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% ------------------------------------------------------

\begin{document}

\begin{titlepage}
\pagestyle{empty}

\title{
 CHARM PHOTOPRODUCTION NEAR THRESHOLD 
}
\centerline{\Large Thomas Jefferson National Accelerator Facility}
\vspace*{0.8cm}
\hfill JLAB-TN-01-007 \\*[-8mm]
\begin{flushright}
  \today
\end{flushright}
\vspace{0.8cm}
\Large
           
\centerline{\Large \bf
 CHARM PHOTOPRODUCTION NEAR THRESHOLD 
}
\large
\vspace{1.cm}
\centerline{Letter of Intent for TJNAF at 12 GeV}
\centerline{Presented to PAC18, July 2000}
\vspace{0.6cm}

\large
\centerline{
  Submitted by
 }
\vspace{0.4cm}
\normalsize

\noindent
%\sloppy
\centerline{
  E.~Chudakov$^\ast$, R.~Ent, J.H.~Mitchell
 }
\centerline{\textit{Jefferson Lab}}
\vspace{0.2cm}

\centerline{
  J.M.~Laget$^\ast$
 }
\centerline{\textit{DAPNIA, Saclay, France}}
\vspace{0.2cm}

\centerline{
  J.A.~Dunne
 }
\centerline{\textit{Mississippi State University}}
\vspace{0.2cm}

\centerline{
  J.A.~Templon
 }
\centerline{\textit{University of Georgia}}
\vspace{0.2cm}

\centerline{
  P.E.~Bosted
 }
\centerline{\textit{University of Massachusetts}}
\vspace{0.2cm}

\centerline{
  A.~Margaryan
 }
\centerline{\textit{Yerevan Physics Institute, Armenia}}
\vspace{0.2cm}

\vspace{0.2cm}
%\begin{flushleft}
%\noindent
\centerline{$^\ast${The names of collaborators presenting the letter of intent}}
%\end{flushleft}

\normalsize
\vspace{2.cm}
\centerline{\underline{\large{Abstract}}}
\vspace{0.5cm}


This letter of intent discusses the physics motivations to measure the charm
photoproduction close to the threshold and possible experiments on this 
subject with the 12~GeV electron beam at Thomas Jefferson National Accelerator
Facility. This program is a part of the proposal for the energy upgrade
of TJNAF continuous electron beam accelerator to 12~GeV. 
\
\end{titlepage}


\pagestyle{plain}
\setcounter{page}{1}

\tableofcontents
\newpage

\section{Introduction}
This letter of intent is a part of a proposal to upgrade the energy of
TJNAF continuous electron beam accelerator (CEBAF) to 12~GeV. It was presented
to TJNAF Program Advisory Committee in July, 2000. Since then, the physics
section of this letter of intent was slightly upgraded and published separately\cite{Brodsky:2000zc}.

\section{Physics of charm production near threshold}

\subsection{General motivations}
\label{sec:gmotiv}

The threshold regime of charmonium and open charm production opens up a new window into QCD dynamics, particularly
 multiquark, gluonic and hidden color correlations in nucleons and nuclei. In contrast to diffractive charm production
 at high energy which tests the behavior of the gluon structure functions at small $x$, charm production near threshold
 tests the structure of the target near $x=1$ and its short range behavior. 
 
This has to do with the kinematics of the reaction products. For $J/\psi$ production on nucleon, the threshold energy 
is $E_{\gamma}= 8.20$ GeV and, due to the large mass of the charmed quark ($m_c\approx 1.5$ GeV),  the $c\overline{c}$
 fluctuation of the photon travels over $l_c\cong 2E_{\gamma}/4m_c^2 = .36$ fm (see Fig.~\ref {time}). The large mass 
of the charmed quark imposes also a small transverse size $r_{\perp}\sim 1/m_c= 0.13$ fm of this fluctuation. The minimum
 value allowed for the momentum transfer is large ($t_{min}\sim 1.7$ GeV$^2$ at the very threshold, 
$\sim 1$ GeV$^2$ at $E_{\gamma} = 10$ GeV). Thus charm production near threshold  implies a small impact distance
 ($b\sim 1/m_c\sim 0.13$~fm). All the five valence quarks (the two heavy charm quarks in the probe and the three
 light quarks in the target) must be in the same small interaction volume.

\begin{figure}[htb]
\begin{center}
% \leavevmode
% \epsfysize=7cm
%  \epsfbox{graphe_gV.eps}
  \scalebox{0.3}{
      \includegraphics{pictures/graphe_gV.eps}
   }
%\vspace{5cm}
\end{center}
\caption{The characteristic time scales in $J/\psi$ production on proton.}
\label{time} 
\end{figure}

Consequently, all the quarks must be involved in the reaction mechanism. On nucleon targets, 
this implies that three gluon exchange may take over two gluon and one gluon exchange, and 
open the way to the study of correlations between valence quarks. On few body targets, each
 exchanged gluon may couple to a colored quark cluster and reveal  the hidden color part of
 the nuclear wave function, a domain of short range nuclear physics  where nucleons lose their identity.
Such exotic configurations are more likely to appear below the threshold for charm creation 
on a nucleon at rest, where quasi free production is suppressed. On deuterium the threshold 
for $J/\psi$ production is $\sim 5.65$ GeV, while on heavy nuclei the threshold is simply the 
$J/\psi$ mass $3.1$ GeV. 

At threshold, the formation length (during which the $c\overline{c}$ pair evolves into a $J/\psi$, 
after its interaction with a nucleon)
\begin{equation}
l_F\cong \frac{2}{m_{\psi'}-m_{J/\psi}}\left[\frac{E_{J/\psi}}{2m_c} \right] \cong 0.11 E_{\gamma}
\end{equation}
 is around 1 fm, closer to the nucleon size than the nucleus size.  This is the ideal situation to 
determine the scattering cross section of a full sized charmed meson on a nucleon, contrary to higher 
energies which rather give access to the nuclear interaction of a compact  $c\overline{c}$ pair. Besides 
its own interest, this may be a useful input in the studies of QGP.


Finally, intrinsic charm components in the proton ground state and possible penta-quark resonances
or charmonium bound states may be revealed near threshold. The discovery of such qualitatively new
 states of matter would be a major success for CEBAF12.

Since no quantitative predictions exist for charm production near threshold, we will rely on interesting 
conjectures on the short distance behavior of hadronic matter, inferred from properties of perturbative 
QCD.  Experiments are mandatory to explore this virgin frontier of our knowledge.

\subsection{Nucleon}
\subsubsection{Higher Twist Effects}
\label{sec:hightwist}

At high energy the dominant contribution to hard processes comes from ``leading twist'' diagrams, 
characterized by only one parton from each colliding particle participating in the large momentum 
($Q$) subprocess. Since the time scale of the hard collision is $1/Q$, only partons within this 
transverse distance can affect the process. The likelihood that two partons are found so close to 
each other is typically proportional to the transverse area $1/Q^2$ and leads to the suppression of 
higher twist, multiparton contributions.

In contrast, higher twist effects are enhanced close to the kinematical boundary. For example, in 
the $\gamma p \rightarrow c\overline{c}p$ reaction near threshold, all the partons have to transfer
 their energy to the charm quarks within their proper creation time $1/m_c$, and must be within this 
transverse distance from the  $c\overline{c}$ and from each other. Hence only compact proton Fock states, 
with a radius equal to the Compton wavelength of the heavy quark, can contribute to charm production at threshold.

\begin{figure}[htb]
\begin{center}
%  \leavevmode
%  \epsfxsize=10cm
%  \epsfbox{cmech.eps}
\scalebox{0.5}{
    \includegraphics{pictures/cmech.eps}
 }
\end{center}
\caption{Two mechanisms for transferring most of the proton momentum to the charm quark pair 
in $\gamma p \rightarrow c\overline{c}p$ near threshold. The leading twist contribution (a) dominates at 
high energies, but becomes comparable to the higher twist contribution (b) close to threshold (adapted from 
Fig.~9 of Ref.~\protect\cite{Hoyer:1997iw}).
}
\label{graphs} 
\end{figure}

The effective proton radius in charm photoproduction near threshold
can be inferred from the following argument~\cite{Hoyer:1997iw,Brodsky:1992dj}. As
indicated in Fig.~\ref{graphs}a, one mechanism is that most of the
proton momentum is first transferred to one (valence) quark, followed
by a hard subprocess $\gamma q\rightarrow c\overline{c}q$. If the
photon energy is $E_{\gamma}=\zeta E_{\gamma}^{th}$, where
$E_{\gamma}^{th}$ is the energy at kinematic threshold ($\zeta \geq1$), 
the valence quark must carry a fraction $x=1/\zeta$ of the proton
(light-cone) momentum. The lifetime of such a Fock state (in the
light-cone or infinite momentum frame) is $\tau = 1/\Delta E$, where
\begin{equation}
\Delta E= \frac{1}{2p}\left[ m_p^2 -\sum_{i}^{} \frac{p_{i\perp}^2 + m_i^2}{x_i}\right]
             \simeq \frac{\Lambda_{QCD}^2}{2p(1-x)}
\end{equation}
For $x=1/\zeta$ close to unity such a short lived fluctuation can be created (as indicated  
in Fig.~\ref{graphs}a)
through momentum transfers from valence states (where the momentum is divided evenly) having
 commensurate lifetimes $\tau$ and transverse extension
\begin{equation}
r_{\perp}^2\simeq \frac{1}{p_{\perp}^2} \simeq\frac{\zeta -1}{\Lambda_{QCD}^2}
\end{equation}
This effective proton size thus decreases towards threshold ($\zeta \rightarrow 1$), reaching 
$r_{\perp}^2 \simeq 1/m_c^2$ at threshold ($\zeta -1 \simeq \Lambda_{QCD}^2/m_c^2$). 

