\documentstyle[epsfig,aps]{revtex}

\newlength{\listwidth}
\textwidth=5.75in
\textheight=8.75in
% Adjust the following two lines to center the manuscript on the page.
%can be printer configuration specific.
\voffset=+.5in
\hoffset=+0.40in

\begin{document}
%from Arie Macros
\input{arie-macros.tex}

\bigskip
\title {\bf Search for Charm, Charm-Strange and Bottom and Bottom-Strange
Pentaquark Baryons and  4-Quark Mesons in P-Pbar Collisions
at CDF}


\author{Arie Bodek, Yeon-Sei Chung, Geum Bong Yu }

\address {Department of Physics and Astronomy,
University of Rochester, Rochester, NY 14627}

\author{ Un-Ki Yang}
\address { Department of Physics and Enrico Fermi Institute, 
University of Chicago, Chicago, IL}

\author{Emails: Bodek@pas.rochester.edu, yschung@fnal.gov, 
gbyu@fnal.gov, ukyang@fnal.gov}
\address { CDF Collaboration Note 6871 B-Group. PRELIMINARY draft 1.5}





\date { February 23, 2004}


\maketitle

%\newpage

%\section*{Abstract}
\section{Abstract}
We search for exotic multiquark states using the high statistics 
charm samples taken with the  CDF RunII detector using
 the Silicon Vertex Trigger,  and final state particle ID including 
 time of flight. We investigate the following final states:
$Proton$ (or $\pi$ or K) plus $D^{-}_{s}$ (charge 0); 
$Proton$(or $\pi$ or K) plus $D^{+}_{s}$ (charge 2) mass
spectra (and corresponding antiparticles); $Proton$ (or $\pi$ or K)
plus $D^{-}$ (charge 0); 
$Proton$(or $\pi$ or K) plus $D^{+}$ (charge 2) mass
spectra (and corresponding antiparticles)
We look at states in both the  short lived (Lxy less than
100 or 700 micron) and long lived categories (Lxy greater than 700
micron).
\section{Summary} 
In order to search for exotic Pentaquark and four-quark
states with massive quarks, we need
to discover the mass range, lifetime and decay modes.
In this note, we outline the motivation and the procedure for a
search for Pentaquarks and exotic mesons. We first search for states
in the charm sector. If such states are found, the observed masses
and decay modes can be used
to predict the masses in the b sector. (We then  plan to search for
Pentquarks in the b sector). 

In the charm sector we first focus on the following final 
states (both prompt short lived and also long lived):

(a) $\Sigma^{0}_{c}$= $P^{0}_{\cbar{s}}$ =$\cbar$$suud$ (if short 
lived)
decays to ($Proton$ $D^{-}_{s}$) and  ($Anti-Proton$ $D^{+}_{s}$).
(In models which predict that Pentaquarks with both s and c quarks are
long lived, it is called the $T^{0}_{s}$ and does not decay to those channels) 


(b) $P^{++}_{\sbar{c}}$ =$\sbar$$cuud$ (if short lived) decays
to ($Proton$ $D^{+}_{s}$) and  ($Anti-Proton$ $D^{-}_{s}$).
(In models which predict that Pentaquarks with both s and c quarks are
long lived, it is called the $F^{++}$)

(c) $\Theta^{0}_{c}$ = $P^{0}_{\cbar{d}}$ =$\cbar$$duud$ (if short 
lived)  decays
to ($Proton$ $D^{-}$) and  ($Anti-Proton$ plus $D^{+}$).
(in models which predict that Pentaquarks with both s and c quarks are
long lived, this state is not stable since it does not
include  strange quarks )

(d)  $P^{++}_{\dbar{c}}$ =$\dbar$$cuud$ (if short lived) decays to
($Proton$ $D^{+}$) and  ($Anti-Proton$ plus $D^{-}$).
(in models which predict that Pentaquarks with both s and c quarks are
long lived, this state is not stable since it does not
include  strange quarks )


(e) We also plan to look for the corresponding states in the b-quark sector.

As a control sample, we use the above channels (with a proton
replaced with a pion or a kaon). This allows us to check
our procedure to to make sure that
we observed the known states  $D^{0*}$ (2460) ( a short lived
state decaying to
$\piplus$ $D^{-}$ and $\piminus$ $D^{+}$  )
as well as the $B^{0}$ and $B^{0}_{s}$ mesons (long lived
states decaying to $\pi$ $D$ or $\pi$ $D_{s}$).
In addition,
this di-meson sample can be used to look for exotic
four-quark states. For example exotic states with charm and strangeness
in the channels 
 $\piplus$ or $K^{+}$ plus $D^{-}_{s}$ (charge 0) and 
$\piminus$ or $K^{-}$ plus $D^{+}_{s}$ (charge 2).

As shown in Table 1, early chiral models predicted that Pentaquarks are very
massive and wide and difficult to see~\cite{chiral}. Some models predict that 
some are unstable, and a few 
are  narrow long-lived and very much below 
threshold~\cite{stable}. Other models predict
that the are narrow short-lived (20 MeV width) and with masses just above
threshold~\cite{heavy,Lipkin1,Lipkin2}. For example The $\Sigma^{0}_{c}$==$P^{0}_{\cbar{s}}$ =$\cbar$$sudd$ is 
estimated to be 3545 MeV in old Chiral~\cite{chiral} models and therefore very
wide.
Another state with the same quark composition 
is called the $T^{0}_{s}$ and is estimated to be 2580 MeV and stable
in the model of Stewart, Wessling and Wise~\cite{stable}. In this model, since
the mass of 2580 MeV is
much below $proton$ $D_{s}$ threshold of 2907 MeV, this
state is  long lived.

Within
the diquark model of Shuryak~\cite{heavy}  $\Sigma^{0}_{c}$ was
estimated to be just below threshold
at 2880 MeV (where it was looked for and not found ~\cite{E791} by E791).
This same state is estimated by in Lipkin's model
~\cite{heavy} to be around 3165 MeV and therefore 20 
MeV wide and above threshold.

Even within those specific models, the 
uncertainty on the predicted mass is about 100 MeV. In addition,
some models predict positive parity, and some negative parity, and some
both~\cite{spect}. If Pentaquarks exist, some models predict various higher mass
excitations~\cite{spect} of different angular momentum states (so each Pentaquark is a series 
of states). Some models predict that only a certain combination of
quarks is stable (e.g. diquarks
are not bound if there are two quarks of the same kind). All models
predict that there could be multiple closely spaced states
above threshold.

Blind searches (like E791) are very good
in setting good limits on particles within a specific model (or looking
for rare decay mode where we know where to look).
However, no new particle has ever been discovered using 
a blind search.   Therefore,  we first do a general search  using
cuts which are based on general physics arguments and are not
dependent on the parity,  spin and mass within
any specific model.
We plan to look at each of the regions in sequence since
each mass region implies different width/lifetime and different
final state decay modes.

We start with a search for narrow states 
(20 MeV wide states) just above threshold, as well as wider
states at higher masses (which would occur as higher
angular momentum spin or radial excitations). 
This mas region region is favored by the 
the constituent diquark-triquark model. 
Within the Lipkin diquark-triquark Pentaquark model we estimate the mass region
that is of interest by assuming that the newly  reported state  
$\Theta^{+}_{\sbar}$(1540) is the 
$\sbar$$uudd$ Pentaquark state.   Using this we 
estimate the following masses for Charm Pentaquarks:


(a)  We use Huang estimate using Likpkin's model of 3165 MeV for
$\Sigma^{0}_{c}$.
(We then correct it since it overestimates the $\Theta_{c}$
(1540) to be 1592 MeV). Therefore, we estimate that
the $\Sigma^{0}_{c}$=$P^{0}_{\cbar{s}}$ =$\cbar$$sudd$ should
is around 3120 MeV and decay to Proton plus $D^{-}_{s}$ (and the corresponding 
antiparticle);

(b) We estimate that (if it exists) the 
$P^{++}_{\sbar{c}}$ =$\sbar$$cudd$ may
be around 3200 MeV and decay to Proton plus $D^{+}_{s}$ (and the corresponding 
antiparticle); 

(c) Using Huang and Cheung we estimate that the 
$\Theta^{0}_{c}$ = $P^{0}_{\cbar{d}}$ =$\cbar$$duud$ should
be around 2980 MeV and decay to Proton plus  $D^{-}$ (and the corresponding 
antiparticle);

(d)  We estimate that if it exists, that the $P^{++}_{\dbar{c}}$ =$\dbar$$cuud$ should
be around 3060 MeV and decay to Proton plus $D^{+}$ (and the corresponding 
antiparticle).  


We investigate states in both the  short lived and long lived categories.

If the above indication is confirmed in the Charm sector, then one 
could   estimate the following masses for the corresponding Pentaquark
states in the b sector:  

(a)  The $\Theta^{+}_{b}$=$P^{+}_{\bbar}$ =$\bbar$$uudd$
(and the corresponding 
antiparticle)
is estimated by Lipkin to be be around 6400 MeV  ;

(b) The $\Sigma^{+}_{b}$= $P^{+}_{\bbar{s}}$ =$\bbar$$sudd$ 
(and the corresponding 
antiparticle)
is estimated by Lipkin to be at 6570 MeV (this is close to our estimate
in the appendix that it should be around 6535 MeV).

Since these particular two body final
state decay channels and mass regions appear to be 
promising, we are doing detailed analysis including both
a side band analysis, and several decay modes of charm mesons.

