NOMAD--STAR. The efficiencies obtained from this
search demonstrate the capabilities of silicon microstrip detectors for charm particle
identification at a future neutrino factory.
\end{abstract}

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%\pacs{13.15.+g; 13.25.Es; 13.25.Ft; 14.60.Lm; 14.60.Pq; 29.40.Gx; 29.40.Wk}

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\vspace*{-0.9cm}
\section{Introduction}
A silicon vertex detector (NOMAD--STAR) was installed upstream of the first NOMAD drift chamber 
\cite{nomad_nim} to test the capabilities of silicon detectors for \osc oscillation searches
\cite{nausicaa1,nausicaa2}.
The target consisted of four layers of boron carbide (B$_{4}$C) 
with a total mass of 45 kg, interleaved with five layers of single--sided silicon microstrip detectors
(see Figures~\ref{fig:nomad} and \ref{fig:nomad_star}).

\vspace*{-0.9cm}
\begin{figure}[htbp]
\begin{minipage}[b]{.50\linewidth}
  \begin{center}
  \epsfig{file=nomadstar.eps,width=.80\linewidth,angle=-90}
  \vspace*{-0.5cm}
  \caption{\label{fig:nomad}The NOMAD detector with the Silicon TARget (NOMAD--STAR).}
  \end{center}
\end{minipage}\hfill
\begin{minipage}[b]{.40\linewidth}
  \begin{center}
  \epsfig{file=star_new.eps,width=.75\linewidth}
  \vspace*{-0.5cm}
  \caption{\label{fig:nomad_star}Side view of NOMAD-STAR.}
  \end{center}
\end{minipage}\hfill
\end{figure}
\vspace*{-0.2cm}

The five layers of silicon detectors had a total active surface of 1.14~m$^2$, with 10 ladders per layer and
12 silicon microstrip detectors per ladder \cite{star2} (at 72~cm, these are the longest working silicon 
ladders ever built). The detectors were
single--sided, 33.5 $\times$ 59.9~mm$^2$ wide, with strip and readout pitches of 25~$\mu$m and
50~$\mu$m, respectively. The 640 read-out strips per detector,
parallel to the NOMAD magnetic field ($x$ axis), measured the $y$ projection
of the track with a point resolution of $5~\mu$m \cite{star1}. 

Charm mesons can mimic the capabilities of NOMAD--STAR for the detection of 
$\tau$ particles. The present paper describes a search for charm inside NOMAD--STAR and consequences 
for future near detectors at a neutrino factory.

\vspace*{-0.3cm}
\section{NOMAD-STAR performance}
The noise performance of most of the long silicon ladders was found to be as expected (a signal-to-noise of 17:1) 
with average hit-finding efficiencies above 98\% \cite{star_perf}). 
Some ladders exhibited variable noise but always with a signal-to-noise above 12:1 and efficiency above 92\%.

A Kalman filter \cite{kalman_star} was used for tracking, vertexing and for the alignment of the silicon ladders
\cite{alignment}. The alignment residuals were 9~$\mu$m for the three inner planes and 12~$\mu$m for the 
two outer planes. After the alignment, hit residuals in the $y$ projection had a RMS of 8.6~$\mu$m, with 
the $y$ and $z$ vertex resolution  19~$\mu$m and 78~$\mu$m and the $y$ double vertex resolution (from $K^0_s$ 
decays) $18\pm 4~\mu$m \cite{kokkonen_thesis}.
 
The impact parameter (defined as the projected signed distance of the $\mu^-$, from a $\nm$ 
charged current, CC, interaction to the vertex produced by the remaining hadronic
jet) was measured to be 33~$\mu$m for all events with three or more 
tracks in the hadronic vertex (see Figure~\ref{fig:ip}), comparing well with \cite{nausicaa1}. 

\begin{figure}[htbp]
\begin{minipage}[b]{.5\linewidth}
  \begin{center}
  \epsfig{file=ip_prim_3tr.eps,width=0.98\linewidth}
  \vspace*{-0.5cm}
  \caption{\label{fig:ip}Impact parameter for $\nm$ CC events with 3 or more hadronic tracks.}
  \end{center}
\end{minipage}\hfill
\begin{minipage}[b]{.5\linewidth}
  \begin{center}
  \epsfig{file=dimurate.eps,width=0.97\linewidth}
  \vspace*{-0.3cm}
  \caption{\label{fig:dimuon} Opposite sign dimuon rate of NOMAD-STAR and other experiments. 
           Overlayed is a charm mass fit of 1.3 GeV/c$^{2}$ \cite{nomad_dimu}.}
  \end{center}
\end{minipage}\hfill
\end{figure}

\vspace*{-0.7cm}
\section{Charm search}
Out of a total of 98,858 triggers, 11,528 were identified as $\nm$ CC events in the fiducial volume of
NOMAD-STAR. Only 1,545 had a minimum of two tracks and a muon (13.4\%), needed to perform an impact 
parameter measurement.
Monte Carlo events were used to determine the reconstruction efficiency and background estimation.
%of 62,880 $\nm$ CC events, 15,011 $\nm$ neutral current (NC) events and 20,388 $\nmb$ CC
%events was used to determine the impact parameter recosntruction efficiency, which was 30.4\% (28.8\%)
%for $\nm$ ($\nmb$) CC events, with a contamination of 0.2\% from the $\nm$ NC sample.
The $\chi^2$ of the fit was minimized while 
constraining the total momentum, the total energy and the $yz$ projected angle of all the decay products 
for a large fraction of the decay hypotheses of the $D^0$, $D^+$ and $D_s^+$.
Further cuts on the invariant mass,
the proper decay time, the reconstructed momentum of the $D$ meson, the fraction of momentum carried by
the $D$ meson and the consistency of the decay angles allow to pick out the charm candidates
\cite{ellis_thesis}.