As the lifetimes of the contributing Fock states approach the time scale of the $c\overline{c}$ creation 
process, the time ordering of the gluon exchanges implied by Fig.~\ref{graphs}a ceases to dominate higher
 twist contributions such as that of Fig.~\ref{graphs}b~\cite{Brodsky:1992dj}. There are in fact reasons to expect 
that the latter diagrams give a dominant contribution to charmonium production near threshold. First, there 
are many more such diagrams. Second, they allow the final state proton to have a small transverse momentum 
(the gluons need $p_{\perp}\simeq m_c$ to couple effectively to the $c\overline{c}$ pair, yet the overall 
transfer can still be small in Fig.~\ref{graphs}b). Third, with several gluons coupling to the charm quark
 pair its quantum numbers can match those of a given charmonium state without extra gluon emission.

The above discussion is generic, and does not indicate how close to threshold the new effects actually manifest 
themselves. While more quantitative model calculations certainly are called for, this question can only be 
settled by experiment. It is desirable to measure both the cross section and polarization for several charmonium 
states, as well as for open charm. 

\subsubsection{A Model for the Cross Section near Threshold}
\label{sec:prodmodel}

In order to estimate the counting rate of charm production near threshold we will rely on a simple model.

Near threshold charm production probes the $x\simeq 1$ configuration in the target, the spectator partons
 carrying a vanishing fraction $x\simeq 0$ of the target momentum. This implies that the production rate 
behaves near $x\rightarrow 1$ as $(1-x)^{2n_s}$ where $n_s$ is the number of spectators. Perturbative QCD
 predicts three different gluonic components of the photoproduction cross-section:
\begin{itemize}
\item The usual one gluon $(1-x)^4$ distribution for leading twist photon-gluon fusion 
$\gamma g\rightarrow c \overline{c}$, which leaves two quarks spectators;
\item Two correlated gluons emitted from the proton with a net distribution 
$\frac{(1-x)^2}{R^2{\cal{M}}^2}$ for $\gamma gg \rightarrow c\overline{c}$, leaving one quark spectator;
\item Three correlated gluons emitted from the proton with a net distribution 
$\frac{(1-x)^0}{R^4{\cal{M}}^4}$ for $\gamma ggg \rightarrow c\overline{c}$, leaving no quark spectators.
\end{itemize}
Here $x \approx ({2m\cal{M}+\cal{M}}^2)/(s-m^2)$ and $\cal{M}$ is the mass of the $c\overline{c}$ pair. 
The relative weight of the multiply connected terms is controlled by the interquark separation $R\simeq 1/m_c$.
  The extra powers of $1/\cal{M}$ arise from the higher twist hard processes (see Ref.~\cite{Berger:1979du}). 

\begin{figure}[htb]
  \setlength{\unitlength}{1mm}
  \begin{center}
  \begin{picture}(100,4)
    \put(15,0){\scalebox{1}{\large a)}}
    \put(85,0){\scalebox{1}{\large b)}}
  \end{picture}
  \end{center}
  \vspace*{-0.5cm}
  \begin{center}
   \begin{tabular}{cc}
    \scalebox{0.5}{
      \rotatebox{-90}{
        \includegraphics{pictures/brodsky_crossec_data_1_nocolor.epsi}
      }
     }
  \hspace{0.4in}
  \scalebox{0.5}{
    \rotatebox{-90}{
      \includegraphics{pictures/slac_cross.epsi}
    }
   }
  \end{tabular}
  \end{center}
  \caption{\label{fig:Xsecthexp}
               Experimental data on \PJgy{} cross-sections measured at low energies and 
               the results of calculations. 
                    On the picture a) the measurements from the SLAC~\cite{Camerini:1975cy} double arm
                    experiment and 
                    from the Cornell~\cite{Gittelman:1975ix} calorimeter experiment are presented.
                    The curves show the results of the fit of Eq.~(\ref{eq:gluonexch})
                    for $n_g$=2 and 3, to the two lowest energy points.  
                    The picture b) shows
                    the cross section measured at $t_{min}$, by the same experiments~\cite{Camerini:1975cy,Gittelman:1975ix},
                    along with unpublished results from the SLAC single arm experiment~\cite{Anderson:1976sd}.
              }
\end{figure}
The two gluon term produces odd C quarkonium 
$\gamma gg\rightarrow J/\psi$, thus permitting exclusive $\gamma p \rightarrow  J/\psi p$ production. The photon 
three-gluon coupling $\gamma ggg \rightarrow c\overline{c}$ produces a roughly constant term at threshold in 
$\sigma/v$, where it is expected to dominate  (here $v=1/16\pi (s-m^2)^2$ is the usual phase space factor). 
It produces the $\eta_cp$, $\chi_cp$ and other C even resonances, but also $J/\psi$. Indeed, there is  
evidence~\cite{Anderson:1976sd} that the $J/\psi$ elastic photoproduction cross section is roughly flat up to $E_{\gamma} 
 \approx 12$ GeV, as depicted in Fig.~\ref{fig:Xsecthexp}~b), contrary to the steep variation at higher energies.

For elastic charm production (when the proton target remains bound),
it is also necessary to take into account the recombination of the
three valence quarks into the proton via its form factor, as well as
the coupling of the photon to the $c\overline{c}$ pair. 
For two gluon
exchange 
the cross section of the $\gamma p \rightarrow J/\psi p$
takes the form:
\begin{equation}
\frac{d\sigma}{dt}={\cal N}_{2g}v \frac{(1-x)^2}{R^2{\cal{M}}^2}
F_1(\frac{t}{4}) (s-m^2)^2
\end{equation}
while for three gluon exchange it takes the form:
\begin{equation}
\frac{d\sigma}{dt}={\cal N}_{3g}v \frac{(1-x)^0}{R^4{\cal{M}}^4}
F_1(\frac{t}{9}) (s-m^2)^2
\end{equation}
where ${\cal N}$ are the normalization coefficients.
$F_1(t)$ is the isoscalar proton form factor and
its argument takes
into account that the momentum transfer is shared between two or three
valence quarks in the proton. This implies that the $t$ distribution
for the three gluon exchange cross section is flatter than for two
gluon exchange cross section. The $(s-m^2)^2$ term comes from the
coupling of the incoming photon to the $c\overline{c}$ pair (see, for
instance, Ref.~\cite{Laget:2000gj}) and compensates the same term in the phase
space $v$. 

One can write these expressions in a form:
\begin{equation}
\frac{d\sigma}{dt}={\cal A}_{n_g} (1-x)^{2(3-n_g)} F_1(\frac{t}{n_g^2}) 
\label{eq:gluonexch}
\end{equation}
where $n_g$ is the number of gluons and ${\cal A}_{n_g}$ are the normalization factors. 

Such a behavior is depicted in Fig.~\ref{fig:Xsecthexp}~a). 
The normalization coefficient ${\cal A}_{n_g}$ is determined assuming that
each channel saturates the experimental cross section measured at
about E$_{\gamma}\approx{}$12~GeV, by fitting the formula to the two lowest energy points
measured by 
Cornell~\cite{Gittelman:1975ix} at 11~GeV and SLAC~\cite{Camerini:1975cy}
at 13~GeV.


Note that such expressions are valid in limited energy range near
threshold, where $x\sim 1$. At higher energies, one has to rely on the
variation of the gluon distribution in the vicinity of $x\sim 0$ to
reproduce the step rise of charm photoproduction~\cite{Brodsky:1994kf,Kharzeev:1999bz}.