\newpage

\begin{table}
    %[th]
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
    $compos.$ & $Mass1$ & $Mass2$ & $Mass3$ &
    $Mass4$ & $Mass5$ & $Mass6$ & $mass7$  & $thresh$ \\
    \hline
$names$ & $1chiral97$ & $2cheung$ & $3Lipkin$ &
    $4Jaffe$ & $5Shuryak$ & $6stable$ &  $7lattice$ & $Decay $ \\
\hline $charge$ & $Genovese$ & $diquark04$ & $Huang04$ &
    $  Huang04$ & $Huang04$ & $steward04$ &  $Sasasi03$& $mode$  \\
\hline
\hline
    ${\bf{uudd}\sbar }$(+)  & $NA$ &  $1562-$ & $1592$ &
    $$ & $$ & $1540$ &   $1760$& $1433.2$  \\
      ${\bf{\Theta^{+}_{s}1540}}$  & $P^{+}_{\sbar}$ &  $-1481$ & $-42=1540 $ &
    $  $ & $$ & $$ &  $-200=1540 $ & $n K^{+}$  \\ 
\hline
\hline
    ${\bf{uudd}\cbar }$(0)  & $3607$ &   $2997-$ & $2990$ &
    $  2710$ & $2700$ & $unstable$ &  $3576$& $2807$  \\ 
           ${{\Theta^{0}_{c}}}$  & $P^{0}_{\cbar}$ &  $2938$ & $-42=2950 $ &
    $  $ & $$ & $Look->$ &  $-200=3376$& $P$ $D^{-}$  \\ 
    ${uudd}\bbar $(+)  & $6889$ &   $6422-$ & $6400$ &
    $6050$ & $6040$ & $unstable$ &  $$& $6219$  \\ 
               $\Theta^{+}_{b}$  & $P^{+}_{\bbar}$ &  $-6370$ & $Lipkin$ &
    $Jaffe  $ & $Shuryak$ & $Stewart$ &  $Sasasi$&   $P$ $B^{0}$  \\ 
 \hline
  \hline
${\bf{uusd}\cbar }$(0)  & $3545$ &   $ $ & $3165$ &
    $  2870$ & $2880$ & $2580$ &  $$ & $2907$  \\ 
               ${\bf{\Sigma^{0}_{c}}}$  & $P^{0}_{\cbar s}$ &  $$ & $-42=3123 $ &
    $  $ & $$ & $T^{0}_{s}$ &  $Look->$& $P$ $D^{-}_{s}$  \\ 
    ${uusd}\bbar $(+)  & $6827$ &   $$ & $6570$ &
    $6210$ & $6220$ & $5920$ &  $$& $6349$ \\ 
                 $\Sigma^{+}_{b}$  & $P^{+}_{\bbar s}$ &  $Cheung$ & $Lipkin $ &
     $Jaffe  $ & $Shuryak$ & $Stewart$ &  $Sasasi$&  $P$ $B^{0}_{s}$  \\ 
\hline  
    ${udsd}\cbar $(-)  & $3545$ &   $$ & $3165$ &
    $ 2870$ & $2880$ & $2580$ &  $$& $3057$  \\ 
               $\Sigma ^{-}_{c}$  & $P^{-}_{\cbar{s}}$ &  $$ & $-42=3123 $ &
    $  $ & $$ & $T^{0}_{s}$ &  $$& $N$ $D^{-}_{s}$  \\ 
    ${udsd}\bbar $(0)  & $6827$ &   $$ & $6570$ &
    $ 6210$ & $6220$ & $5920$ &  $$& $6309$ \\
                  $\Sigma^{0}_{b}$  & $P^{0}_{\bbar {s}}$ &  $Cheung$ & 
                  $Lipkin $ &
      $Jaffe  $ & $Shuryak$ & $Stewart$ &  $Sasasi$&  $N$ $B^{0}_{s}$  \\ 
\hline
\hline
${udss}\cbar $(-)  & $3630$ &   $$ & $3340$ &
    $3135$ & $3060$ & $2770$ &  $$& $3084$ \\ 
                   $\Xi^{-}_{c}$  & $P^{-}_{\cbar{ss}}$ &  $$ & 
                   $-42=3298 $ &
    $  $ & $$ & $T^{-}_{ss}$ &  $$& $\Lambda^{0}_{s}$ $D^{-}_{s}$  \\  
   ${udss}\bbar $(0)  & $6911$ &   $$ & $6740$ &
    $6475$ & $6400$ & $6100$ &  $$& $6485$  \\ 
                      $\Xi^{+}_{b}$  & $P^{+}_{\bbar {s}}$ &  $$ & $ $ &
    $$ & $$ & $R^{0}_{ss}$ &  $$ & $\Lambda^{0}_{s}$ $B^{0}_{s}$  \\ 
\hline
 ${uuss}\cbar $(0)  & $$ &   $$ & $3340$ &
    $ $ & $$ & $unstable$ &  $$ & $$  \\ 
                   $\Xi^{0}_{c}$  & $P^{0}_{\cbar{ss}}$ &  $$ & $-42=3298 $ &
    $$ & $$ & $$ &  $$& $$  \\  
   ${uuss}\bbar $(0)  & $$ &   $$ & $6740$ &
    $$ & $$ & $unstable$ &   $$& $$  \\ 
                      $\Xi^{+}_{b}$  & $P^{+}_{\bbar{ss}}$ &  $Cheung$ & $Lipkin $ &
     $Jaffe  $ & $Shuryak$ & $Stewart$ &  $Sasasi$& $$  \\
\hline
 ${ddss}\cbar $(--)  & $$ &   $$ & $3340$ &
    $$ & $$ & $unstable$ &  $$& $$ \\ 
                   $\Xi^{--}_{c}$  & $P^{--}_{\cbar{ss}}$ &  $$ & 
                   $-42=3298 $ &
    $  $ & $$ & $$ &  $$& $\Sigma^{-}_{s}$ $D^{-}_{s}$  \\  
   ${ddss}\bbar $(-)  & $$ &   $$ & $6740$ &
    $$ & $$ & $unstable$ &   $$& $6559$  \\ 
                      $\Xi^{-}_{b}$  & $P^{-}_{\bbar{ss}}$ &  $$ & $ $ &
    $$ & $$ & $$ &  $$& $\Sigma^{+}_{s}$ $B^{0}_{s}$  \\ 
\hline
\hline
${usss}\cbar $(-)  & $3940$ &   $$ & $$ &
    $$ & $$ & $unstable$ &  $$& $$  \\
                   $$  & $P^{-}_{\cbar{ss}}$ &  $$ & $ $ &
    $  $ & $$ & $$ &  $$& $\Xi$ $D^{-}_{s}$  \\  
       ${usss}\bbar $(+)  & $7223$ &   $$ & $$ &
    $$ & $$ & $unstable$ &  $$& $$ \\ 
                    $$  & $P^{+}_{\bbar{sss}}$ &   $Cheung$ & $Lipkin $ &
     $Jaffe  $ & $Shuryak$ & $Stewart$ &  $Sasasi$& $\Xi$ $B^{0}_{s}$  \\ 
\hline
\hline
${dscd}\ubar $(-)  & $$ &   $$ & $$ &
    $$ & $$ & $stable?$ &  $$& $$  \\
  $$  & $P^{-}_{\ubar{cs}}$ &  $$ & $ $ &
     $  $ & $$ & $F^{-}_{s}$ &  $$& $$  \\ 
\hline
     ${sucu}\dbar $(++)  & $$ &   $3460,3541$ & $v.narrow$ &
    $\Lambda^{+}_{c}K^{-}\piplus\piplus$ & $maybe(ccu)$ & $stable?$ &  $$& $$  \\
  $SELEX?$  & $P^{++}_{\dbar{cs}}$ &  $3780$ &$26MeVwide $ &
     $ seen? $ & $maybe(ccu*)$ & $F^{++}_{s}$ &  $$& $\Sigma^{+}_{s}$ $D^{+}$  \\ 
\hline
     ${dscs}\ubar $(-)  & $$ &   $$ & $$ &
    $$ & $$ & $stable?$ &  $$& $$  \\
  $$  & $P^{-}_{\ubar{css}}$ &  $$ & $ $ &
     $  $ & $$ & $F^{-}_{ss}$ & $$ & $$  \\
\hline
          ${uscs}\ubar $(+)  & $$ &   $$ & $$ &
    $$ & $$ & $stable?$ &  $$& $$  \\
  $$  & $P^{+}_{\ubar{css}}$ &  $$ & $ $ &
     $  $ & $$ & $F^{+}_{ss}$ &  $$& $$  \\
     \hline
               ${\bf{udcu}\sbar }$(++)  & $$ &   $$ & $3200$ &
    $$ & $$ & $stable?$ &  $$& $2906$  \\
  $$  & ${{P^{++}_{\sbar{c}}}}$ &  $$ &$Bodek$   &
     $  $ & $$ & $F^{++}_{}$ &  $Look->$& $P$ $\Dsp$  \\
\hline
                   ${udcd}\sbar $(+)  & $$ &   $$ & $$ &
    $$ & $$ & $stable?$ &  $$& $2906$  \\
  $$  & $P^{+}_{\sbar{c}}$ &  $$ & $ $ &
     $  $ & $$ & $F^{+}_{}$ &  $$& $N$ $\Dsp$  \\
\hline
 \hline
              ${\bf{udcu}\dbar (++)}$  & $$ &   $$ & $3060$ &
    $$ & $$ & $unstable$ &  $non-exotic$& $2807$  \\
  $ucu(also)$  & ${P^{++}_{\dbar{c}}}$ &  $$ &$Bodek$   &
     $  $ & $$ &  &  $Look->$& $P$ $D^{+}$  \\ 
 \hline
      ${sucd}\dbar $(+)  & $$ &   $3443,3520$ & $v.narrow$ &
    $\Lambda^{+}_{c}K^{-}\piplus$ & $maybe(ccd)$ & $unstable?$ &  $$& $$  \\
  $SELEX?$  & $P^{+}_{\dbar{cs}}$ &  $$ &$$ &
     $ seen? $ & $maybe(ccd)$ & $$ &  $$& $\Lambda^{0}_{s}$ $D^{+}$  \\ 
\hline
\end{tabular}
\caption{Pentaquark states in various theoretical models.}
\label{table0}
\end{center}
\end{table}




 
 \begin{figure*}[htb]
\centerline{\psfig{figure=sbartable,width=3.0in,height=3.0in}}
    \caption[diagram ]
     { Quantum numbers of strangeness +1 (anti-strange) Pentaquarks
    ( Brian G. Wybourne hep-ph/0307170, note that there
    is mistake in this table and the $uudd\sbar$
    state has $I_{z}$ of zero (and not 2 as shown))}
\label{tablesB}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=lowesttable,width=4.in,height=3.5in}}
    \caption[diagram ]
    { Quantum numbers of lowest lying Pentaquark states
    (from Brian G. Wybourne hep-ph/0307170)}
\label{tablesA}
\end{figure*}

 \begin{figure*}[htb]
\centerline{\psfig{figure=strangePenta.eps,width=6.in,height=3.0in}}
\caption[diagrams]
{ Diagram of Pentaquark low lying Pentaquark
states as proposed originally by
Polyakov hep-ph/9703372. Only the three states
 in the corner are exotic. Note that the best estimate of
 these masses in 2004 is that the Z(1530) is at 1540 MeV,
 the N(1710) is at 1650 MeV, the $\Sigma$ (1890) is at 1750 MeV
 and the $\Xi$ (2070) is either at 1780 or 1869 MeV.
The state with one anti-strange quark (top 
corner)is exotic.  The two states in the bottom 
corners are exotic.}
\label{diagrams}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=group.eps,width=6.in,height=3.0in}}
\caption[diagrams]
{ Quark assignments of lowest lying Pentaquark multiplet.
Note that there
is mistake in this figure and the bottom right
hand corner should be a $uuss\dbar$
state (not $uuss\ubar$). (from  Brian G. Wybourne hep-ph/0307170)
The state with one anti-strange quark (top 
corner)is exotic.  The two states in the bottom 
corners are exotic.}
\label{diagrams1}
\end{figure*}




 \begin{figure*}[htb]
\centerline{\psfig{figure=charmPenta.eps,width=6.in,height=3.0in}}
    \caption[diagram ]
    {Diagram of Pentaquark states with one anticharm quark.
     Not shown are states with a bottom quark (e.g. instead of a strange quark) 
     which may
     also be possible; or states with an antibottom antiquark instead
     of anticharm.  Figure from Cheung, hep-ph/0308176)}
\label{diagram}
\end{figure*}

 \begin{figure*}[htb]
\centerline{\psfig{figure=dse791.eps,width=6.in,height=4.0in}}
    \caption[e791]
    {E791 Ds mass peak used for their search for Pentaquarks}
\label{e791A}
\end{figure*}

 \begin{figure*}[htb]
\centerline{\psfig{figure=pentae791.eps,width=6.in,height=4.0in}}
    \caption[e791]
    { E791 Blind analysis for long lived Pentaquarks with
     a mass of 2.8 GeV}
\label{e791B}
\end{figure*}



\section{Introduction}

Recently, there have been number of reports of exotic 5-quark 
baryons~\cite{pentaq} (Pentaquarks) and  four-quark 
mesons~\cite{babar,belle}. The  first Pentaquark that was reported
reported consists of four light quarks and one anti-strange quark.
This $\Theta^{+}_{\sbar}$(1540) state has been identified with  
$\sbar$$uudd$ 5-quark combination as shown in  the top
corner of Fig.~\ref{diagrams}


The
anti-strangeness is what makes this  particular Pentaquark an exotic state. 
It is possible that there are other
anti-stange Pentaquarks that include an $\sbar$
with the four-quark combinations (uuuu, uuud, uudd, uddd and dddd). If such
states exist, then one expects corresponding states in the anticharm, 
anticharm-strange, and 
charm-antistrange sectors and similarly in the bottom quark sector.
For example in the 
anticharm
sector one could have a $\cbar$ with a (uuuu, uuud, uudd, uddd and dddd) 
as shown in Fig.~\ref{diagram}.
In the antistrange-charm sector one expects a $\sbar$$c$ pair with a
(uuu, uud, udd and ddd) combinations.  We therefore begin
our search with the $D_{s}$ sample, as described below.  If there are
any Baryons with either antistrange or anticharm quantum numbers,
they would be considered exotic.