The total number of charm events obtained can be found in Table~\ref{table:charmrec}. The efficiency for
both $D^{0}$ and $D^{+}$ identification was 3.5\% and for $D_{s}^{+}$ was 12.1\%. The total charm meson
production rate is $7.2\pm 2.4$\% of the $\nm$ CC rate, at an average energy of 33~GeV. These rates compare 
well with the emulsion experiments E531 \cite{E531} and CHORUS \cite{chorus_charm}. Assuming
the semi-leptonic branching ratio of charm particles \cite{PDG}, we can also compare the dimuon rate expected
in NOMAD-STAR with that observed at other experiments \cite{nomad_dimu} (see Figure \ref{fig:dimuon}).

\vspace*{-0.5cm}
\begin{table}[htbp]
\caption{\label{table:charmrec}Number of charm mesons in $\nu_{\mu}$ CC interactions from NOMAD-STAR.
         The last column shows the resulting production rates of charm mesons as a fraction of 
         $\nu_{\mu}$ DIS CC interactions.}
\begin{indented}
\item[]\begin{tabular}{|c|c|c|c|} \hline
Meson & Reconstructed & Background &  Production Rate \\ \hline 
$D^{0}$       & 24 & $13.33 \pm 0.98$ & $4.2  \pm 2.0$  \% \\ \hline
$D^{+}$       & 10 & $ 3.79 \pm 0.53$ & $2.4  \pm 1.3$ \% \\ \hline
$D_{s}^{+}$   & 11 & $ 5.17 \pm 0.61$ & $0.64 \pm 0.36$ \% \\ \hline 
Total Charm   & 45 & $22.3 \pm 1.3$ & $7.2  \pm 2.4$  \% \\ \hline 
\end{tabular}
\end{indented}
\end{table}
\vspace*{-0.6cm}

\section{Discussion}
\vspace*{-0.2cm}
The flux of neutrinos at a near detector (30 metres downstream) of a 50 GeV muon storage ring
\cite{nufact_near} would produce 200 million $\nm$ CC events per year in a detector of the same mass as
NOMAD-STAR (45 kg). With the measured efficiencies from the previous analysis, this would correspond to more 
than 0.6 million charm events reconstructed per year.

With this number of reconstructed charm events, the production cross-sections, 
the strange quark content of the sea and the CKM parameter $V_{cd}$ (currently known to $5 \%$) could be 
accurately measured. In addition, a neutrino factory beam could be used to search 
for CP violation in $D^{0}$ - $\overline{D^{0}}$ mixing. 
The sign of the lepton produced at the primary vertex can be used to tag the initial charm particle,
with the decay products determining whether there was any change in the flavour 
of the charm meson.

\vspace*{-0.3cm}
\ack
\vspace*{-0.1cm}
Thanks to the support of all the NOMAD collaboration and to
A.~Cervera--Villanueva, E. do Couto e Silva, D.~Ferr\`ere, 
J.J.~G\'omez--Cadenas, J.A.~Hernando, W.~Huta, J.~Kokkonen, V.E.~Kuznetsov, L.~Linssen, \"{O}. Runolfsson
and G.~Vidal-Sitjes.

\vspace*{-0.3cm}
\section*{References}
\begin{thebibliography}{<99>}
\bibitem{nomad_nim} J. Altegoer \emph{et al.}, The NOMAD Collaboration,
  Nucl. Instr. and Meth. A404 (1998) 96.
\bibitem{nausicaa1} J.J. G\'omez-Cadenas, J.A. Hernando and A. Bueno,
  Nucl. Instr. and Meth. A378 (1996) 196.
\bibitem{nausicaa2}  J.J. G\'omez-Cadenas
and J.A. Hernando, Nucl. Instr. and Meth. A381 (1996) 223-235.
\bibitem{star2}
  G.~Baricchello \emph{et al.}, Nucl. Instr. and Meth. A419 (1998) 1.
\bibitem{star1}
  G.~Baricchello \emph{et al.}, Nucl. Instr. and Meth. A413 (1998) 17.
\bibitem{star_perf} G. Barichello \emph{et al.},
  ``Performance of the NOMAD-STAR detector", To be published in Nucl. Instr. and Meth. A.
\bibitem{kalman_star} A. Cervera-Villanueva {\it et al.},  Nucl. Instr. and Meth. A 486 (2002) 639-662.
\bibitem{alignment} A. Cervera-Villanueva, Nucl. Instr. and Meth. A 447 (2000) 100-109.
\bibitem{kokkonen_thesis} J. Kokkonen, ``A Silicon Detector for Neutrino Physics", Doctoral Thesis,
  Helsinki University of Technology, (2002), ISBN 951-45-8937-8, ISSN 1455-0563.
\bibitem{ellis_thesis} M. Ellis, "A Study of Charm Production by Neutrinos in the NOMAD--STAR Detector",
 PhD Thesis, University of Sydney, March 2001.
\bibitem{E531} N. Ushida et al., Phys. Lett. B 206 (1988) 375 and 380.
\bibitem{chorus_charm}
  A. Kayis-Topaksu {\emph et al.}, CHORUS Collaboration, Phys. Lett. B 527 (2002) 173-181.
\bibitem{PDG} Particle Data Group, Eur. Phys. J. C (2000), 163.
\bibitem{nomad_dimu} P. Astier et al., NOMAD Collaboration,  Physics Letters B 486 (2000), 35-48.
\bibitem{nufact_near} K. McFarland, Nucl. Instr. and Meth. A 451 (2000) 218.

\end{thebibliography}

\end{document}