In addition, possible penta-quark resonances in the $s$-channel may
modify this picture as schematically depicted in Fig.~\ref{fig:res}. Also
Final State Interactions (FSI) may affect these predictions, but it is
very likely that the trend of the cross-sections will remain unchanged
(near threshold their differ by orders of magnitude).  Only
experiments can answer these open questions, and the proposed cross
sections should be considered as an educated guess for a feasibility
study.

\begin{figure}[htb]
 \begin{center}
%  \leavevmode
%  \epsfysize=7cm
%  \epsfbox{spd-figure_new.eps}
  \scalebox{0.6}{
    \rotatebox{-90}{
      \includegraphics{pictures/spd-figure_new.epsi}
    }
   }
\end{center}
\caption{\label{fig:res} A possible signal of a $s$-channel resonance, on top of the three gluon contribution.}
\end{figure}
\vspace{0.2cm}



\subsection{Nuclei}
\subsubsection{Subthreshold Photoproduction}
\label{sec:subthresh}

The high luminosity of CEBAF12 will allow detailed study of
subthreshold production of charm(onium). It is well established that
antiprotons and kaons (and even anti-deuteron) are produced on nuclear
target at substantially lower energies than is kinematically possible
on free nucleons~\cite{Ca89}. Scattering on a single nucleon in the
nucleus would at these energies require a Fermi momentum in the
vicinity of 800 MeV/c. While the $pA$ data can be fit assuming such
high Fermi momenta, this assumption leads to an underestimate of
subthreshold production in $AA$ collisions by about three orders of
magnitude~\cite{Shor:1990qw}.

\begin{figure}[htb]
\begin{center}
  \scalebox{0.4}{
      \includegraphics{pictures/submech.eps}
   }
\end{center}
\caption{\label{nucleus} Two conceptual mechanisms for subthreshold
$\overline{p}$ in $hA$ collisions. In (a) the production occurs
locally off a hot spot (black circle) of high energy density in the
nucleus. In (b) the light quarks gain momentum over an extended
nuclear region (grey).}
\end{figure}


There are at least two qualitatively different scenarios for the
observed subthreshold production of antiprotons~\cite{Hoyer:1997iw}. Either
(Fig.~\ref{nucleus}a) the projectile strikes a local ``hot spot" with
a high energy density in the nucleus. The effective mass of the
scatterer is high, lowering the kinematical threshold. Alternatively
(Fig.~\ref{nucleus}b) the momentum required to create the anti proton
is not transferred locally, but picked up in an extended longitudinal
region: the nucleus plays the role of a
``femtoaccelerator''. Establishing either scenario would teach us
something qualitatively new about rare, highly excited modes of the
nucleus.

Photoproduction of charm below threshold would be of crucial help in
distinguishing the correct mechanism, at least for the two following
reasons:
\begin{itemize}
\item The $c\overline{c}$ component of the photon is almost point like
at the charm threshold and below. In particular, effects due to the
shrinking effective size of the hadron probe near threshold are
eliminated;
\item The $c\overline{c}$ pair is created locally, within a proper
time $\tau \simeq 1/m_c$. The extended acceleration scenario of
Fig.~\ref{nucleus}b is thus not effective for charm
photoproduction. If significant subthreshold charm photoproduction
occurs (beyond what can be ascribed to standard Fermi motion) this
selects the hot spot scenario of Fig.~\ref{nucleus}a.
\end{itemize} 

\subsubsection{Interaction of $c\overline{c}$ Pairs in Nuclei}
\label{sec:interinnuclei}


Close to threshold for the process $\gamma p \rightarrow J/\psi p$ on
stationary protons the energy of the $J/\psi$ is $E_{J/\psi}\simeq 7$
GeV. This corresponds to a moderate Lorentz $\gamma$ factor
$E_{J/\psi} /M_{J/\psi} \simeq 2.3$.  Hence a significant expansion of
the $c\overline{c}$ pair occurs inside a large nucleus, and effects of
charmonium bound states in nuclei may be explored.


The dependence of the ratio $\sigma{}_{A}(J/\psi)/\sigma{}_{N}(J/\psi)$,
between production on a nucleus and the nucleon, on the target size A and on
the projectile energy indicates the amount of re-scattering in the
nucleus.  The presently available data on the A-dependence of
charmonium production is at much higher energies, and thus measures
the nuclear interactions of a compact $c\overline{c}$ pair rather than
of the full sized charmonium. Further information about the
significance of the radius of the charmonium state can be obtained by
comparing $\psi'$ to $J/\psi$ production on various nuclei. In high
energy $hA$ and $\gamma A$ scattering both states have similar
A-dependence~\cite{Ba83}.

Even though the $c\overline{c}$ pair is created with rather high
momentum at threshold, it may be possible to observe reactions where
the pair is captured by the target nucleus, forming ``nuclear-bound
quarkonium''~\cite{Brodsky:1990jd}. This process should be enhanced in
subthreshold reactions. There is no Pauli blocking for charm quarks in
nuclei, and it has been estimated that there is a large attractive Van
der Waals potential binding the pair to the nucleus~\cite{Luke:1992tm}.

Information about the propagation of charmonium in nuclei is also very
important for relativistic heavy ion collisions, where charmonium
production may be a signal for quark-gluon plasma
formation. Charmonium photoproduction near threshold provides us with
the unique possibility to study the propagation of a full fledged
charmonium state in cold hadronic matter. 
An important parameter -- the absorption cross-section of \PJgy{} on nucleons \SigPN{}
has been measured using various techniques:
\begin{enumerate}
                                     {\setlength{\itemsep}{0.cm}
                                      \setlength{\leftmargin}{0.6cm}\setlength{\topsep}{0.cm}}
      \item   
              from photoproduction data in a framework of Vector Dominance model (VDM), along with optical theorem 
              and certain assumptions on the ratio of real and imaginary parts of the scattering
              amplitude;
      \item   from A-dependence of the photo and hadro-production cross-section,
              using models of nuclear scattering like Glauber model.   
\end{enumerate}

The first result obtained from the method 1 was \SigPN{}$\approx{}1~$mb\cite{Camerini:1975cy},
while the A-dependence measurement (method 2) at SLAC at 20~GeV\cite{Anderson:1977hi} gave a value
of $3.5\pm{}0.8\pm0.5$~mb. The first estimates of \SigPN{} derived from \PJgy{} hadroproduction,
gave a value of $\approx{}7$~mb\cite{Gerschel:1992uh}. Since then, a number of corrections
have been made for both methods. For the method 1 it was argued\cite{Hufner:1998jg}
that the VDM should be extended to a multi-channel case, which provided a value of  
\SigPN{}$\approx{}2.8-4.1~$mb instead of 1~mb. The method 2 was reconsidered taking into
account possible color transparency effects\cite{Farrar:1990ei,Farrar:1990vr,Kopeliovich:1991pu,Benhar:1992df}
and it was concluded that at low energy photoproduction the color transparency did not make
a sizable contribution, and that the SLAC results at 20~GeV were reliable. At higher energies
it may not be the case. The results of \PJgy{} hadroproduction have been also reconsidered
taking in account energy loss of the beam particle and quantum coherence effects,
and a value of \SigPN{}$\approx{}3.6~$mb was obtained, instead of 7~mb. \\

One may conclude that data on A-dependence of photoproduction plays the most important
role in deriving the \SigPN{} cross-section, providing a measurement not calling so far for 
subsequent corrections.
Only one such measurement has been done in the range free from possible 
color transparency corrections - at
20~GeV\cite{Anderson:1977hi}. In that measurement the signal was obtained by subtraction of
a large calculated background, and no information on the \PJgy{} kinematics was available.
Therefore the signal included both coherent and incoherent contributions.
Only two targets were compared. All this calls for a new measurement, and 10~GeV
is the perfect energy range.
The systematic error of such a measurement could 
be better than in \cite{Anderson:1977hi}, if the \PJgy{} momentum is measured and several
targets are used.
The statistical error was estimated using the same model
for nuclear transparency as was used for the SLAC experiment\cite{Anderson:1977hi}.
This model, based on a semi-classical eikonal approximation for the re-scattering  
\cite{Gottfried:1969aa,Laget:1972aa}, predicts the values for nuclear transparency
$T=\sigma{}_{\gamma{}A}/(A\cdot{}\sigma{}_{\gamma{}N})$,
given in Table~\ref{tab:nuclabs}.