In addition, there have been two recent reports of
four-quark states~\cite{babar,belle}.
One of them
is the exotic $\Dsp$(2317) reported by the BaBar collaboration (a narrow 
state decaying into a $\Dsp$ and a $\pizero$).
If this state is a $c\sbar({u}\ubar{d}\dbar)$(+) four quark exotic 
state, then there could be analogous states
	$c\sbar{d}\ubar$(0) ($2325$ ??)  decaying to  $\Dsp \piminus $  or
	$c\sbar{u}\dbar$(++)( $2325$ ??) decaying to  $\Dsp \piplus$.
We therefore also search for these charged analogue 
states decaying into $D_{s}$ mesons in combination with charged pions and 
kaons.

 \begin{figure*}[htb]
\centerline{\psfig{figure=dspizero.eps,width=6.in,height=6.0in}}
    \caption[ ]
    { This figure taken from the BaBar paper on the $\Dsp$(2317) 
    in the ($\Dsp$ $\pizero$) final state.
    If this state is a $c\sbar({u}\ubar{d}\dbar)$(+) four-quark exotic 
state, then there could be analogous states
	$c\sbar{d}\ubar$(0) ($2325$ ??)  decaying to  $\Dsp \piminus $  or
	$c\sbar{u}\dbar$(++)( $2325$ ??) decaying to   $\Dsp \piplus$.
We therefore also search for these charged analogue 
states decaying int $D_{s}$ mesons in combination with charged pions and 
kaons.
    }
\label{belle}
\end{figure*}


Since the $D_{s}$ sample contains also Cabbibo suppressed charged D decays,
we also use the D meson Cabbibo suppressed events to check our procedure 
and 
normalize to known decay modes of  $B^{0}$ (long lived), and 
$D^{0*}$(2460) (short lived)  mesons which decay
to  $D^{+}$ plus a $\piminus$. 
In addition, we also check that our samples show the
known $\Dsp$ plus $\piminus$ decays of the  both the $B^{0}$ and 
$B_{s}$  long lived mesons.

Therefore, the di-meson samples should have both  
 short-lived known states
 and well as known long lived states to provide checks on the
 search procedure, and a normalzation sample.

\subsection{Recent Limits and models}

It is expected that in bound
hadrons (including Pentaquarks), the constituent mass of the 
light quarks (e.g. up, down, strange) is reduced in the presence of 
heavyier quarks (e.g. strange, charm, bottom). Therefore, 
the initial predictions for Pentaquark states
stated that Pentaquarks were long
lived (because the mass could be below threshold for a strong decay).
Based on the prediction of 
severalsuch  models, the E791 collaboration~\cite{E791} searched for 
a long lived   $\Sigma^{0}_{c}$=$P^{0}_{\cbar{s}}$ =$\cbar$$sudd$ in 
the interactions of 500 GeV negative pions with nuclear targets. No
such Pentaquarks were found (assuming a lifetime of 0.4 ps and masses
between 2.75 and 2.91 GeV).  The decay mode that was assumed was
a proton and a virtual (below threshold) $D_{s}$  (i.e. a $K^{*0}$ $K^{-}$ 
$proton$ final state).  This was a blind search that masked this
region and looked for long lived (stable) Pentaquarks predicted to be 2.88 GeV
(by Shuryak and Zahed), 2.87 GeV by Jaffe and Wilcek. The E791
results are shown in the  Fig.~\ref{e791A} and Fig.~\ref{e791B}.

In contrast, the recently observed Pentaquark state in the 
antistrange sector is above threshold
for hadronic decays is short lived with a width of 20 MeV (e.g. 
the $\Theta^{+}_{\sbar}$(1540) resonance).  
Such a narrow width can be explained by an 
isopspin-violating hadronic decay (for states above threshold).

Therefore, now that the $\Theta^{+}_{\sbar}$(1540) mass
is known, 
a recent calculation using
a model by Lipkin (see hep-ph/040119) indicates that the Pentaquark
state which includes both strange and charm quarks
 $\Sigma^{0}_{c}$= $P^{0}_{\cbar{s}}$ =$\cbar$$sudd$ 
 should be short lived (with a width of 20 MeV) and at a mass
 of 3.165 GeV (i.e. above threshold for strong decays)
 (Since this same model
 also predicts that the state found
 at 1540 should be at 1592, we think that the $\Sigma^{0}_{c}$
 may be about 3123 Mev). In
 addition, the same model predicts that
 there should be also charm Pentaquark without
 strangeness at a mass of 2990 MeV. 
 
 On the
 other hand Stewart, Wessling and Wise (hep-ph/0402076) assert
 that although the $\Theta^{+}_{\sbar}$(1540) resonance is
 above threshold and wide, the situation is much different
 when a charm quark is in the picture. This paper claims that
 , E791
 did a blind analysis in the wrong mass region (2800).
 Using the mass of the $\Theta^{+}_{\sbar}$(1540)
they predict that the  
$\Sigma^{0}_{c}$= $P^{0}_{\cbar{s}}$ =$\cbar$$sudd$ state
should be long lived and stable with a mass of 2580 MeV.
In their model, only state which have BOTH charm and strangeness
are stable. Therefore, a charm Pentaquark without strangeness
is not stable in this particular model.

In contrast to the stable model, a lattice QCD calculation
by Sasaki (hep-lat/0310014) gets a mass of 1760 for the
$\Theta^{+}_{\sbar}$(1540) if it is negative
parity and 2620 if it is positive parity.
The same lattice calculation for the  $\Theta^{0}_{\cbar}$
(negative parity) yields a mass of 3578.  More refined lattice calculations
which first agree with the measurement of 1540 are needed.


To date, we have not found any published searches (in journals
or conference proceedings) for above threshold narrow short lived
(20 MeV width) Pentaquark
states in the charm, charm-strange and bottom sectors. We have been 
told that some there were some low
statistics unpublished searches by  experiments E400~\cite{e400} and 
SELEX~\cite{selex} at Fermilab. However, SELEX~\cite{selex}
has reported some states that could be interpreted
as a Pentaquark. First they see two narrow(++)  states and one 
wider (++)
state in the $\Lambda_{c} {K^{-}} \piplus \piplus$ which have
the quantum numbers of  a $\dbar {cusu}$(++) Pentaquark.  The charge
2 baryon states that were observed by Selex are at 3460 MeV and 3541 MeV 
(narrow) and at 3780 MeV (with a width of 26 MeV).  
If not identified as exotics, then these
states may be related to  $ccu++$ and $ccu*++$ baryons. 
Secondly,  they also see two narrow states
states in the $\Lambda_{c} {K^{-}}  \piplus$ which have
the quantum numbers of  a $\dbar {cdsu}$(+) Pentaquark.  The charge 1 
baryon
states that were observed by Selex are at 3443 MeV and 3520 MeV.  
If not identified as exotics, then these
states may be related to  $ccd+$ and $ccd*+$ baryons.


\begin{figure*}[htb]
\centerline{\psfig{figure=selex2002.eps,width=6.in,height=6.0in}}
    \caption[selex 2002 ]
    {Select 2002 Data and 2003 data (next figure):  SELEX
has reported some states that could be interpreted
as a Pentaquark. First they see two narrow(++)  states and one 
wider (++)
state in the $\Lambda_{c} {K^{-}} \piplus \piplus$ which have
the quantum numbers of  a $\dbar {cusu}$(++) Pentaquark.  The charge
2 baryon states that were observed by Selex are at 3460 MeV and 3541 MeV 
(narrow) and at 3780 MeV (with a width of 26 MeV).  
If not identified as exotics, then these
states may be related to  $ccu++$ and $ccu*++$ baryons. 
Secondly,  they also see two narrow states
states in the $\Lambda_{c} {K^{-}}  \piplus$ which have
the quantum numbers of  a $\dbar {cdsu}$(+) Pentaquark.  The charge 1 
baryon
states that were observed by Selex are at 3443 MeV and 3520 MeV.  
If not identified as exotics, then these
states may be related to  $ccd+$ and $ccd*+$ baryons.}
\label{selex2002}
\end{figure*}

 \begin{figure*}[htb]
\centerline{\psfig{figure=selex2003.eps,width=6.in,height=6.0in}}
    \caption[Mx0-baryon long]
    {Selex 2003 data (and 2002 data previous figure):
     SELEX~\cite{selex}
has reported some states that could be interpreted
as a Pentaquark. First they see two narrow(++)  states and one 
wider (++)
state in the $\Lambda_{c} {K^{-}} \piplus \piplus$ which have
the quantum numbers of  a $\dbar {cusu}$(++) Pentaquark.  The charge
2 baryon states that were observed by Selex are at 3460 MeV and 3541 MeV 
(narrow) and at 3780 MeV (with a width of 26 MeV).  
If not identified as exotics, then these
states may be related to  $ccu++$ and $ccu*++$ baryons. 
Secondly,  they also see two narrow states
states in the $\Lambda_{c} {K^{-}}  \piplus$ which have
the quantum numbers of  a $\dbar {cdsu}$(+) Pentaquark.  The charge 1 
baryon
states that were observed by Selex are at 3443 MeV and 3520 MeV.  
If not identified as exotics, then these
states may be related to  $ccd+$ and $ccd*+$ baryons.}
\label{selex2003}
\end{figure*}





Note that it is also expected (e.g. in the model of Stewart et al.) 
that bottom Pentaquark states should decay into charm Pentaquark
states. Therefore, if by accident, the bottom pentaquarks are long
lived and decay to short lived charm Pentaquarks, then one
would have a state with a width of 20 MeV, but with a displaced
vertex. Therefore, a-priori we need to look at all these 
options. OPbservation of one of these possible new states
will greatly help narrow down the range of possible options.

