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\title{Search for Pentaquark States at CLAS}

\author{R.~De~Vita\address[INFNGE]{Istituto Nazionale di Fisica Nucleare,
        Via Dodecaneso 33, 16146 Genova, Italy}%
        ~and the CLAS Collaboration
        }
       
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\begin{document}

\begin{abstract}
After the initial claim of discovery of a possible pentaquark state named $\Theta^+(1540)$, 
many experiments reported positive and negative results opening a discussion about the 
existence of such exotic particle. Most of the experimental evidence was obtained from data 
previously collected for other purposes in many reaction channels and under very different 
kinematic conditions, so that direct comparison of the results of the different experiments 
are very difficult.
New experiments with high resolution and high statistics are needed to solve the controversy. 
A comprehensive program to search for pentaquark in photoproduction reaction on proton and 
deuteron was undertaken at Jefferson Laboratory. These second generation experiments cover 
the few GeV region where most of the positive evidences were found, collecting more than 10 
times the existing statistics. First experiments on proton and deuteron were completed 
showing no evidence for the $\Theta^+(1540)$ and setting upper limits on the production 
cross section at the level of few nb. 
\vspace{1pc}
\end{abstract}

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\section{INTRODUCTION}
A fundamental issue in hadronic physics is the the possible existence of states beyond 
the usual $qqq$ and $q\bar q$ configuration. In particular search for pentaquarks, i.e. 
states with minimal $qqqq\bar q$ configuration, started several decades ago. 
The interest in this topic was recently renewed by the prediction by Diakonov and 
collaborators \cite{diakonov} of a decuplet of such states with relatively low masses 
($1.5 -2.1$ GeV) and narrow widths. First evidence for the lower mass pentaquark, 
an exotic state with positive strangeness named $\Theta^+(1540)$, was reported in 2002 by 
the LEPS collaboration \cite{nakano}. 

After this initial claim, data already collected by several collaboration where analyzed 
finding both positive results, that confirmed the initial evidence, as well as negative 
results \cite{burkert}. The very different kinematic conditions and experimental setups 
of these experiments make a direct comparison of their results very difficult, leaving 
therefore an open controversy on whether pentaquarks have been really seen so far.

\section{SEARCH FOR PENTAQUARKS AT CLAS}
In order to solve the experimental situation, a second generation of dedicated experiments 
was undertaken at Jefferson Lab with the CLAS detector. These experiments are designed 
to search for pentaquarks states in photoproduction reactions covering the few GeV region 
where most of the positive evidences were reported and accumulating at least an order 
of magnitude more statistics than previous measurements. A first experiment ($g10$)
on deuteron target with beam energy in the range 1.0-3.5 GeV was completed in 2004, 
followed by an experiment on proton target ($g11$) with beam energy in the range 
$1.6-3.8$ GeV. A second run on deuteron target ($eg3$) with beam energy of $4.0-5.4$ GeV
was completed in 2005, while a second run on proton target ($super-g$) with energies 
up to 5.7 GeV is planned for the near future. The mass resolutions are of few MeV and 
the accuracy in the mass determination is of $1-2$ MeV, allowing a precise determination 
of any possible narrow peak in the measured mass spectra.


\section{EXPERIMENTAL SETUP}
The measurements were performed with the CLAS detector in Hall B \cite{clas} using a 
bremsstrahlung photon beam produced by a continuous electron beam impinging on 
thin gold foils. The photons, whose energies are determined on event-by-event basis 
by a tagging system, interact with a liquid hydrogen or deuterium target. 
Outgoing hadrons were detected by the CLAS spectrometer. The large acceptance of the 
detector allows the measurement of multi-particle final states. The momentum of charged 
particles was determined via tracking through three regions of drift chambers immersed 
in a toroidal magnetic field, with a typical resolution of the order of 0.5-1\%. 
Particle identification was obtained from time-of-flight measurements (TOF), while 
the photon interaction time was determined by the Start Counter (ST).
Coincidences between the photon tagger and CLAS triggered the recording of an event. The CLAS trigger, 
defined by the coincidences between the TOF and ST system elements, is set to select events with 
two or more particle tracks. In this way, simultaneous measurement of several different 
multi-particle final states was possible keeping the same experimental setup.