\begin{table}[h]
\begin{center}
\scalebox{1.0}{
 \begin{tabular}{|c|r|r|r|r|r|r||r|}
  \hline
  \hline
    A                     &   9   &   12  &  27   &  63   & 108   &  207  &  $\sigma$(\SigPN), mb\\  
  \hline
      T for \SigPN=1.0~mb & 0.982 & 0.980 & 0.974 & 0.963 & 0.952 & 0.929 & 0.28  \\
      T for \SigPN=3.5~mb & 0.938 & 0.931 & 0.908 & 0.870 & 0.833 & 0.751 & 0.24  \\
      T for \SigPN=7.0~mb & 0.876 & 0.863 & 0.816 & 0.740 & 0.665 & 0.502 & 0.17  \\
  \hline
  \hline
 \end{tabular}
 }
\end{center}
\caption{The values of nuclear transparencies for \PJgy{}, calculated in the model used
         by the SLAC measurement\cite{Anderson:1977hi}, for 3 values of \SigPN{}. The last column
         presents the expected statistical error for a \SigPN{} measurement, assuming
         a statistical error of 3\% for the yields on every target.}
\label{tab:nuclabs}
\end{table}
\vspace{0.4cm}


\subsubsection{Hidden Color Configurations}
\label{sec:hiddencolor}


When the nucleon is embedded in the nuclear medium, two mechanisms
govern the photo- and the electroproduction of $J/\psi $ mesons.  The
first is trivial: it is the quasi-free production mechanism.  The
second is much more interesting.  
While a free nucleon is required to be in a color singlet state, there 
is in principle no such restriction for a bound nucleon; only the
nucleus as a whole must be colorless. The existence of such "hidden
color" configurations are predicted by QCD evolution
equations~\cite{Brodsky:1983vf}.

\begin{figure}[htb]
\begin{center}
%\leavevmode \epsfysize=7cm \epsfbox{hid_color.eps}
  \scalebox{0.3}{
      \includegraphics{pictures/hid_color.eps}
   }
\end{center}
\caption{\label{hidden_col} The simplest diagram to reveal hidden
color state in deuterium~\cite{Laget:1995ba}.}
\end{figure}

Such a component of the nucleon wave function would enable charmonium
production via the exchange of two gluons, each of  them
coupled  to a  quark belonging  to a  different nucleon
(Fig.~\ref{hidden_col}).
Since the coupling of a single gluon to a quark changes its color, two
gluon exchange provides us with a way to look for hidden color
components, or more generally for the correlation between two quarks
in hadronic matter.  A coincidence experiment, for instance
$D(\gamma,J/\psi p)n$ or $^3He(\gamma,J/\psi 2p)n$, must be performed
to disentangle them.

It is striking that in
$\gamma d\rightarrow J/\psi pn$ the $|8_c8_c>$ hidden color state of
the deuteron couples so naturally by two gluons to the $J/\psi pn$
final state~\cite{Laget:1995ba}.  Such a contribution may dominate
subthreshold production, since the high momentum of the nucleon
suppresses quasi free mechanisms. It may imply the detection of one of
the nucleons.

The cross section of the quasi-free process in the $D(\gamma,J/\psi
p)n$ reaction takes the form~\cite{Laget:1981jq}:
\begin{equation}
\frac{d\sigma}{dt d\vec{n}}= (1\;+\;\beta_n\cos \theta_n)
\left. \frac{d\sigma}{dt}\right|_{\gamma p\rightarrow J/\psi p} \rho
(\mid \vec{n} \mid)
\end{equation}
where $\mid\vec{n}\mid$, $\theta_n$ and $\beta_n$ are respectively the
momentum, the polar angle and the velocity of the spectator neutron,
and where $\rho (\mid \vec{n} \mid)$ is nothing but the nucleon
momentum distribution in deuterium. When integrated against the angles
of the spectator neutron, this expression reduces to:
\begin{eqnarray}
\frac{d\sigma}{dt d\!\mid\vec{n}\mid}=
\left. \frac{d\sigma}{dt}\right|_{\gamma p\rightarrow J/\psi p} 4\pi
\vec{n}^2\rho (\mid \vec{n} \mid)
\end{eqnarray}
with $\int\rho (\mid \vec{n} \mid) d\vec{n}=1$.

It decreases very quickly~\cite{Laget:1981jq} as the undetected neutron
momentum increases.  Consequently, selecting high values of neutron
momentum is the way to suppress the contribution from such a trivial
mechanism.  The quasi-free contribution in Fig.~\ref{d_psi} has been
computed with the Paris wave function~\cite{Lacombe:1981eg} of the deuterium.

\begin{figure}[htb]
\begin{center}
%  \leavevmode \epsfysize=9cm \epsffile{gdjpsi.eps}
  \scalebox{0.4}{
      \includegraphics{pictures/gdjpsi.eps}
   }
\end{center}
\caption{\label{d_psi} The variation of the cross-section of the
reaction $\gamma D\rightarrow pn J/\psi$ against the neutron momentum
$|\vec{n}|$, at fixed $t$. Solid line: quasi-free contribution. Dashed
line: contribution of hidden color component when its probability is
0.1\%. Dash-dotted curve: the same for a probability of 1\%}
\end{figure}

The cross section corresponding to the exchange of each of the two
gluons with a different quark cluster is expected to exhibit a flatter
momentum distribution, since the recoil momentum is shared between the
two nucleons.  However it is very difficult to make a reliable
quantitative estimate of its magnitude.

A rough, approach would be to write the corresponding cross section
as~:
\begin{equation}
\frac{d\sigma}{dtd\!\mid\vec{n}\mid}= \left.
\frac{d\sigma}{dt}\right|_{\gamma p\rightarrow J/\psi p} 4\pi\vec{n}^2\left[ \varphi_{cc} 
(\frac{\vec{n}}{2}) \right]^2 \frac{F_1^4(\frac{t}{4})}{F_1^2 (t)} \label{ampd}
\end{equation}
where the fourth power of the nucleon form factor comes from the fact
that two nucleons have to recombine, each at the momentum transfer
$t/4$. It is assumed that the form factor of the transition between a
colored cluster and the nucleon does not differ too much from the
nucleon form factor.  The ratio of the nucleon form factors acts as an
enhancement factor $\simeq 7$ at $-t=1\;GeV^2$, for example. It is
also assumed that the recoil momentum is equally shared between the
two colored clusters whose wave function is $\varphi_{cc}
(\frac{\vec{n}}{2})$.  This component of the deuterium wave function
is unknown, and only few predictions are available. As an example and
to set the order of magnitude, the hidden color contribution in
Fig.~\ref{d_psi} has been obtained by using the Fourier transform of
the wave function depicted in Fig.~11 of Ref.~\cite{Yamauchi:1986cv}.  Since it
exhibits a node around 500 MeV/c, a node appears in the cross-section
around $n\simeq 1\;GeV/c$.  This is unphysical, since in a more
elaborate calculation the integration against the nucleon internal
momentum washes it out.  Anyway, this rough estimate shows that the
hidden color component contribution dominates the cross-section above
0.5 GeV/c.  The calculation reported in~\cite{Yamauchi:1986cv} predicts a
probability of finding a hidden color component in the deuterium wave
function of the order of $0.1\%$.  Fig.~\ref{d_psi} also shows what
one may expect for a probability around $1\%$.

Assuming that the three gluon exchange dominates at threshold and
 below, the energy dependence of the elementary charm production
 process is constant and the energy variation of the integrated
 cross-section of the reaction $\gamma D\rightarrow pn J/\psi$ below
 threshold is driven by the recoil neutron minimum momentum $n_{min}$
 and the minimum four-momentum $t_{min}$: \begin{equation} \sigma
 (E_{\gamma}) \propto \int _{n_{min}}^{n_{max}}
 \int_{t_{max}}^{t_{min}} \frac{d\sigma}{dtd\!\mid\vec{n}\mid} \;
 dtd\!\mid\vec{n}\mid
\end{equation}

The dependence upon $t_{min}$ is the same, or very similar, for the
quasi-free and the hidden color contributions: in both cases it is
controlled by the nucleon form factor. On the contrary, their
dependence upon $n_{min}$ is quite different. As the photon energy
$E_{\gamma}$ decreases below threshold, the allowed minimum momentum
of the recoil neutron increases: as it can be inferred from
Fig.~\ref{d_psi}, the quasi-free contribution is suppressed as $\rho
(n_{min})$, in contrast to the hidden color contribution which is
roughly constant and depends slowly on the value of $(n_{min})$.

In order to increase the probability of the hidden color component, or
to enhance the effect of correlations between quarks, one would like
to increase the density of the target nucleus.  The reactions
$^3He(\gamma,J/\psi 2p)n$ and $^4He(\gamma,J/\psi 2p)nn$ are good
candidates.  A further advantage comes from the fact that the target
$pp$ pair is almost in a pure $^1S_0$ state (see for
instance~\cite{Ha81}), contrary to the deuterium which has a sizable
$D$ wave component. The high momentum tail of the quasi-free process
is reduced accordingly, leaving more room for two gluon exchange quark
rearrangement processes.