Therefore, we take the approach that we do not know where Charm
Petaquark states should exit. Table 1 below shows the range
of predictions in various models. Therefore, to do a search
one needs to look in a wide mass range, in different decay
modes, and look for both short lived and long lived states. As a check
on various biases, we make sure that in the sample, we optimize cuts
on states which are known to exit. As a furtrher, if any state is
observed we then search for it
in different decay modes.

\begin{figure*}[htb]
\centerline{\psfig{figure=soliton-statefig.eps,width=6.in,height=3.0in}}
    \caption[ ]
    {Figure from rom hep/0304058 Walliser and Kopeliovich  - Soliton states for 
    lowest level strange pentaquarks for two different models 
    assumptions. We use model B in our estimates of state mass splittigs.}
\label{soliton-state}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=soliton-table.eps,width=6.in,height=3.0in}}
    \caption[ ]
    {Table from hep/0304058 Walliser and Kopeliovich  - Soliton states for 
    lowest level strange pentaquarks for two different models 
    assumptions. We use model B in our estimates of state mass splittigs.}
\label{soliton-table}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=soliton-figure.eps,width=6.in,height=3.0in}}
    \caption[ ]
    {Figure from hep/0304058 Walliser and Kopeliovich  - Soliton 
    multiplets for 
    lowest level strange pentaquarks.}
\label{soliton-figure}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=ellis-soliton.eps,width=6.in,height=4.0in}}
    \caption[ ]
    {Mass levels from the soliton model of Ellis.  for 
    lowest level strange pentaquarks. It is similar to model B of
     hep/0304058 Walliser and Kopeliovich, except that 
     Ellis constrains the double strange state at 1750 Mev at the
     Walliser model to be at 1860 MeV, under the assumption that
     the NA49 state is a pentaquark}
\label{ellis-soliton}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=slide4.eps,width=6.in,height=6.0in}}
    \caption[ ]
    {Mass values of the lowest lying pentaquark multiplet
    with strange quarks within the soliton model.
    We use the second number which is  model B of
     hep/0304058 Walliser and Kopeliovich. The model of Ellis gets
     similar results except that
     Ellis constrains the double strange state at 1750 Mev at the
     Walliser model to be at 1860 MeV, under the assumption that
     the NA49 state is a pentaquark}
\label{slide4}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=slide5.eps,width=6.in,height=6.0in}}
    \caption[ ]
    {Mass value of the second lowest lying pentaquark multiplet
    with strange quarks within the soliton model.
    We use the second number which is  model B of
     hep/0304058 Walliser and Kopeliovich
     and compare it to the values from the soliton model of Ellis}
\label{slide5}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=slide6.eps,width=6.in,height=6.0in}}
    \caption[ ]
    {Mass value of the third lowest lying pentaquark multiplet
    with strange quarks within the soliton model.
    We use the second number which is  model B of
     hep/0304058 Walliser and Kopeliovich}
\label{slide6}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=slide7.eps,width=6.in,height=6.0in}}
    \caption[ ]
    {Predictions of the model of Lipkin for the
 lowest lying multiplet of pentaquarks which include
 one heavy (charm or bottom) antiquark.}
\label{slide7}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=pentaxls.eps,width=6.in,height=6.0in}}
    \caption[ ]
    {Combining the predictions of the model of Lipkin for the
 lowest lying multiplet of pentaquarks which include
 one heavy (charm or bottom) antiquark, with the spectrum
 of the strange-antiquark pentaquarks to get a mass estimate
 of higher level exitation of pentaquark states which
 contain at least one heavy antiquark. }
\label{pentaxls}
\end{figure*}


\section{Multiple States are Expected}

We now show that multiple pentaquarks are expected for every quark
combination. Therefore, even if there are stable long lived 
pentaquarks, it is expected that there are higher level excitation,
and there can be some which are very close to each other in mass,
and others which are not.


Fig.~\ref{soliton-state} and Fig.~\ref{soliton-table} shows the predicted states for the lowet lying
strange Pentaquark states within the soliton model of Walliser and 
Kopeliovich (hep/0304058) for the first three multiplets. As shown in
Fig.~\ref{soliton-figure} the states are similar to those of the
constituent quark model.  Fig.~\ref{ellis-soliton} shows how the masses
change within the soliton model of Ellis (hep-ph/0401127) 
for which the $\Xi_{3/2}$ is constrained to 
be at a mass of 1860 Mev (which assumes that the state published by
NA49, but not confirmed by CDF is a pentaquark). 
Fig.~\ref{slide4} shows the masses within the soliton model for
the first multiplet. Figure 
Fig.~\ref{slide5} shows the masses for the second multiplet and
Fig.~\ref{slide6} shows the masses for the third multiplet.

Fig.~\ref{slide7} show the lowest lying multiplet within the model
of Lipkin for Pentaquarks with charm and bottom quarks.   Figure
Fig.~\ref{pentaxls} shows a spreadsheet which assumes that
the level spacing for the Pentaquarks in the strange quark multiplets
are similar to the level spacing in the charm and bottom sector.  
We also assume that the $\Theta_{s,0,1,2}$ Pentaquarks
occur at 1540, 1597 (spin 3/2 second multiplet) and 1960 MeV.
We assume that the lowest level $\Theta_{c}$ and $\Theta_{b}$
Pentaquarks are at 2950 and 6350 MeV, respectively (we lower all values by
50 MeV from Lipkins predictions since his model predicts
1590 instead of 1540 for the $\Theta_{s}$).
Similarly, we assume that the $\Sigma_{5c}$ and $\Sigma_{5b}$
Pentaquarks 
are at 3125 and 6530 MeV, respectively, and the
 $\Xi_{5c}$ and $\Xi_{5b}$ are at 3310 and 6700, respectively.


 Using the above information
one expects  $\Theta_{c,0,1,2}$ Pentaquarks at 2950, 3007 and 3370 MeV and
 $\Theta_{b,0,1,2}$ states at 6350, 6407 and 6770 MeV.  Similarly
 if the $\Sigma_{5s}$ states are at 1750, 1695 and 1900 MeV in
 the strange sector, then one expects the charm-strange 
 $\Sigma_{5c,0,1,2}$
 pentaquarks to be at 3125, 3070 and 3275 MeV and the
 bottom-strange  $\Sigma_{5b,0,1,2}$
 Pentaquarks to be at 6530, 6475 abd 6680 MeV.
 
 Since all of these multiple states have different spins and
 parity, one expects to see different peaks at different masses
for different decay channels for Pentaquark states which have the same
quark composition. The above scenario shows that there could
be states which are very close to each other in mass.




\section{Procedure}

A first look at the following Data Set:

We use the Two Track Trigger with:  dataset-hbot1i; 
stripping-4.8.4; alignment is with ofotl-prd-read 100040 1 good.
The run range is 152598�168889 with about 162 pb (good runs only).


$D_{s}$ cuts: Use $D_{s}$ to $\phi\pi$ decy mode with $\phi$ to $KK$.
The $K^{-} \piplus$ form a trigger pair. We require a $K K$ mass 
between 1.0 and 1.04 GeV. The transverse momentum of the $D_{s}$ is
required to be greater than 6.0 GeV.  The Lxy of the $D_{s}$ is
greater than 500 micron. The DeltaZ0 between the two tracks is
required to be less than 5 cm. The $d0_{track}$ is required to be
greater than 0.012 cm and less than 0.1 cm. The PT of the offline 
tracks is required to be greater than 0.5 GeV.  the PT(SVT Matched 
Tracks) is required to be greater than 2.0 GeV. The Chi-squared
is less than 30 for the three vertex fit. (later we plan to remove 
events with a cosine of the angle between the $D_{s}$ and the Kaon 
in the $\Phi$ rest
frame less than 0.4 as done in the $D_{s}$  Phys. Rev. D article
to lower the background, but have not done this yet).

Proton (and Antiproton) selection:  The PT of the proton is required 
to be greater than 3 GeV.  The SVX phi side hits is required to be
greater than 2. The COT (axial and stereo hits) are required to
be more than 25.  The PId (TOF and dEdX) is require to be Proton
versus pion.  The Cos($\theta{*}$) is required to be less than
0.9 (where $\theta{*}$ is the angle between the momentum
of the Pentaquarks and the Proton track at the Pentaquark
rest frame.  The $P_{balance}$ = (p(Ds)-p(proton)/p(Ds+proton) is 
required to be less than 0.8.

In parallel we are re-processing the first 200 pb-1 of
data to do the following: 
(a) Side band subtractions, (b) Additional Ds decay mode to (K 
K+*(892). (c) reduce PT cuts on $D_{s}$ and Proton to increase
statistics. (d) Remove 
events with a cosine of the angle between the $D_{s}$ and the Kaon in the $\Phi$ rest
frame less than 0.4 as done in the $D_{s}$  Phys. Rev. D article.
(e) Look the other Pentaquark channels (e.g. in the Proton $D^{+}$,
Proton $D^{-}$,Proton $D^{0}$).

In addition, we are also doing the 4-quark exotic search described
above (which is also to check on our efficiency by 
making sure that we observe the known decays of $D*$ and neutral B
mesons. We look for exotic
four-quark states with charm and strangeness in the channels
 $meson+$ plus $D^{-}_{s}$ (charge 0) and 
$meson-0$ plus $D^{+}_{s}$ (charge 2).

\begin{figure*}[htb]
\centerline{\psfig{figure=PhiPi_mass_2.5MeV.eps,width=6.in,height=3.0in}}
    \caption[ ]
    {$\phi\pi$ mass plot showing both $D^{+}_{s}$ and $D^{+}$ (Cabbibo
    suppressed mass peaks.})
\label{phi-pi}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=KstarK_mass_2.5MeV.eps,width=6.in,height=3.0in}}
    \caption[ ]
    {$K K^{*}$ mass plot showing both $D^{+}_{s}$ and $D^{+}$ (Cabbibo
    suppressed mass peaks.})
\label{KKS}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=K2pi_mass_2.5MeV.eps,width=6.in,height=3.0in}}
    \caption[ ]
    {$K \pi \pi $ mass plot showing the $D^{+}$ peak}
\label{K2p}
\end{figure*}




 \begin{figure*}[htb]
\centerline{\psfig{figure=PentaQuark_right.eps,width=6.in,height=3.0in}}
    \caption[Mx0-baryon ]
    {Short Lived (Lxy less than 500 micron) Charge 0 Baryon Pentaquark Search: $proton$ plus  $\Dsm$ (and $antiproton$ plus $\Dsp$) mass plot using
      the $D_{s}$ to $\phi \pi$ decay mode only. Here we are looking for a
      $P^{0}_{\cbar{s}}$ =$\cbar{sudd}$ Pentaquark at an expected mass of 3100 MeV. 
       There is an indication of a peak around this mass value which 
       we are investigating. We are currently 
 also running the $KK*$ spectrum as an independent sample.}
\label{baryon0}
\end{figure*}

 \begin{figure*}[htb]
\centerline{\psfig{figure=PentaQuark_wrong.eps,width=6.in,height=3.0in}}
    \caption[Mx0-baryon ]
    { Short Lived (Lxy less than 500 micron) Charge +2 and -2 Baryon Pentaquark Search: $proton$ plus $\Dsp$ 
    (and $antiproton$ plus $\Dsm$) mass plot using
      the $D_{s}$ to $\phi \pi$ decay mode only.
      Here we are looking for a $P^{++}_{\sbar{c}}$ =$\sbar{cudd}$
      Pentaquark at an expected mass of 3220. There is an indication of a peak around this mass value which 
       we are investigating. We are currently 
 also running the $KK*$ spectrum as an independent sample.
}
\label{baryon2}
\end{figure*}

\section{Initial results and future plans}
 
 We form the $\phi\pi$ invariant mass and the  
 invariant mass plots that show the $D_{s}$  peak and the Cabbibo suppressed 
 $\Dp$ peak (as shown in Fig.~\ref{phi-pi}).  We are currently 
 also running the $KK*$ spectrum as an independent sample.
 