\begin{figure}[htb]
\vspace{4.2cm}
\special{psfile=fig_g11_nkp.eps hscale=36 vscale=30 hoffset=0 voffset=-28}
\caption{The $nK^+$ invariant mass spectrum for the reaction 
$\gamma p \to  \bar K^0 K^+ n$. The spectrum is smooth and shows 
no evidence of a structure or peak that could be associated to 
the $\Theta^+$ pentaquark.}
\label{fig:g11_nk+}
\end{figure}

\vspace{-0.3in}
\section{RESULTS ON THE $\Theta^+(1540)$ SEARCH}
The first result was obtained from the reaction $\gamma p \to \bar K^0 K^+ n$ 
searching for evidence of the $\Theta^+\to nK^+$ \cite{prl}. The $K^+$ was 
detected by the spectrometer, the $\bar K^0$ was reconstructed via its $K_S$
component decay to $\pi^+\pi^-$ and the neutron was reconstructed with the 
missing mass technique. After rejection of known hyperons ($\Sigma^{\pm}$,
$\Lambda^*(1520)$) decaying to the same final state a total of $160\,000$ 
events were retained. The $nK^+$ invariant mass spectrum is shown in Fig.  
\ref{fig:g11_nk+}. The spectrum is smooth and structureless showing no evidence 
of a structure that could be associated with the $\Theta^+(1540)$. From the 
analysis of the mass spectrum, an upper limit on the production cross section 
at the 95\% Confidence Level of 0.5-1.2 nb was set in the mass range $1.5-1.6$ 
GeV. This result directly contradicts the SAPHIR experiment \cite{saphir} 
that reported a cross section of 50 nb. In the CLAS data $\sim 99\,000$ 
$\Lambda^*(1520)$ were observed, corresponding to a ratio of the $\Theta^+$ 
to $\Lambda^*(1520)$ yields of less than 0.22\% (95\% C.L.).

\begin{figure}[htb]
\vspace{5.2cm}
\special{psfile=fig_g11_pk0.eps hscale=36 vscale=36 hoffset=0 voffset=-28}
\caption{The $pK_S$ invariant mass (top) and $K_S$ missing mass 
(bottom) for the reaction $\gamma p \to \bar K^0 K^0p$.
 Shoulders corresponding to excited $\Sigma$ states are visible 
in both spectra.}
\label{fig:g11_pk0}
\end{figure}
\vspace{-0.2in}
These results were then confirmed by the analysis of the reaction 
$\gamma p \to \bar K^0 K^0 p$ where the $\Theta^+$ was searched in the decay 
to $pK^0$ \cite{prd}. In this case the proton was detected in CLAS and a $K_S$ meson was
reconstructed from its $\pi^+\pi^-$ decay. The second neutral kaon was reconstructed
via the missing mass technique. After rejection of the reaction $\gamma p \to p\phi \to p K_L K_S$ 
and $\gamma p  \rightarrow  \Lambda(1116) \pi^+ K^0 \rightarrow  p \pi^-  \pi^+  K^0$,
approximately $550\,000$ events were obtained. Since the selected final state has two neutral 
kaons, the $\Theta^+$ peak could appear both in the invariant mass spectrum of the 
$pK_S$ system as well as in the missing mass spectrum of the $K_S$. Both spectra are shown 
in Fig. \ref{fig:g11_pk0} with no evidence of a narrow peak or enhancement. The 
combined analysis of the spectra from the reactions $\gamma p \to \bar K^0 K^+ n$ 
and $\gamma p \to \bar K^0 K^0 p$ yielded to a final upper limit on the production 
cross section for the reaction $\gamma p \to \bar K^0 \Theta^+$ of 0.7 nb at the
95\% Confidence Level.