% ------------------------------------------------------
%



\newpage
\clearpage

\section{Experimental program on charm production}
\label{sec:experprog}


The high luminosity at the 100\% duty cycle at CEBAF12 will open 
the way to the determination
of the cross section of selected channels on nucleon and few nucleon
targets.
%We have chosen to study the feasibility of reactions where
%the charmed particle is identified by its charged decay products.
In this section the experimental program is discussed and its feasibility
is analyzed.
%In this section different options for the charm studies at JLab are discussed. 
It is evaluated
whether the standard JLab equipment would be adequate to
the task, or a new apparatus should be built in order to fulfill the program. 

\subsection{Reactions Accessible at CEBAF12}
\label{sec:reactions}

The physics program discussed includes the topics as follows: 
\begin{itemize}
      \item  Measurements of the energy dependence of charm photoproduction differential cross-section,
             in an energy range of 8.5-11~GeV, on protons. 
      \item Measurements of $\Psi$-Nucleon cross-section. This measurement can be done at the highest
            energy available, using several target materials.
      \item A search for rare effects, like the ``hidden color'' is of considerable interest.
            ``Hidden color'' can manifest itself in the \PJgy{} production on deuterium or helium.
\end{itemize}

The measurements of the first item might be carried out in several
ways. As far as the theoretical predictions are concerned, the full charm production is easier
to interpret than the charmonia production, since the final state interaction can be neglected
in the former case but may play an important role for the latter. On the experimental side,
it is easier to detect charmonia, and \PJgy{} in particular, than the full charm production, 
which would require a detection
of several types of charmed particles like \PaDz{} and \PDpm{} on a typically higher background level. 
  
\begin{table}[h]
%\begin{center}
\scalebox{1.0}{
 \begin{tabular}{|r|l|r|l|r|r|r|} \hline
  \# & reaction & $E_{\gamma}$ GeV & useful decay mode & BR & E$_{\gamma}$,     & $\sigma$ nb \\
     &          & threshold        &                   &    &               GeV &             \\
  \hline 
   1 & {\color{\Pcol} \Pgg{}p $\rightarrow$\Pcgh{}p}          &  {\color{\Fcol}  7.7 GeV} & \Pcgh{}$\rightarrow$\Pgg\Pgg       & 0.03\%  &  -  &  -  \\
     &                                                        &                           & \Pcgh{}$\rightarrow$p\Pap          & 0.12\%  &  -  &  -  \\
   2 & {\color{\Pcol} \Pgg{}p $\rightarrow$\PJgy{}p}          &  {\color{\Fcol}  8.2 GeV} & \PJgy{}$\rightarrow$\Pem\Pep       & 6.0\%   & 11. & 0.5$\pm$0.2 \\
     &                                                        &                           & \PJgy{}$\rightarrow$\Pgmm\Pgmp{}   & 6.0\%   &     &  \\
   3 & {\color{\Pcol} \Pgg{}p $\rightarrow$\PcgLp{}\PaDz{}}   &  {\color{\Fcol}  8.7 GeV} & \PaDz{}$\rightarrow$\PKp{}\Pgpm{}  & 4.0\%   & 20. & $\sim{}63.\pm$30. \\
   4 & {\color{\Pcol} \Pgg{}p $\rightarrow$\PcgLp{}\PDstza{}} &  {\color{\Fcol}  9.4 GeV} & \PDstza{}$\rightarrow$\PaDz{}X     &100.0\%  & 20. & $\sim{}63.\pm$30. \\
   5 & {\color{\Pcol} \Pgg{}p $\rightarrow$\PcgSp{}\PDm{}}    &  {\color{\Fcol}  9.5 GeV} &                                    &         & 20. &   \\
   6 & {\color{\Pcol} \Pgg{}p $\rightarrow$\Pcgcz{}p}         &  {\color{\Fcol}  9.6 GeV} & \Pcgci{}$\rightarrow$\PKp{}\PKm{}  & 0.71\%  &     &                  \\
   7 & {\color{\Pcol} \Pgg{}p $\rightarrow$\Pcgci{}p}         &  {\color{\Fcol} 10.1 GeV} & \Pcgci{}$\rightarrow$\PJgy{}\Pgg{} & 27.0\%  & 90. & $<7\%$ J/$\Psi$  \\
   8 & {\color{\Pcol} \Pgg{}p $\rightarrow$\Pcgcii{}p}        &  {\color{\Fcol} 10.3 GeV} & \Pcgci{}$\rightarrow$\PJgy{}\Pgg{} & 13.0\%  & 90. & $<27\%$ J/$\Psi$  \\
   9 & {\color{\Pcol} \Pgg{}p $\rightarrow$\Pgya{}p}          &  {\color{\Fcol} 11.0 GeV} & \Pgya{}$\rightarrow$\Pem\Pep       & 0.8\%   & 21. & 1.1$\pm$0.4  \\
     &                                                        &                           & \Pgya{}$\rightarrow$\Pgmm\Pgmp     & 0.8\%   &     &  \\
  10 & {\color{\Pcol} \Pgg{}p $\rightarrow$\PD{}\PaD{}p}      &  {\color{\Fcol} 11.1 GeV} &                                    &         & 20. & $\sim{}63.\pm$30. \\
  \hline 
 \end{tabular}
 }
%\end{center}
\caption{The thresholds of several channels of charm photoproduction reactions reside in the energy
         range below 12~GeV. The thresholds of similar reactions with an additional pion
         are about 0.6~GeV higher. The decay modes, convenient for detection and their branching ratios are shown. 
         The last columns indicates whether this reaction has been detected in photoproduction at low energies
         and the cross-section measured. The open charm cross-section measurement was inclusive. The cross-section of
         a particular channel is a part of the full one of 63$\pm$30~nb.
        }
\label{tab:thresholds}
\end{table}

\vspace{0.4cm}

\begin{figure}[htb]
\begin{center}
  \scalebox{0.8}{
    \rotatebox{-90}{
      \includegraphics{pictures/brodsky_crossec_data_3.epsi}
    }
   }
\end{center}
\caption{A sample of the existing data on \PJgy{} and open charm photoproduction cross-sections in a wide range of energies
        ~\cite{Camerini:1975cy,
        Gittelman:1975ix,
        Knapp:1975nf,
        Anderson:1977hi,
        Aston:1980fk,
        Binkley:1982kv,
        Abe:1983pe,
        Abe:1984ck,
        Denby:1984az,
        Sokoloff:1986bu,
        Barate:1987fq,
        Adamovich:1987gx,
        Anjos:1990be,
        Alvarez:1993yb,
        Frabetti:1993ux,
        Adloff:2000vm}
        The ratio between open charm and \PJgy{} varies from 10 at 20~GeV to 100 at 300~GeV.}
\label{fig:charmmeasurements}
\end{figure}

A number of various channels of charm photoproduction on the nucleon open between 8 and 12 GeV
(see Table~\ref{tab:thresholds}). 
% The open charm threshold is at 8.7~GeV.
The cross-section of open charm photoproduction at 
20~GeV~\cite{Abe:1983pe,Abe:1984ck}
is about 10 times higher than the \PJgy{} production~\cite{Camerini:1975cy} (see Fig.~\ref{fig:charmmeasurements}).
Therefore the \PJgy{} production may be affected somewhere above the open charm threshold of 8.7~GeV.
% There should be an interval above this threshold where the open charm cross-section
% is still much lower than the \PJgy{} cross-section, due to a low phase space. In this region the influence
% of the open charm channels on the \PJgy{} should be still low. 
%In order to find this region
%the open charm production should be also measured. 
There are no data on the open charm photoproduction below 20~GeV. 
It would be interesting to measure the open charm cross-section in the same energy range as \PJgy{}.
In a range from 8.7 to about 9.4~GeV the open charm
necessarily includes a \PaDz{}, while above that energy \PDm{} can be also produced. \PDp or \PDz can not
be produced below the \PD{}\PaD{} threshold of 11.1~GeV. \\

The lowest threshold reaction involving charm is \Pcgh{} production. Unfortunately, 
the branching ratios of this particle's 2-body decay modes are very low, which may explain 
why it has not been observed in photoproduction up to now. An upper limit of about 30~nb was measured
at 11~GeV~\cite{Theodosiou:1976fn}, with the \Pgg\Pgg{} decay mode.

Another interesting process would
be the \Pcgci{} production. So far, an upper limit for the ratio of \Pcgci{} to \PJgy{} cross-sections of 7\% was measured at
about 90~GeV~\cite{Barate:1987fq}. On the other hand, in hadroproduction about 30\% of all \PJgy{}
come from $\chi_c{}$ particles~\cite{Lemoigne:1982jc}. \\

The measurement  of $\Psi$-Nucleon cross-section involves measurements of 
\PJgy{} production cross-section on several nuclear targets, from which one can extract the 
$\Psi$-Nucleon cross-section using the Glauber methods. 
The ``hidden color'' can be looked for in \PJgy{} production on deuterium and requires a high sensitivity.
Therefore, all the tasks discussed are technically similar to each other, though different targets
should be used. 