 We look for both short lived (Lxy less than 500 microns)
 and long lived (Lxy greater than 500 microns) particles.
 


\begin{figure*}[htb]
\centerline{\psfig{figure=pq_rightsign_gt500.eps,width=6.in,height=3.0in}}
    \caption[Mx0-baryon long ]
    {Long Lived (Lxy greater than 500 micron) Charge 0 Baryon Pentaquark Search: $proton$ plus  $\Dsm$ (and $antiproton$ plus $\Dsp$) mass plot using
      the $D_{s}$ to $\phi \pi$ decay mode only.}
\label{baryon0long}
\end{figure*}

 \begin{figure*}[htb]
\centerline{\psfig{figure=pq_wrongsign_gt500.eps,width=6.in,height=3.0in}}
    \caption[Mx0-baryon long]
    {Long Lived (Lxy less than 500 micron) Charge +2 and -2 Baryon Pentaquark Search: $proton$ plus $\Dsp$ 
    (and $antiproton$ plus $\Dsm$) mass plot using
      the $D_{s}$ to $\phi \pi$ decay mode only.}
\label{baryon2long}
\end{figure*}

We now define the $D_{s}$ mass peak as with a width of D  we also define
left and right side bands with the same width D. We plan to use 
side bands for background subtraction (we will leave
a gap D between the side bands and the peak to make
sure that we do not include any $D_{s}$ mesons 
in the side bands. We also do the same for the 
Cabbibo suppressed D+ peak (and also for a higher sample D+ sample as 
well).

We form the invariant masses of the $D_{s}$ with protons, Kaons and pions
using particle ID criteria (with both charge 0 and charge 2 
combinations) for the central, and left and right side band 
combinations for both the $\Dsp$ and $D^{+}$.  By using the measured 
masses we can remove the measurement error
in the D mass as follows.


Mx (Central) = (Measured mass of D meson and charged track combination) - 
MDmeson(measured) +MDmeson(PD)

Mx (left) = (Measured mass of D meson and charged track combination) - 
MDmeson(left) +MDmeson(PD)

Mx (right) = (Measured mass of D meson and charged track combination) - 
MDmeson(right) +MDmeson(PD)

The distribution of Mx(left) and Mx(right) are compared to make sure 
that the background distributions are the same. The average is taken
and it is used as Mx(Backgroud)

X0 is calculated for   ($\Dsm$ $proton$ and $\Dsp \pbar$ combination)
X++ is calculated for  ($\Dsp$ $proton$ and $\Dsm \pbar$ combination)

And similarly with $\Dsm$ replaced with a $D^{+}$, and with the proton
replaced with a pion, and with a proton replaced with a Kaon.

The plot for short lived (Lxy less
than 500 micron) charge 0 Pentaquark search in  the $\Dsm$ $proton$ and $\Dsp$ $pbar$ 
mass combination
is shown in Fig.~\ref{baryon0}.  For this figure, we only used the $\Dsm$ and $\Dsp$ 
to $\phi\pi$ decay mode.  A factor of 2 in statistics is expected when we add
the other $D_{s}$ decay mode.  Here we are looking for a Pentaquark at an
expected mass of 3100 MeV. There appears to be a hint of
a signal in that region. We now plan to see if the same signal
is there after side band subtraction, and if it is there
in other decay modes of the Ds are included.
 Fig.~\ref{baryon2} shows the same plot for the short
 lived charge 2 Pentaquarks. Here we are looking for a Pentaquark at an expected mass of 3220.

The following is the total number of events that contribute to
the mass distribution.
( $\Dsm$ $Pbar$  : 188 events (charge -2) $\Dsp$ $Proton$     : 190 
events (charge +2)
 $\Dsm$ $Pbar$  : 380 events (charge 0)  $\Dsm$ $proton$     : 420 events 
 (Charge 0). 

 Fig.~\ref{baryon0long} and Fig.~\ref{baryon0long} show the mass plot for long lived (Lxy
 greater than 500 microns) Pentaquarks with charge 0 and charge 2, 
 respectively. 
 Since we are looking above threshold, we do not expect to 
 see any long lived pentquark states (except for the possibility
 that short lived charm pentaquark states could be produced in the decays
 of  stable long lived bottom pentaquark states).


 For the $\pi$ $D_{s}$ mass spectra
we use some of the standard B-group cuts:
The Mass
of the $D_{s}$ between 1.9585 and  1.9785 GeV,
The  Pt of the state we look for above 5 GeV.
The Pt of the pion above 0.6 GeV.  Chi2(X) less than 20.
The mass of the $\phi$ between 1.016 and 1.023 GeV. We
looked at charge zero (right sign) and charge 2 (wrong sign) with 
(Lxy greater than 700 micron and  Lxy less than 700 micron.  
All these spectra have already been looked at by the B-group, so
these are mostly to be used as checks of the analysis.


\begin{figure*}[htb]
\centerline{\psfig{figure=xm_pitot_PQ_2_4_less0.7.eps,width=6.in,height=3.0in}}
    \caption[Mx0-meson ]
    {Di-Mesons charge zero: $\piplus \Dsm$ (and $\piminus \Dsp$) mass plot using
     the $D_{s}$ to $\phi \pi$ decay mode only.
     Here we are looking for a exotic 4-quark state at a mass 
around  2325 MeV. Here Lxy is less than 700 microns.Unfortunately, 
 we had a cut of a mass of 4 GeV.
We expect
to see the B0 and Bs peaks at mass of 5300 MeV for normalization.}
\label{meson01}
\end{figure*}




 \begin{figure*}[htb]
\centerline{\psfig{figure=xm_pitot_PQ_2_4_gra0.7.eps,width=6.in,height=3.0in}}
\caption[]
    { Di-Mesons charge zero: $\piplus \Dsm$ (and $\piminus \Dsp$) mass plot using
     the $D_{s}$ to $\phi \pi$ decay mode only.
     Here Lxy is greater than 500 microns.
   }
\label{meson02}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=xm_pitot_WS_2_4_less0.7.eps,width=6.in,height=3.0in}}
    \caption[Mx0-meson ]
    {Di-Mesons charge +2: $\piplus \Dsp$ (and $\piminus \Dsm$) mass plot using
     the $D_{s}$ to $\phi \pi$ decay mode only.
     Here we are looking for a exotic 4-quark state at a mass 
around  2325 MeV. Here Lxy is less than 700 microns.}
\label{meson03}
\end{figure*}




 \begin{figure*}[htb]
\centerline{\psfig{figure=xm_pitot_WS_2_4_gra0.7.eps,width=6.in,height=3.0in}}
\caption[]
    { Di-Mesons charge +2: $\piplus \Dsp$ (and $\piminus \Dsm$) mass plot using
     the $D_{s}$ to $\phi \pi$ decay mode only.
     Here Lxy is greater than 500 microns.
   }
\label{meson04}
\end{figure*}


Fig.~\ref{meson01}
 shows the mass plot for a di-meson search
 (which includes 4-quark states) in the $\Dsp \piminus$ and $\Dsm \piplus$ 
combination). Here we are looking for a exotic 4 quark state at a mass 
around  2325  MeV.   Unfortunately, the we had a cut of a mass of 4 GeV.
We expect
to see the B0 and Bs peaks at mass of 5300 MeV for normalization.  
This plot is for Lxy less than 700 microns.
Fig.~\ref{meson02} shows the same plot with Lxy greater than 700 microns.

Fig.~\ref{meson03} and Fig.~\ref{meson04} shows the same plots
for charge 2 combination (wrong sign) with Lxy greater than 500 microns.


We are planning to redo all the analysis to extend the mass values
up to 7 GeV, include all the Ds decay modes, and include all D+
decay modes, and include the side bands.  When these are done,
we will check that we see the D0*(2420), the B0 and BS (5300) in the $D^{+} \piminus$
and $D^{+} \piminus$ channels (as seen in Fig.~\ref{repro1}),
and the B0 and BS (5300) in the $D^{+}_{s} \piminus$
and $D^{+}_{s} \piminus$ channels (as seen in Fig.~\ref{repro2})
(both of these figures are taken
from other B group analyses). 

We will also look at the charm Pentaquark (charge 0 and 
+2) candidates which we estimate to have a mass  of about 2980 MeV in the
$proton$ with a $D^{+}$ or $D^{-}$ (and $antiproton$ with $D^{+}$ or $D^{-}$) combinations.

At the moment, we are not able to do the side band subtractions, but
this will be done in the next stage.

The following 
is a summary figures of kinds of figures that we plan to reproduce
as part of the checks taken from other B group talks. 

(1) Fig.~\ref{repro1} taken from
    other B group analyses,  shows that as a check we 
    expect to see the B0 and BS (5300) in the $D^{+} \piminus$
and $D^{+} \piminus$ channels.

(2)  Fig.~\ref{repro2}  taken from
    other B group analyses shows that as a check we expect to see
    the B0 and BS (5300) in the $D^{+}_{s} \piminus$
and $D^{+}_{s} \piminus$ channels.

(3) Fig.~\ref{repro3} taken from
    other B group analyses (Bauer and Paus),  shows that we as a check
    expect to see the $D*$ mesons in the  $D^{+} \piminus$
and $D^{+} \piminus$ channels.