\begin{figure}[htb]
\vspace{5.4cm}
\special{psfile=fig_g10_nkp.eps hscale=45 vscale=45 hoffset=0 voffset=-35}
\caption{Top: the $nK^+$ invariant mass spectrum for the reaction 
$\gamma d \to p K^+ K^- (n)$ for two magnetic field settings of 
the spectrometer. Bottom: cross section for mass bin along with 
a polynomial fit.}
\label{fig:g10_nkp}
\end{figure}
\vspace{-0.3in}
The $g10$ deuteron data set was analyzed searching for the $\Theta^+\to nK^+$
in the reaction $\gamma d \to p K^- K^+ n$ \cite{g10} with the aim of verifying 
the previous CLAS observation of a narrow resonance in the same reaction \cite{g2a}. 
The integrated luminosity of the present measurement was more than 30 times larger
than the previous experiment.
The proton, $K^+$ and $K^-$ were detected in the spectrometer and the 
neutron was reconstructed from the overdetermined kinematics. As in the other 
analyses, contribution from $\phi$-meson and $\Lambda^*(1520)$ production were 
removed to reduce the background. The $nK^+$ invariant mass spectra obtained 
with two different magnetic field settings of the spectrometer are shown in 
the top panels of Fig. \ref{fig:g10_nkp}. The spectra show no indication of a 
peak or structure. The two spectra were corrected for the detector acceptance
and integrated luminosity and them combined obtaining the mass dependent cross 
section shown in the bottom panel of Fig. \ref{fig:g10_nkp}. The analysis 
of this spectrum sets an upper limit (95\% C.L.) on the $\gamma d \to p K^-\Theta^+$ 
of 0.3 nb in the mass range $1.52-1.56$ GeV. Using an phenomenological approach based 
on $\Lambda^+(1520)$ production to empirically measure the re-scattering of the 
proton in the deuteron, this upper limit was converted into an upper limit on 
the elementary process $\gamma n \to K^- \Theta^+ \to K^- K^+ n$ of $\sim 3$ nb
(95\% C.L.). These results clearly contradict the previous low statistics data. 
In order to understand this discrepancy, the new data were analyzed using the same
event selection and photon energy range of the previous analysis. The comparison
of the two spectra showed that in the previous analysis the background in the signal
region was underestimated. The significance of the original structure
was determined using a background distribution extracted from the new high statistic 
run obtaining $\sim 3.1\sigma$ compared to the $(5.2\pm 0.6)\sigma$ published.

The same data set was also analyzed searching for evidence of the reaction
$\gamma d \to \Lambda \Theta^+ \to \Lambda nK^+$ \cite{silvia}. As for the other 
reaction channels no evidence for $\Theta^+$ production was observed and upper limits 
on the total cross section were set between 5 and 25 nb, depending on the production 
model assumed.


\section{SEARCH FOR THE $\Theta^{++}$ STATE}
The new high statistics CLAS data have been analyzed searching for evidence 
of other pentaquark states as the $\Theta^{++}$, the isospin partner of the 
$\Theta^+$, and $\Xi^{--}$. Results on the $\Theta^{++}$ search in the $g11$ data set
were recently published \cite{vpk}. Evidence for the $\Theta^{++}\to pK^+$ was searched
in the reaction $\gamma p \to K^- K^+ p$. This final state was selected either detecting
the three charged particles in CLAS or detecting only the proton and $K^+$ and reconstructing
the $K^-$ via the missing mass technique. The $pK^+$ invariant mass spectra for these
two event topologies are shown in Fig. \ref{fig:g11_pkp}. Both spectra are smooth and
show no evidence of narrow structures in the mass range $1.5-2.0$ GeV. In the same data set
approximately $1\,000\,000$ $\Lambda^*(1520)\to pK^-$ were observed.
From the bottom panel of Fig. \ref{fig:g11_pkp} the 95\% Confidence Level upper limit 
on the total production cross section for the reaction $\gamma p \to  K^- \Theta^{++}$ 
was extracted. This was found to be 0.15 nb on average in the mass range $1.5-2.0$ GeV, 
corresponding to $\sigma(\Theta^{++})/\sigma(\Lambda^*(1520))<2.3\times 10^{-4}$ (95\% C.L.).
This negative result challenges the positive observation recently reported by the STAR 
Collaboration \cite{star} putting very strong limits on the possible production of 
an isovector pentaquark.