The program requires very sensitive experiments, also providing reasonably low systematic errors. 
The existing \PJgy{} data~\cite{Camerini:1975cy,Gittelman:1975ix} at low energy has a systematic error 
due to an inelastic component of the production. This component was estimated as about 30\%.
The new experiment should be able to identify the recoil particle in order to identify the elastic
production.
\\

In order to decide on the best strategy for these measurements, the experimental methods to detect
the charmed particles should be considered.\\

% ---------------------------------------------------------------------------------------

\subsection{Experimental ways to detect charmed particles}
\label{sec:experways}

%Detecting the \PaDz{}
%is easier than detecting \PDpm{} or charmed baryons since the 2-body decay 


Detecting charmed particles is difficult, in particular at low energies, because
of a low  production cross-section (below 1~nb) and low
branching ratios of the decay modes convenient for detection (a few percent).
The cross-section at the lowest 
             energy point can be as low as 0.005~nb. 
One can compare the photoproduction of \PJgy{} at 11~GeV with the photoproduction of \Pgf{}
in an energy range of 2-4~GeV.
The yield of \PJgy{}$\rightarrow$\Pep\Pem{} is about 10$^{-4}$ of the \Pgf{} $\rightarrow${}K$^+$K$^-$
yield. 

Nevertheless, several experiments have proven that charm detection at low energies is possible.
The key signatures for charm are: 
\begin{enumerate}
      \item small or zero (for particles decaying weakly) particle widths;
      \item high free energy of 2-body decays;
      \item short, but detectable decay paths of weakly decaying particles;
      \item semileptonic decays have relatively high probabilities of $\sim{}10\%$;
      \item decays of the associated charmed particle may provide an additional signature.
\end{enumerate}

For charmonia, only the items 1 and 2 are valid. The reliable way to identify a photoproduced charmonium 
is to observe an appropriate peak in the mass distribution of its decay products. The lowest background
is usually observed for 2-body decays with the highest free energy. For the decays to a lepton pair
like \Pep\Pem{} or \Pgmp\Pgmm{} the main background comes from the Bethe-Heitler process. Hadronic decays
of charmonia have many particles in the final state and a high combinatorial background. The experiment
should provide as high mass resolution as possible and a reasonably good identification of leptons.
This technique worked out in a broad energy range, including low energies of 13-20~GeV at SLAC~\cite{Camerini:1975cy} and
11~GeV at Cornell~\cite{Gittelman:1975ix}. 
The former experiment used the SLAC high resolution
spectrometers and observed about 1200 \PJgy{} particles on a very low background, while the latter
used a calorimeter to detect the \Pep\Pem{} decays, providing a mass resolution about 10 times
worse than the SLAC experiment, and observed about 500 \PJgy{} on a 20\% background.
There were experiments at SLAC detecting only one lepton from \PJgy{} decays~\cite{Anderson:1977hi}.
 This method based
on subtraction of a calculated background did not work well at energies below 11-13~GeV
because of a high background level~\cite{Anderson:1976sd}. \\
 
Identification of open charm is also based on a good mass resolution, and the lowest background has been
observed for 2-body decays of \PDz{}. Additionally, the items 3-5 are valid. At high energies, where the charm
cross-section is higher than 50~nb, measuring
the decay path of charmed particles (0.5-10~mm) became a very successful technique to identify
charm. 
The lowest energy at which the open charm has been
observed in photoproduction is 20~GeV, a high resolution bubble chamber at SLAC~\cite{Abe:1983pe,Abe:1984ck}, 
measuring the decay paths, was used. Unfortunately, all the vertex detector techniques are poorly compatible with
very high luminosity experiments, needed to measure a cross-section of about 0.01~nb.
% However, since measuring the paths needs a technique like a thin target and a vertex detector very close to it, 
% this technique is hardly applicable when the cross-section is two orders of magnitude lower
% and a high luminosity is essential. 
In a number of experiments, the detection of 
the semileptonic decays of the associated particle helped to reduce the background by a factor of several. 
However, the charm signal is reduced by a factor of at least 10, which makes such a technique 
not attractive at low energies. One might consider an experiment detecting only the lepton from
a semileptonic decay. Such an experiment, providing a high rate, would be based on subtraction of the
calculated background imposing a large systematic error. 
% It has been reported that \PDz{} 2-body decays had bees observed without a special tagging based on the decay paths
% or associated leptons, but using two high resolution spectrometers. 

At the energies of 20-70~GeV~\cite{Aston:1980fk}
\PDz{} production has been measured, on a thick 67~cm hydrogen target and without a special tagging, using
a spectrometer with a mass resolution for \PDz of about $\sigma{}(M)/M\approx{}$0.5\%. The signal to background ratio
observed was about 1/5. In order to see charm at low energies one should provide a considerable improvement of
the mass resolution.
Detecting the \Dpm{} or charmed baryons can be more difficult, since the detectable decays include at least 
3 charged particles in the final state and one may expect a higher combinatorial background. Such higher
backgrounds were indeed observed in a number of experiments.

With a tagged photon beam it is possible to identify a 2-body reaction detecting only one final state particle.
This would identify the ``elastic production'' of quarkonia on protons. With the open charm, one can identify
the associated charmed particle by measuring the missing mass and therefore reduce considerably
the background.
With an untagged beam
one can identify a 2-body reaction by detecting the recoil proton along with
the quarkonium, and selecting the ``elastic production'' kinematically. 
Identifying a certain open charm reaction in an untagged beam is more
problematic since the associated particle most likely stays unidentified. 
\\

% and in order to measure the full cross-section
%one should include the final states with additional pions produced. 
%The threshold of the reaction 3 with an additional pion is very close to the threshold 4.
%All the experiments observing charm have so far detected one charmed particle or a charmonium inclusively. 
%At high energies one may expect
%that the contributions from different channels do not depend dramatically on the energy. At low energies
%the final state interaction may play a very important role, in particular it may affect the \PJgy{} production
%at the open charm threshold of 8.7~GeV, since the open charm production afar from the thresholds 
%is about 10 times higher than the \PJgy{} production. Therefore, along with \PJgy{} production, one should measure 
%the open charm production. 
%Below 9.5~GeV only one channel is allowed and this channel contains is favorable for detection \PaDz{}
%Though \Pcgh{} would be the most interesting particle to look for the processes of has not been detected but in???

% ---------------------------------------------------------------------------------------

\subsection{Evaluation of the experimental possibilities}
\label{sec:charmjlab}

In this section the methods used for evaluation of the experimental possibilities at JLab
are discussed. The methods include the simulation of reactions involving charm, background
estimates and other details.

% ---------------------------------------------------------------------------------------

\subsubsection{Simulation}
\label{sec:simulation}

In order to evaluate the acceptance, resolution and the statistical accuracy of possible experiments
a simple simulation of charm production and detector performance was done.

The kinematics of photoproduction of \PJgy{} was described by a differential cross-section 
of Eq.~\ref{eq:gluonexch}.
%\begin{equation}
%      \frac{d\sigma}{dt}=A\cdot{}(1-x)^{n}\cdot{}e^{\beta{}t}
%\label{eq:brodsky2}
%\end{equation}
%with $\beta{}$=1.0~(GeV/c)$^{-2}$ and n=2. The value of $x$ is define in \ref{sec:brodskyxdep}.
The cross-section for \PJgy{} was normalized to the measurements
at 11~\cite{Gittelman:1975ix} and 13~GeV~\cite{Camerini:1975cy}, so at 11~GeV the full cross-section
was 0.32~nb. For the open charm the same differential cross-section was taken, scaled by a factor of 10.

The angular distribution of \PJgy{} leptonic decays were simulated assuming helicity conservation:
$(1+\cos^2{\theta{}_{CM}})$. 

For simulation of the standard JLab spectrometers no particle tracking and interaction
with media was simulated. 
The decay probability of charged kaons was taken into account.
The acceptance was supposed to be flat within certain windows. 

Simulation of a new setup was done using GEANT~\cite{GEANT321}.