(3) Fig.~\ref{repro4} taken from
    other B group analyses (Bauer and Paus), shows
    the mass spectrum for  $D^{+}_{s} \piminus$
and $D^{+}_{s} \piminus$ channels. This figure does not show the
peak around 2.12 that we see in our spectrum. We plan to follow
up on this as the analysis progresses. Their $D^{+}_{s} \piminus$
mass spectrum looks more like our $D^{+}_{s} \piplus$




 \begin{figure*}[htb]
\centerline{\psfig{figure=BdDpPi-PrFit.eps,width=6.in,height=3.0in}}
    \caption[ ]
    {A Figure that we plan to reproduce as a check, taken from other
    B group analyses. It shows the B0 and BS (5300) in the $D^{+} \piminus$
and $D^{+} \piminus$ channels.}
\label{repro1}
\end{figure*}

 \begin{figure*}[htb]
\centerline{\psfig{figure=BsDsPi-PrFit.eps,width=6.in,height=3.0in}}
    \caption[ ]
    { A Figure that we plan to reproduce as a check, taken from
    other B group analyses. the B0 and BS (5300) in the $D^{+}_{s} \piminus$
and $D^{+}_{s} \piminus$ channels.}
\label{repro2}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=Dpionbauer.eps,width=5.in,height=6.0in}}
    \caption[ ]
    {This figure taken from
    other B group analyses (Bauer and Paus),  shows that we as a check
    expect to see the $D*$ mesons in the  $D^{+} \piminus$
and $D^{+} \piminus$ channels.}
\label{repro3}
\end{figure*}

 \begin{figure*}[htb]
\centerline{\psfig{figure=Dspibauer.eps,width=5.in,height=6.0in}}
    \caption[ ]
    { This figure taken from
    other B group analyses (Bauer and Paus), shows
    the mass spectrum for  $D^{+}_{s} \piminus$
and $D^{+}_{s} \piminus$ channels.}
\label{repro4}
\end{figure*}


 \section{Next phase}
 
Plans for optimizing cuts: For the di-meson four-quark states we aim as much as 
possible to use   standard B-group cuts, e.g. 
the cuts the for $D_{s}$. For example, we plan to use
the same cuts as were used optimized by the B-group
study of  ($\piplus$ $D^{-}$) spectrum, where they observed the D*(2460),
and their study of  $piplus$ $D^{+}_{s}$ spectrum. These cuts
are shown in Fig.~\ref{repro3} and Fig.~\ref{repro4}. The B group
$\Dsp \piminus$ cuts are: (a) $\Dsp$ mass within 20 MeV.(b)  Pt of the
($\Dsp \piminus$) greater than 5 GeV.(c)  PT of the $\piminus$ greater 
than  600 MeV. (d) Chisquare(3D) less thab 20 with mass contraint. $\phi$ 
mass within 7 MeV. (e) Cosine ($\theta_{helicity}$) greater than 0.4.
(f) Prompt selection d0($\Dsp \piminus$) less than 100 micron;
Lxy ($\Dsp \piminus$)) greater than -500 micron and less than 700 
micron;  and Lxy greater than -4 sigma.

In that search, one searches for a particle of mass around 2.4 GeV 
decaying to a $D_{s}$ with mass 1.9 GeV and a pion. Therefore, one expects
the Ds to carry most of the transverse momentum.  This is why this
search required the minimum 0.6 GeV Pt cut on the momentum of the
pion and a 5 GeV Pt cut on the momentum of the D meson.

However, when a  Pentaquark
state decays into a final state pion is replaced with a proton, it is 
expected that the proton carries a much higher fraction of the momentum
of the Pentaquark. Therefore, the transverse momentum cut on the proton
must be higher than the 0.6 GeV cut on
the pion which is used in the ($\Dsp \piminus$) search. The cut should
closer to the Pt cut that is used to initially select the Ds.  We are 
looking for a state of a mass of about 3 GeV decaying to a Ds of mass
1.9 GeV and a proton of mass 0.93 GeV. Therefore, the Pt cut of on the
proton should be about half of the Pt cut on the pair. If
we use the B group cut of Pt greater 5 GeV for the
then the cut on ($\Dsm$ $proton$) pair, than the Pt cut on
the proton should be about 2.5 GeV.

In order to study the effect of the Pt cut on the proton in an 
unbiased way, we plan to use a sample of $\Lambda_{C}$ decays
to $proton$ $\phi$ (very low branching ratio).
For the $\Lambda_{C}$ of mass 2.285 GeV, a proton
mass lf 0.93 GeV and a $\Phi$ mass of 1.02 GeV we expect that the 
optimal Pt cut of the proton should also be about half of the Pt
of the $proton$ $\phi$ pair. 

 \begin{figure*}[htb]
\centerline{\psfig{figure=lambdacpkk.eps,width=5.in,height=3.0in}}
\centerline{\psfig{figure=mkklambdac.eps,width=5.in,height=3.0in}}
    \caption[ ]
    { $\Lambda^{+}_{c}$ to pKK from Belle (top). Bottom plot
      shows the KK mass spectrum for the events in the $\Lambda_{c}$ 
      peak. Branching ratios are showing in the next figure.}
\label{lambdac}
\end{figure*}

\begin{figure*}[htb]
\centerline{\psfig{figure=lambdacbr.eps,width=4.0in,height=5.0in}}
    \caption[ ]
    { $\Lambda^{+}_{c}$ to proton plus other particle
    branching ratios.}
\label{lambdabr}
\end{figure*}


           
 \section{Conclusion}
 
 This is a progress report on a  a search for
Charm, Charm-Strange, Bottom and Bottom-Strange Pentaquark and
other Multiquark States in P-Pbar Collisions
at CDF. For Charm and  Charm-Strange exotic states we search for states
in the following  two body final states: 
(1) Neutral and charge +2 (and -2) bound-state Pentaquarks which decay
into one Charm or Charm-Strange Meson (e.g. $\Dp$, $\Dm$, $\Dsp$, $\Dsm$) plus 
another Baryon  (e.g.  proton or antiproton); 
(2)  Neutral and charge +2 (and -2) bound-state exotic four-quark states which decay
into one Charm or Charm-Strange meson ($\Dp$, $\Dm$, $\Dsp$, $\Dsm$) and another 
charged meson ($\pi^{+}$,$\pi^{-}$,  $\Kplus$, $\Kminus$).

We see preliminary indication of Pentaquark peaks (at 3100 and 3200 Mev) 
 in two Meson-Baryon 
 final state channels that we  
 have investigated. We have also seen peaks in the 4-quark search 
 Meson-Meson final state. which
 need to be further investigated. We plan to double or triple the
 statistics by using additional decay mode, somewhat reducing both
 Pt cuts (keeping
 the ratio fixed), and using more of the data taken so far. A side
 band subtraction analysis is under way.
 



 If these charge 0 and 2 are confirmed in the charm sector,
we plan to 
expand the search to similar particles with charge +1 and -1 in
the charm sector (by including neutral $D^{0}$ mesons in the search).
In addition, we will study the  corresponding neutral, charge +1, +2 and
-1 and -2 in the Bottom, Bottom-Strange and Bottom-Charm quark sector.

 \section{Current Plans}
 

Baryon-Meson Studies
 
A. Pentaquark Search in Charge 0 $\Dsm$-$proton$ and 
$\Dsp$-$antiproton$. For each plot, calculate DM by
subracting the measured $D_{s}$ mass from the unconstrained
mass and then adding back the $D_{s}$ mass from the PDG.
Do the follwing studies for both Lxy less than 500 and Lxy greater
than 500 microns.

1. compare $\Dsm$-$proton$ and $\Dsp$-$antiproton$ and total.
   (look at ratio  versus mass of first two plots)
   
2. Compare left and tight side bands mass distributions and total.
  (look at ratio  versus mass of first two plots)
  
3. Fit the total sid- band background to a function.

4. Normalize the side band function to the total number of events
in each plot and show it on  each of the above plots.

B. Repeat as above for  Pentaquark Search in Charge 2 $\Dsp$-$proton$ and 
$\Dsm$-$antiproton$

C. Repeat as above for  Exotic Meson Search in Charge 0 $\Dsp$-$\piminus$ and 
$\Dsm$-$\piplus$.  Check that we see the known
 $B^{0}_{s}$ peak at 5300 (in Lxy greater than 500 microns). Also look 
 at  $\Dsp$-$\Kminus$ and  $\Dsm$-$\Kplus$.   

Di-Meson Studies
 
D. Repeat as above for  Exotic Meson Search in Charge 2 $\Dsp$-$\piplus$ and 
$\Dsm$-$\piminus$; and for  $\Dsp$-$\Kminus$ and 
$\Dsm$-$\Kplus$  

E. Repeat as above for  Pentaquark Search in Charge 0 $\Dp$-$proton$ and 
$\Dm$-$antiproton$ for both the Cabbibo suppressed channel and for
the high statistics $D$ sample.


F. Repeat as above for  Pentaquark Search in Charge 2 $\Dp$-$proton$ and 
$\Dm$-$antiproton$ for both the Cabbibo suppressed channel and for
the high statistics $D$ sample.

G. Repeat as above for  Exotic Meson Search in Charge 0 $\Dp$-$\piminus$ and 
$\Dm$-$\piplus$ for both the Cabbibo suppressed channel and for
the high statistics $D$ sample. Here check that we see the known 
$D*(2460)$ (in Lxy less that 500 microns) and that we see the known
$B^{0}$ and $B^{0}_{s}$ peaks at 5300 (in Lxy greater than 500 microns)
Also look at  $\Dp$-$\Kminus$ and  $\Dm$-$\Kplus$.  

H. Repeat as above for  Exotic Meson Search in Charge 2 $\Dp$-$\piplus$ and 
$\Dm$-$\piminus$ for both the Cabbibo suppressed channel and for
the high statistics $D$ sample. Also look at  $\Dp$-$\Kplus$ and 
$\Dm$-$\Kminus$  

Subsequent Steps

G. Include searches with a $D^{0}$ in the final state instead of a
charged D, and also look at more Charm pentaquarks possibilities
with other charge and strangeness quantum numbers.

H. Look for long lived below threshold Pentaquark states as
predicted in the Stewart et al. model.

J. Expand the search to the B-quark sector.



B. 

 
  \section{Appendix A}

The following figures are taken from 
 R. Bijker et. al. Spectroscoy of Pentaquarks 
     States hep-ph/0310281 and show all possible low lying
 (exotic) pentaquark states and predicted masses.
 
 \begin{figure*}[htb]
\centerline{\psfig{figure=pentaspect.eps,width=6.0in,height=7.0in}}
    \caption[ ]
    { Spectrocopy of low lying exotic Pentaquark from hep-ph/0310281}
\label{pentaspect}
\end{figure*}
 
     \begin{figure*}[htb]
\centerline{\psfig{figure=pentaT6.eps,width=4.0in,height=5.0in}}
    \caption[ ]
    { Spectrocopy of low lying exotic Pentaquark from hep-ph/0310281
    table 8}
\label{pentaT6}
\end{figure*}

 \begin{figure*}[htb]
\centerline{\psfig{figure=pentaT8A.eps,width=5.0in,height=6.0in}}
    \caption[ ]
    { Spectrocopy of low lying exotic Pentaquark from 
    hep-ph/0310281 Table 8A.}
\label{pentaT8A}
\end{figure*}

 \begin{figure*}[htb]
\centerline{\psfig{figure=pentaT8B.eps,width=5.0in,height=6.0in}}
    \caption[ ]
    { Spectrocopy of low lying exotic Pentaquark from 
    hep-ph/0310281 Table 8B.}
\label{pentaT8B}
\end{figure*}

 \begin{figure*}[htb]
\centerline{\psfig{figure=pentaT9A.eps,width=5.0in,height=6.0in}}
    \caption[ ]
    { Spectrocopy of low lying exotic Pentaquark from 
    hep-ph/0310281 Table 9A.}
\label{pentaT9A}
\end{figure*}

 \begin{figure*}[htb]
\centerline{\psfig{figure=pentaT9B.eps,width=5.0in,height=6.0in}}
    \caption[ ]
    { Spectrocopy of low lying exotic Pentaquark from 
    hep-ph/0310281 Table 9B.}
\label{pentaT9B}
\end{figure*}


\section{Appendix B: Our own best estimates using constituent 
diquark-triquark
concepts}


As described below,  we assume that the newly  reported state  
$\Theta^{+}_{\sbar}$(1540) and
 is identified with the Pentaquark states
$\sbar$$uudd$. We assume that state 
$\sbar$$uuud$ has a mass of 1540+(1232-938)=1834 (assuming
it is heavier by the Delta(1232)-proton mass difference,. Using these values, we 
estimate the following masses for the corresponding Pentaquark
states in the charm sector:  (a)  The $P^{0}_{\cbar{s}}$ =$\cbar$$sudd$ should
be around 3120 MeV and decay to Proton plus $D^{-}_{s}$ (and the corresponding 
antiparticle); (b)  The $P^{++}_{\sbar{c}}$ =$\sbar$$cudd$ should
be around 3200 MeV and decay to Proton plus $D^{+}_{s}$ (and the corresponding 
antiparticle); (c)  The $P^{0}_{\cbar{d}}$ =$\cbar$$duud$ should
be around 2960 MeV and decay to Proton plus  $D^{-}$ (and the corresponding 
antiparticle);(d)  The $P^{++}_{\dbar{c}}$ =$\dbar$$cuud$ should
be around 3060 MeV and decay to Proton plus $D^{+}$ (and the corresponding 
antiparticle). 