\begin{figure}[htb]
\vspace{5.5cm}
\special{psfile=fig_g11_pkp.eps hscale=40 vscale=40 hoffset=0 voffset=-30}
\caption{The $pK^+$ invariant mass spectrum for the reaction $\gamma p \to  K^- K^+ p$ 
when all three final state particles are detected (top) or when only the proton 
and $K^+$ are detected (bottom). The insets show an enlargement of the mass 
region of the previously reported $\Theta^+$.}
\label{fig:g11_pkp}
\end{figure}

\vspace{-0.3in}
\section{CONCLUSIONS}
A comprehensive physics program to search for evidence of pentaquark 
states in photoproduction reaction is in progress at Jefferson Lab with 
the CLAS detector. These new experiment were explicitly designed to provide
high statistics and high resolution data in the few GeV energy region were
positive evidence for pentaquark states was reported. The analyses of several
reaction channels on proton and deuteron show no evidence of the $\Theta^+$ 
pentaquarks setting upper limits on the total production cross section at the 
few nb level. Search for the isovector $\Theta^{++}$ pentaquark on proton
target also yields a null result. Further searches for pentaquark states in
other reaction channels and in wider kinematic range are planned in the near future.
These include the search for $\gamma p \to K^+\pi^-\Theta^+$, $\gamma p \to K^*\Theta^+$,
and $\gamma d \to K^+K^+ p \Xi^{--}$ up to a maximum photon energy of 5.7 GeV.
These new analyses together with the results presented above could clear up the debate on 
the pentaquark existence.

\begin{thebibliography}{99}
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\bibitem{nakano}  T. Nakano {\it et al.} (LEPS Collaboration), Phys. Rev. Lett. {\bf 91}, 012002 (2003).
\bibitem{burkert} See for example V. D. Burkert, Int.\ J.\ Mod.\ Phys.\ A {\bf 21}, 1764 (2006), and references therein.
\bibitem{clas} B. Mecking {\it et al.}, Nucl. Instr. and Meth. {\bf A503}, 513  (2003).
\bibitem{prl} M.~Battaglieri {\it et al.} (CLAS Collaboration), Phys. Rev. Lett. {\bf 96}, 042001 (2006).
\bibitem{saphir} J. Barth {\it et al.} (SAPHIR Collaboration), Phys. Lett. B {\bf 572}, 127 (2003); M. Ostrick, Prog. Part. Nucl. Phys. {\bf 55}, 337 (2005).
\bibitem{prd} R. De Vita {\it et al.} (CLAS Collaboration), Phys. Rev. D {\bf 74}, 032001 (2006).
\bibitem{g10} B.~McKinnon {\it et al.} (CLAS Collaboration), Phys. Rev. Lett. {\bf 96}, 212001 (2006). 
\bibitem{g2a} S. Stepanyan {\it et al.} (CLAS Collaboration), Phys. Rev. Lett. {\bf 91}, 252001 (2003).
\bibitem{silvia} S. Niccolai {\it et al.} (CLAS Collaboration), Phys. Rev. Lett. {\bf 97}, 032001 (2006).
\bibitem{vpk} V. Kubarovsky {\it et al.} (CLAS Collaboration), accepted by Phys. Rev. Lett., arXiv:hep-ex/0605001.
\bibitem{star} H.~Z.~Huang, Int.\ J.\ Mod.\ Phys.\ A {\bf 21}, 825 (2006).
\end{thebibliography}


\end{document}