The acceptance and the mass resolution were calculated. In order to estimate the particle yield
additional factors were considered: 
\begin{itemize}
      \item  0.5 - efficiency of the trigger, event reconstruction etc;
      \item  0.7 - beam delivery efficiency.
\end{itemize}

% ---------------------------------------------------------------------------------------

\subsubsection{Measuring the photon energy}
\label{sec:photonenergy}

In order to measure a steep energy dependence of the cross-section the energy
bins used should be small enough that the cross-section does not change for more than
a factor 3-5 within the bin. Assuming the cross-section described by Eq.~(\ref{eq:gluonexch})
one would define a maximum bin size of about 0.4~GeV. This requires that 
the photon energy should be measured with a precision better than $\sim$0.1~GeV.  \\

For a tagged beam, like one designed for Hall D, the photon energy resolution is about
0.1\%, which is more than enough. For an untagged beam, one can derive the incident photon
energy from the kinematics of the observed particle (\PJgy{} or D), assuming a certain 2-body
reaction. Using the known mass of \PJgy{} and its decay kinematics one can considerably improve
the resolution. If the typical double arm JLab spectrometers are used to detect the
products of a 2-body decay a resolution of about 0.2\% can be achieved. A certain 2-body reaction
is defined if either the other particle (say, proton for \PJgy{} ``elastic production'') has been detected 
or only one reaction is allowed for the given end point energy of the photon beam.
  
  
% ---------------------------------------------------------------------------------------

\subsubsection{Background estimates}
\label{sec:background}

Because of the low cross-section of charm production the level of background is a very important 
item limiting the ability to extract charm signals and the statistical accuracy one can achieve. 

%Based on the Cornell results~\cite{Gittelman:1975ix},  we are confident that
%even experiments with a poor energy resolution of about 5\% are able to extract the lepton decays of 
%\PJgy{} from background. 
The Cornell experiment~\cite{Gittelman:1975ix}, providing a mass resolution for \PJgy{}$\rightarrow$\Pep\Pem
of 5\%, observed a signal to background ratio of about 5/1 with 11~GeV photons on beryllium.
Most of the background was described by the Bethe-Heitler process. We assume that the experiments
we consider at JLab would have the similar power to identify electrons like the Cornell
experiment. 
So, we used the same signal to background
ratio, scaled for the mass resolution of the experiment considered, and assumed that
this background at a mass of 3.1~GeV/c$^2$ scales with the beam energy in the same way as the Bethe-Heitler
process. The energy dependence of the latter was calculated and approximated by a formula $BH\propto{}(E_{\gamma}-8.1)^{2.5}$. 
We also assumed that at the Cornell conditions there
was an additional 5\% flat background, independent on the beam energy. The same background was considered
for \PJgy{}$\rightarrow$\Pgmp\Pgmm{}.\\

The 2-body decay of \PaDz{} is a more difficult task if no background
suppression technique, like measuring the decay paths, is used. An experiment~\cite{Aston:1980fk} in 
a photon beam of 20-70~GeV on a 67~cm long liquid hydrogen target, with a mass resolution of
0.5\%, observed a signal to background ratio of about 1/5. At the moment we do not know how this background 
would scale with the beam energy. 
The background would depend on the power to identify charged kaons.

For a tagged beam there is an independent way to reduce the background by selecting a certain
2-body reaction with the missing mass calculation. This technique could be useful at low energies.
Above the beam energy of 9.4~GeV one extra pion can be produced and at higher energies
the 2-body reactions comprise a small part of the full charm cross-section. 

For the moment we assumed that at 11~GeV the signal/background for D-meson search is 1/5 and
that the one half of this background scales with the energy like the charm cross-section,
while the other half does not depend on the energy.

%The high resolution spectrometers with a good kaon identification may have a certain
%advantage over Hall~D. 
%On the other hand, for 2-body reactions
%Hall D can measure the missing mass and identify the ``recoil'' charm baryon, providing a strong background suppression.
%Hall~D is also able to detect multi-body decays. At the moment it is difficult to estimate 
%the background levels in this situation. 

  
  
% ---------------------------------------------------------------------------------------

\subsection{Charm studies using the JLab standard spectrometers}
\label{sec:existspec}

The parameters of the existing or planned JLab spectrometers are shown in Table~\ref{tab:existspecpar}.

\begin{table}[h]
\begin{center}
\scalebox{1.0}{
% \begin{tabular}{@{\hspace{0.cm}}lc@{\hspace{0.cm}}|rllrlll|}
 \begin{tabular}{|l|c|r|l|l|r|l|l|l|}
  \hline
  hall & beam     & setup & $\Delta{}\Omega$ & P$_{max}$ & $\frac{\Delta{}P}{P}$ & $\frac{\sigma{}(P)}{P}$  
                                                                & $\sigma{}\theta{}_{in plane}$ & $\sigma{}\theta{}_{out plane}$  \\
       & $\mu{}A$ &         & ster             & GeV     & \% & \% & mrad & mrad \\
  \hline
  Hall A & {\color{\Fcol}  40}  & HRS &  0.006 &  4.0 &  9 & 0.01 & 0.6 & 2.0 \\  
         &                      & HRS &  0.006 &  3.2 &  9 & 0.01 & 0.6 & 2.0 \\  
         &        & {\color{black}MAD}
                                      &  0.030 &  6.0 & 15 & 0.3  & 1.0 & 2.0 \\  
  Hall C & {\color{\Fcol}  40}  & HMS &  0.006 &  7.5 & 18 & 0.1  & 0.8 & 0.8 \\  
         &                      & SOS &  0.009 &  1.8 & 40 & 0.1  & 1.0 & 1.0 \\  
         &        & {\color{black}SHMS} &  0.003 &  12. & 18 & 0.1  & 1.0 & 1.0 \\  
%  Hall B & {\color{\Fcol} 0.01} &CLAS & $\sim{}2\pi$ & - & -  & 0.5 & & \\  
  {\color{black}Hall D} & {\color{\Pcol} $\gamma$} &   & $\sim{}4\pi$ & - & -  &$<$1. & & \\  
  \hline
 \end{tabular}
 }
\end{center}
\caption{The parameters of the existing or planned spectrometers. MAD (Medium Acceptance Device)
         is a spectrometer being designed for Hall A. This spectrometer would have a variable position
         along the beam, allowing to reduce the minimal angle while loosing the acceptance.
         The second column indicates the maximum beam current which the accelerator can provide at 12~GeV and 
         allowed by the hall environment.
         The photon flux of Hall D is discussed in the text.
         Since the Hall~B CLAS abilities for charm detection are unlikely 
            better than those of Hall~D, they have not been evaluated here. 
         } 
\label{tab:existspecpar}
\end{table}
\vspace{0.4cm}

It was assumed that Halls A and C would use a 11~GeV 40$\mu$A beam on a 6\% radiator, which provides
a photon flux of about $1.2\cdot{}10^{12}\gamma$/s/GeV. For Hall~D~\cite{HallD:1999} it was assumed that the coherent
bremsstrahlung flux has a trapezoidal shape and ranges from 8.5 to 9.1~GeV, while the incoherent component 
is flat in a range of 8.2-11~GeV, and that both components have the same total fluxes of 
$2\cdot{}10^{7}\gamma$/s in the ranges given. \\

The photon energy range was split into 0.4~GeV bins. 
Halls A and C are using an untagged
beam and have no means to detect the recoil particle (proton for \PJgy{} production).
Therefore one can not be sure of the reaction observed and of the photon energy. 
One has to make measurements at several endpoints matching the energy bins,
and obtain the result for a given bin by subtraction. The exposition time given
for every point was optimized assuming the cross-section Eq.~(\ref{eq:gluonexch}) by minimizing
the maximum error of all the bins except the first one (the lowest energy bin). 


The results of calculations for a 90~day running period are summarized in Table~\ref{tab:existspecres}. 