And in the b sector: (a)  The $P^{+}_{\bbar}$ =$\bbar$$uudd$  should
be around 6400 MeV  (and the corresponding 
antiparticle); (b) The $P^{+}_{\bbar{s}}$ =$\bbar$$sudd$ should
be around 6535 MeV (and the corresponding 
antiparticle)

There are many different models for Pentaquark states, which result
in different quantum numbers and masses for the various baryons. 
These include Skyrmion or chiral-soliton models, Lattice QCD 
calculations, and constituent quark models including diquark and 
triquark states.  Within the constituent quark model of Cheung~\cite{cheung}
the $\Theta^{+}_{\sbar}$(1540) = $\sbar$$uudd$ is predicted to be 
between 1481 and 1562 
MeV (a range of 81 MeV).
The Cheung model also predicts that  the $P^{0}_{\cbar{d}}$ =$\cbar$$duud$  has a 
mass between 2938 and 2997 MeV, a range of 59 MeV. Since the upper
estimate of 1562 MeV is 22 MeV higher than the measured mass of 1540
MeV, we estimate $P^{0}_{\cbar{d}}$ =$\cbar$$duud$
mass to be 2997-22x(59/81) =2997-16 MeV 
or 2980 MeV.

Lipkin estimates the mass of the $P^{0}_{\cbar{d}}$ =$\cbar$$duud$
to be 2985 MeV. Huang uses Lipkins model and gets 2990 MeV. 
Lippkin also states that his 
prediction for the $P^{0}_{\cbar{d}}$ =$\cbar$$duud$ of 2985 MeV ~\cite{Lipkin1}
(with an error of 50 MeV) may be an 
overestimate since the same model predicts a mass of 1592 for the 
$\Theta^{+}_{\sbar}$(1540)).

Cheung's model also predicts that
the $P^{+}_{\bbar}$ =$\bbar$$uudd$ has a mass between  6340 and 6422 MeV (a range of 80 MeV). 
Based on this we estimate the $P^{+}_{\bbar}$ =$\bbar$$uudd$ mass to be
6422 -22x(80/81) = 6400 MeV. Lipkin's estimate for the mass of this 
state is similar (as shown in the Table below)

Lipkin's model~\cite{Lipkin1} attempts to fit the baryon masses with
the assumption
that the constituent quark masses for the (u, s, c and b) of
360, 540, 1710 and 5050 MeV   depend on the flavor of the
spectator quark.   For example, the difference between
the strange and u quark masses
is 179 MeV when the spectator is a d-quark, 103 MeV when the spectator
is a c-quark and 91 MeV when the spectator is a b quark. 

Therefore, the anticharm-strange Pentaquarks
should be between 103 and 179 MeV more massive then the anticharm
Pentaquarks with only light quarks. We take the average of 140 MeV
as the difference between the strange and u quark mass in a Pentaquark
that already contains one charm quark.
Similarly, the antistrange-bottom Pentaquark and the antibottom-strange
Pentaquarks
should be between 91 and 179 MeV more massive then the antibottom
Pentaquark with only light quarks (i.e. 135 MeV on average).

Within Lipkin's model, the charm quark is heavier than the u quark
by 1360 MeV when the d quark is a spectator
(Table 4 in hep-ph/0307243). If we assume that $P^{++}_{\sbar}$ 
$\sbar$$uuud$ Pentaquark has a mass of 1834 MeV (194 MeV higher than
 the 1540 to account for $\Delta$(1232) nucleon(938) mass difference),
 then the mass
of the $P^{++}_{\sbar{c}}$ =$\sbar$$cudd$ should be 1834+1360 = 3194 MeV
(or about 3200 MeV). We have not found any other estimates for the
mass of this state.

In summary the following are the expected mass ranges for the
various Pentaquark states that we look for. When there are more
than one estimate, the second entry is our best estimate. The tables 
below are preliminary and we plan to update it in the near future.

In the tables we use the following
masses from the particle data group: $\pizero$ (u$\ubar$) = 135 Mev,
$\piplus$(u$\dbar$) = 139.6 
MeV,Proton  (uud) = 938.3 , Neutron(ddu)=939.6 MeV, 
$\Phi$(s$\sbar$)=1020.0 MeV, 
$K^{0}$ (d$\sbar$) = 497.7 MeV, $K^{+}$(u$\sbar$)= 393.7, $\Lambda^{0}$ (uds) = 1115.7 MeV,
$\Sigma^{+}$(uus)=1189.4,
$D^{0}$(u$\cbar$) = 1864.5  MeV, $\Dp$(c$\dbar$) =1869.3 MeV, $\Dsp$(c$\sbar$) =1968.6 MeV, 
$\Lambda^{+}_{c}$(udc) =2284.9 MeV, $\Sigma^{++}_{c}$(uuc) = 2452.8,  
MeV.  

In addition, if the state
$D_{s}*$(2317) which was observed by BaBar to decay into a $\Dsm$ plus 
a $\pizero$ is a (c$\sbar$)(d$\dbar$)    (c$\sbar$)(u$\ubar$) four-quark state. 
Then a similar four-quark state  (c$\sbar$)(u$\dbar$) decaying into 
$\Dsm$ $\piplus$ and the state (c$\sbar$)(d$\ubar$) decaying into a 
$\Dsm$ $\piminus$
should be there at a somewhat higher mass (e.g. 2325 MeV).  By 
replacing the proton with charged a pion or kaon in the final state, 
we search for exotic four-quark states, as well as known non-exotic
states (as shown in the Table).

\newpage



\begin{table}
    %[th]
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
    $composition+charge$ & $Expected Mass$ &   $Decay mode$& $threshold$   &  
    $allowed?$ \\
\hline
    &  Cheung,(Lipkin)      &        &      &      \\
\hline
    $\sbar{uudd}$(+)  & 1540 (measured)   &  n $K^{+}$ & 1433.2 & Yes 
    $\Theta^{+}_{\sbar}$(1540) seen\\
    $\sbar{uudd}$(+)  & 1481, $1540$, 1562,  (1592)   & n $K^{+}$ & 
    1433.2 & Yes $\Theta^{+}_{\sbar}$(1540) seen\\
      $\ubar{dssd}$(--)    & 1860 (?)   & &  & $\Xi^{--}$ seen by NA49 
      but not CDF\\     
    $\sbar{duuu}$(++)    & 1540+1232-938=1834(?)   & &  &  $P^{++}_{\sbar}$ \\
                        & +1360      &        &      & c to u mass diff)     \\  
    $\sbar{cuud}$(++)  & 3194=3200       & p$\Dsp$    & 2907 &  $P^{++}_{\sbar{c}}$ \\
        $\sbar{cuud}$(++)  & 3194=3200       & $\Lambda^{+}_{C}{K^{+}}$    & 
        2679 &  $P^{++}_{\sbar{c}}$ \\ 
     $\sbar{cudd}$(+)  &  1540+1360=2900 ?       &  &  &  $P^{+}_{\sbar{c}}$ \\ 
     $\sbar{cddd}$(0)  &                   &  &  &  $P^{0}_{\sbar{c}}$ \\  
     $\sbar{uuub}$(++)  &      &  &  &  $P^{++}_{\sbar{b}}$ \\ 
     $\sbar{cuub}$(++)  &          &  &  &  $P^{++}_{\sbar{bc}}$ \\ 
\hline
   $\cbar{duud}$(0)  & 2938, $2980$, 2997, (2985)   & n $D^{0}$ & 2804 & Yes  $P^{0}_{\cbar}$\\
   $\cbar{duud}$(0)  & 2938, $2980$ ,2997,(2985)   & p $\Dm$    & 2807 & Yes   $P^{0}_{\cbar}$\\
                  &  +103,  +140,  +179 ,+140     &        &      & s 
                  to u mass dif     \\    
     $\cbar{uusd}$(0)  &  3041,$3120$, 3176,(3125)    & p $\Dsm$ & 2907 & Yes $P^{0}_{\cbar{s}}$\\
     $\cbar{uusd}$(0) & 3041,$3120$, 3176 ,(3125)    & $\Lambda^{0}$ 
     $D^{0}$& 2980 & $P^{0}_{\cbar{s}}$\\
     $\cbar{uusd}$(0)  & 3041,$3120$, 3176 ,(3125)  & $\Sigma^{+}$ $\Dm$    & 3059 & $P^{0}_{\cbar{s}}$\\
 $\cbar{uubd}$(0)  & 3120+4510=7630?    & & & $P^{0}_{\cbar{b}}$\\
 $\cbar{uubs}$(0)  & 7630+91=7720    & & & $P^{0}_{\cbar{bs}}$\\
 \hline
 $\sbar{cuud}$(++)  &     3200     & p$\Dsp$    & 2907 & Yes $P^{++}_{\sbar{c}}$ \\
 \hline
                 &        -140      &        &      & s to u     \\  
    $\dbar$$cuud$(++)   &   3060     & p $\Dp$    & 2807 & Non exotic $P^{++}_{\dbar{c}}$\\
\hline
    $\bbar$$uudd$(+) & 6370, $ 6400$, 6422,  (6398)   &  & &  $P^{+}_{\bbar}$\\
                  & +103,  +135,+179, (+135) &       &      & s to u 
                  mass diff     \\  
    $\bbar$$uusd$(+) & 6473, $ 6535$, 6601,  (6533)   &  & &  $P^{+}_{\bbar{s}}$\\
    $\bbar$$uucd$(++) & 6535+991=7526?  &  & &  $P^{++}_{\bbar{c}}$\\
    $\bbar$$uucs$(++) &7526+91=7617?   &  & &  $P^{++}_{\bbar{cs}}$\\   
\hline
\hline
\end{tabular}
\caption{Pentaquark states, expected mass, and threshold mass
for various decay modes.}
\label{table1}
\end{center}
\end{table}

 
\begin{table}
    %[th]
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
    $composition+charge$ & $Expected Mass$ &   $Decay mode$& $threshold$   &  $allowed?$ \\
\hline
    &        &        &      &      \\
\hline  
      $c\sbar({u}\ubar{d}\dbar)$(+)  & 2317 (measured BaBar)   & $\Dsp \pizero$    & 2104 &  seen  $\Dsp*$(2317)\\
\hline  
	$c\sbar{d}\ubar$(0)  & $2325$ ??  & $\Dsp \piminus $   &   2108 &   YES-search\\
	$c\sbar{u}\dbar$(++)  & 2325 ??   & $\Dsp \piplus$    &   2108 &   YES-Search\\
\hline
	$b\sbar$(0)  & 5370(measured)  & $\Dsp \piminus$    &   2108 &    seen  $B_{s}^{0}$ \\
	$b\dbar$(0) & 5279(measured)  & $\Dsp \piminus$  &   2108 &   seen $B_{0}$ \\
\hline
	$b\sbar$(0)   & 5370(measured)  & $\Dp \piminus$    &   2009 &   seen  $B_{s}^{0}$ \\
	$b\dbar$(0)  & 5279(measured)  &$\Dp \piminus$    &   2009 & seen  $B_{0}$ \\
	$b\dbar$(0)  & 5279(measured)  & $\Dm K^{+}$    &   2462 &   seen  $B_{0}$\\
\hline
        $c\ubar$(0)  & 2459(measureed)  & $\Dp \piminus$      &   2009 &   seen $D_{0}^{*}$(2459) \\
        $c\ubar$(0)  & high-mass  & $\Dp \piminus$      &    &   YES look for $D_{0}^{*}$(high mass) \\
\hline
        $c\ubar$ (0)  & 2459(measured)  &$\Dsp K^{-}$ &    &   No $D_{0}^{*}$ (2462) \\
        $c\ubar$ (0)  & some-high-mass  &$\Dsp K^{-}$ &   &   Yes $D_{0}^{*}$ (high mass) search  \\
        $c\ubar$ (0)  & some-high-mass  &$\Dsp \piminus$ reflection from $K$ &   &   Yes $D_{0}^{*}$ (high mass) search  \\
\hline
\hline
\end{tabular}
\caption{non-exotic mesons (to be used for normalization)
and checks and exotic four quark states, expected mass, and threshold mass
for various decay modes.}
\label{table2}
\end{center}
\end{table}

 \begin{figure*}[htb]
\centerline{\psfig{figure=quarks.eps,width=6.0in,height=3.0in}}
\centerline{\psfig{figure=mesontable.eps,width=6.0in,height=5.0in}}
\centerline{\psfig{figure=mesonfig.eps,width=6.0in,height=4.0in}}
\centerline{\psfig{figure=baryonfig.eps,width=6.0in,height=4.0in}}
\centerline{\psfig{figure=baryontable.eps,width=6.0in,height=5.0in}}
    \caption[ ]
    { }
\label{pdgquarks}
\end{figure*}
 

\begin{table}
    %[th]
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
    $SU_{f}(3)$ & $Y$ &   $I$ & $Q$   & $flavor states$ & $Notation$ \\
 \hline
     $[33]_{10}$ & $2$ &   $0 $ & $1$   &  $dduu\sbar$ & $\Theta^{+}$ \\
     $[33]_{10}$ & $-1$ &  $3/2$ & $-2,1$& 
     $ddss\ubar,uuss\dbar$ & $\Xi_{3/2}$ \\
 \hline
    $[42]_{27}$ & $2$ &   $1$& $0,1,2$   &   
    $dddu\sbar,dduu\sbar,duuu\sbar$ &  $\Theta_{1}$\\
    $[42]_{27}$ & $0$ &   $2$& $-2,2$   &   $ddds\ubar,uuus\dbar$ &  $\Gamma$ \\
    $[42]_{27}$ & $-1$ &  $3/1$& $-2,1$   &   $ddss\ubar,uuss\dbar$ &  $\Pi$ \\
    $[42]_{27}$ & $-2$ &  $1$& $-2,0$ &
    $ddss\ubar,usss\dbar$ &  $\Omega_{1}$ \\ 
 \hline
 $[51]_{35}$ & $2$ &   $2$ & $-1,0,2,3$ & 
 $dddd\sbar,dddu\sbar,dduu\sbar,duuu\sbar,uuu\sbar$ & $\Theta_{2}$ \\
 $[51]_{35}$ & $1$ & $5/2$ & $-2,3$   &   $dddd\ubar,uuuu\dbar$& $\Phi$ \\
 $[51]_{35}$ & $0$ &   $2$ & $-2,2$   &   $ddds\ubar,uuus\dbar$& $\Gamma$ \\
 $[51]_{35}$ & $-1$ &$3/2$ & $-2,1$   &   $ddss\ubar,uuss\dbar$& $\Pi$ \\
 $[51]_{35}$ & $-2$ &$1$   & $-2,0$   &   $ddss\ubar,usss\dbar$& $\Omega_{1}$ \\
 $[51]_{35}$ & $-3$ &$-1/$ & $-2,-1$   &  $sss\ubar,sss\dbar$& $\Psi_{2}$ \\
 \hline
\end{tabular}
\caption{Spectroscopy oflow lying exotic pentaquarks from 
hep-ph/0310281 Table 8 reproduced. Charge  Q=$I_{3}+Y/2$}
\label{T-sbar}
\end{center}
\end{table}

\begin{table}
    %[th]
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
    $SU_{f}(3)$ & $Y$ &   $I$ & $Q$   & $flavor states$ & $Notation$ \\
 \hline
     $[33]_{10}$ & $2$ &   $0 $ & $1$   &  $dduu\bbar$ & $\Theta^{+}_{b}$\\
     $[33]_{10}$ & $-1$ &  $3/2$ & $-2,1$& 
     $ddss\cbar,uuss\bbar$ & $\Xi_{3/2}$ \\
 \hline
    $[42]_{27}$ & $2$ &   $1$& $0,1,2$   &   
    $dddu\bbar,dduu\bbar,duuu\bbar$ &  $\Theta_{1,b}$\\
    $[42]_{27}$ & $0$ &   $2$& $-2,2$   &   $ddds\cbar,uuus\bbar$ &  $\Gamma$ \\
    $[42]_{27}$ & $-1$ &  $3/1$& $-2,1$   &   $ddss\cbar,uuss\bbar$ &  $\Pi$ \\
    $[42]_{27}$ & $-2$ &  $1$& $-2,0$ &
    $ddss\cbar,usss\bbar$ &  $\Omega_{1}$ \\ 
 \hline
 $[51]_{35}$ & $2$ &   $2$ & $-1,0,2,3$ & 
 $dddd\bbar,dddu\bbar,dduu\bbar,duuu\bbar,uuu\bbar$ & $\Theta_{2,b}$ \\
 $[51]_{35}$ & $1$ & $5/2$ & $-2,3$   &   $dddd\cbar,uuuu\bbar$& $\Phi$ \\
 $[51]_{35}$ & $0$ &   $2$ & $-2,2$   &   $ddds\cbar,uuus\bbar$& $\Gamma$ \\
 $[51]_{35}$ & $-1$ &$3/2$ & $-2,1$   &   $ddss\cbar,uuss\bbar$& $\Pi$ \\
 $[51]_{35}$ & $-2$ &$1$   & $-2,0$   &   $ddss\cbar,usss\bbar$& $\Omega_{1}$ \\
 $[51]_{35}$ & $-3$ &$-1/$ & $-2,-1$   &  $sss\cbar,sss\bbar$& $\Psi_{2}$ \\
 \hline
\end{tabular}
\caption{Spectroscopy oflow lying exotic pentaquarks from 
hep-ph/0310281 Table 8 with $\dbar$, and $\sbar$
replaced with $\bbar$ and with $\ubar$ replaced with $\cbar$. Charge  Q=$I_{3}+Y/2$}
\label{T-bbar-scarr}
\end{center}
\end{table}


\section{References} 

%\vfill
%\pagebreak

\begin{thebibliography}{22}
    
     \bibitem{pentaq} Experimental evidence for $\Theta^{+}_{\sbar}$(1540)
     strageness +1 15 MeV width. 
     from LEPS Japan(nK+ T. Nakanao, et al., Phys. Rev. Lett., 92, 012002 (2003))
     ,DIANA-ITEP (K+p to KoN hep-ex/0304040),CLAS(K+K-np  hep-ex/0307018),
      SAPHIR at ELSA (Ks K+ n hep/ex-0307083),HERMES,ZEUS;
     Note that the
     $\Xi^{--}$($\dbar{s}sdd$)
     (1862) from NA49,SPS hep-ex/0310014, (but not seen in CDF) 
     
    \bibitem{babar}
B. Aubert et al (BaBar)
\verb+hep-ex/0304021+ observation of  narrow meson decaying to Ds 
Pizero at a mass of 2.32 GeV (Phys. Rev. Lett. 90,242002 (2001);
see also hep-ex/0310050 (state decaying to Ds, pizero and gamma
at 2.458).

    \bibitem{belle}
S. K. Choi et al (Belle)
\verb+hep-ex/0309032+ observation of a narrow charmonium like state at 
a mass of 3872

 
 \bibitem{E791} 
E. M. Aitala et. al. (E791 Coll.), Phys. Rev. Lett. {\bf 81}, 44
(1998); F. Gilman, 
Phys. Lett. {\bf B448}, 303 (1999).
%
 %%
    \bibitem{cheung}
Kingman Cheung,
\verb+hep-ph/0308176+, Pentaquark theta+, constituent quark structures and 
prediction of bound charmed thetac0 and bottomed thetab+ baryons.
 %
    \bibitem{Lipkin1}
Marek Karliner and Harry J. Lipkin,
\verb+hep-eph/0307343+, The anticharmed exotic barion ThetaC and its 
relatives

%
    \bibitem{Lipkin2}
Marek Karliner and Harry J. Lipkin,
\verb+hep-eph/0307443+, The Constituent quark model revisited, quark 
masses, new predictions for hadron mases and KN 
Pentaquark.

\bibitem{group}  Brian G. Wybourne hep-ph/0307170

\bibitem{polya}  D. Diaonot, V. Petroc and M. Polyakov hep-ph/9703372

   \bibitem{e400} FNAL E400: PRODUCTION OF CHARM MESONS BY HIGH-ENERGY NEUTRONS.
By Calvin Leroy Shipbaugh (Illinois U., Urbana). FERMILAB-THESIS-1988-21, RX-1221 (ILLINOIS), 1988. 134pp.
Ph.D. Thesis. http://home1.gte.net/res04m7h/
   
    \bibitem{selex} FNAL SELEX Experiment http://fn781a.fnal.gov/

    \bibitem{heavy} P. Z. Huang et. al.  Heavy Pentaquarks  
    hep-ph/0401191
    
    \bibitem{stable} I. Stewart et. al. Stable  Heavy Pentaquarks  
    hep-ph/0402076
    
     \bibitem{spect} R. Bijker et. al. Spectroscopy of Pentaquarks 
     States
    hep-ph/0310281
    
    \bibitem{chiral} M. Genovese et. al. Hevay-Favor Pentaquarks 
     in a chiral constituent quark model (pre Jlab discovery)
    hep-ph/9712452
    
     \bibitem{lattice} S. Sasaki, Lattice student of exotic S=+1 
     Baryon.
    hep-lat/0310014
 
    






\end{thebibliography}
%{22}

\end{document}
\bye