\begin{table}[h]
\begin{center}
%\scalebox{1.0}{
%\renewcommand{\arraystretch}{0.95}
% \begin{tabular}{@{\hspace{0.cm}}l@{\hspace{0.cm}}r@{\hspace{0.2cm}}r@{\hspace{0.2cm}}r@{\hspace{0.2cm}}r@{\hspace{0.2cm}}r}
 \begin{tabular}{|l|l|r|r|r|r|r|}
  \hline
  \hline
  \multicolumn{2}{|l|}{meaning}& \scalebox{1.0}{\color{black}Hall  D} &  \scalebox{1.0}{HRS} & \scalebox{1.0}{HRS} 
                                                  & \scalebox{1.0}{HMS} & \scalebox{1.0}{HMS} \\ 
  \multicolumn{2}{|l|}{}       &                                      &  \scalebox{1.0}{HRS} & \scalebox{1.0}{{\color{black} MAD}} 
                                                  & \scalebox{1.0}{SOS} & \scalebox{1.0}{SHMS} \\ 
  \hline
  \hline
  \multicolumn{2}{|l|}{tagged \Pgg{}}      &  yes  & & & & \\
  \multicolumn{2}{|l|}{target LH    }      &  30~cm   &  15~cm  &  15~cm   &  4~cm   &  15~cm   \\
  \hline
  \hline
  \multicolumn{7}{|c|}{{\color{\Pcol} \PJgy{}}$\rightarrow$ \Pepem{},\Pmpmm{}} \\ 
  \hline
  \multicolumn{2}{|l|}{$E_{\gamma}$ range GeV}      &  8.3-11.                    &  8.3-11.               &   8.3-11.              &  8.3-9.5               &  8.3-11.     \\
  \multicolumn{2}{|l|}{decay angle CM       }       & -                           & -                      & 100$^{\circ}$          & 51$^{\circ}$           & 90$^{\circ}$ \\
  \multicolumn{2}{|l|}{Acceptance \%        }       & {\color{\Fcol} $\sim 40$}   & -                      & {\color{\Fcol} 0.027}  & {\color{\Fcol} 0.026}  & {\color{\Fcol} 0.009} \\
  \multicolumn{2}{|l|}{$\sigma{}(M)/M$      }       & {\color{\Fcol} $\sim 1\%$}  & -                      & {\color{\Fcol} 0.24\%} & {\color{\Fcol} 0.2\%}  & {\color{\Fcol} 0.2\%} \\
  \hline
  $\frac{d\sigma}{dx}\propto(1-x)^2$& events/90days & {\color{black}260}          & -                      & {\color{black}2400}    & {\color{black}100}     & {\color{black}800}  \\
           & days required{\color{black}}           & {\color{black}640}          & -                      & {\color{black}190}     & -                      & {\color{black}560} \\
  \hline
  $\frac{d\sigma}{dx}\propto(1-x)^0$& events/90days & {\color{black}2100}         & -                      & {\color{black}28000}   & {\color{black}4100}    & {\color{black}9500} \\
           & days required{\color{black}}           & {\color{black}40}           & -                      & {\color{black} 45}     & -                      & {\color{black} 130} \\
  \hline
  \hline
  \multicolumn{7}{|c|}{{\color{\Pcol} \PaDz{}$\rightarrow$\PKp{}\Pgpm{}} } \\
  \hline
  \multicolumn{2}{|l|}{$E_{\gamma}$ range GeV }     &  8.7-9.3                    &  8.7-11.               &   8.7-11.              &  8.7-10.               &  8.7-11.     \\
  \multicolumn{2}{|l|}{decay angle CM        }      & -                           & 90$^{\circ}$           & 100$^{\circ}$          & 66$^{\circ}$           & 80$^{\circ}$  \\
  \multicolumn{2}{|l|}{Acceptance \%         }      & {\color{\Fcol} $\sim 40$}   & {\color{\Fcol} 0.003}  & {\color{\Fcol} 0.022}  & {\color{\Fcol} 0.026}  & {\color{\Fcol} 0.008} \\
  \multicolumn{2}{|l|}{$\sigma{}(M)/M$       }      & {\color{\Fcol} $\sim 1\%$}  & {\color{\Fcol} 0.17\%} & {\color{\Fcol} 0.2\%}  & {\color{\Fcol} 0.2\%}  & {\color{\Fcol} 0.2\%} \\
  \hline
  $\frac{d\sigma}{dx}\propto(1-x)^2$& events/90days & {\color{black}540}          & 400                    & {\color{black}2900}    & {\color{black}120}     & {\color{black}1100} \\
%          & days required{\color{black}}           & {\color{black}???}          & -                      & {\color{black} ??}     & -                      & {\color{black} ???} \\
  \hline
  $\frac{d\sigma}{dx}\propto(1-x)^0$& events/90days & {\color{black}3400}         & 13000                  & {\color{black}29000}   & {\color{black}4600}    & {\color{black}10000} \\
%          & days required{\color{black}}           & {\color{black}??}           & -                      & {\color{black} ??}     & -                      & {\color{black} ???} \\
  \hline
  \hline
 \end{tabular}
%\renewcommand{\arraystretch}{1}
  
% }
\end{center}
\caption{The prospects of the charm studies with the standard JLab equipment.
         The decay angle accepted may be constrained for 2-arm spectrometers
         due to their limitations on the minimum angle and maximum momentum. Measurements
         by 2-arm spectrometers have to be done at several endpoints with a 0.4~GeV step.
         The number of days required was estimated for a condition that the relative
         statistical error averaged for all the bins except the first one does not exceed 10\%.
         This estimate was not done for D production since for the moment we have no reliable estimate of 
         the background level.}
\label{tab:existspecres}
\end{table}

\vspace{0.4cm}

\begin{figure}[htb]
\begin{center}
   \scalebox{0.75}{
%    \rotatebox{-90}{
        \includegraphics{pictures/brodsky_crossec_proj_d_nocolor.epsi}
%    }
   }
\end{center}
\caption{Expected results for the cross-section measurements for 
         %         MAD+HRS on the top plot and 
         Hall D, % on the bottom plot, 
         assuming the cross-section behavior described by Eq.~(\ref{eq:gluonexch}).
         The theoretical curves were normalized to the existing measurements
         at 11 and 13~GeV. On the top of the plots the thresholds of various
         charm channels are shown.
        }
\label{fig:expresstan}
\end{figure}

The best results can be obtained by Hall~D and the MAD+HRS spectrometers of Hall~A. One should point out
that Hall~D can perform the charm studies in parallel with the other programs and therefore accumulate
a longer running time, providing that the beam tagging system covers the full energy range.  
The expected measurements for a 300~day run of Hall~D with their errors are presented on Fig.~\ref{fig:expresstan}.
Although Hall~D can provide a lower sensitivity than MAD+HRS,
it has a considerable
advantage of the beam tagging and of a large acceptance which allow to select certain 2-body reactions,
including the ``elastic'' production of \PJgy{}. 


% ---------------------------------------------------------------------------------------

\subsubsection{Summary on cross-section measurements}
\label{sec:existsumm}

\begin{list}{{\color{black}$\bullet$}}
                                     {\setlength{\itemsep}{0.2cm}
                                      \setlength{\leftmargin}{0.4cm}\setlength{\topsep}{0.cm}}
      \item {} The {\color{black}\PJgy} measurements:
           \begin{list}{{\color{black}$\circ$}}
                                     {\setlength{\itemsep}{0.1cm}
                                      \setlength{\leftmargin}{0.4cm}\setlength{\topsep}{0.cm}}
               \item {} Halls A/C (mainly HRS+MAD):
                   \begin{list}{}
                                     {\setlength{\itemsep}{0.cm}
                                      \setlength{\leftmargin}{0.4cm}\setlength{\topsep}{0.cm}}
                      \item {\color{black}+} enough statistics for  $\sigma{}>\sim{}0.01$nb;
                      \item {\color{black}--} the recoil particle is not detected;
                      \item {\color{black}--} the decay angular distribution not measured - no polarization
                                              study is possible.
                   \end{list} 
               \item {} Hall D has some advantages:
                   \begin{list}{}
                                     {\setlength{\itemsep}{0.2cm}
                                      \setlength{\leftmargin}{0.4cm}\setlength{\topsep}{0.cm}}
                      \item {\color{black}+} the recoil and other particles are detected;
                      \item {\color{black}+} the angular distribution is measured;
                      \item {\color{black}+} the photon energy is known and no end point tunes are needed;
                      \item {\color{black}--} about 2 years running is needed;
                      \item {\color{black}+} running parallel with the other programs. 
                   \end{list}
           \end{list}

      \item {} The open charm measurements:
           \begin{list}{{\color{black}$\circ$}}
                                     {\setlength{\itemsep}{0.0cm}
                                      \setlength{\leftmargin}{0.4cm}\setlength{\topsep}{0.cm}}
               \item {} results are dependent on the level of background (no experimental
                        data exists on this matter);
               \item {} halls A (HRS+MAD) has a statistical advantage over Hall~D and
                        needs 3-5 months to make a useful measurement, while Hall~D may be able
                        to reduce the background.
           \end{list}
\end{list}
\vspace{0.2cm}

\noindent
The standard equipment at JLab allows to make a pilot experiment and
obtain results on the \PJgy{} production with a statistical accuracy of about 10\%
if the cross-section behaves like $(1-x)^2$, or about 3\% if the cross-section behaves 
like $(1-x)^0$. Also, one may be able to measure the open charm cross-section,
depending on the level of background.

%    The standard equipment at JLab may be enough for a cross-section measurement
%    on one target (Hydrogen) for both {\color{black}\PJgy} and open charm, in case
%    the cross-section does not fall steeper than $(1-x)^2$.
It would not be possible  
to measure the rare effects like hidden color. Only Hall~D can in principle do that because 
the recoil nucleon or nucleons have to be detected. Since the effect could be less than 
1\% of the full cross-section, even for the $(1-x)^0$ dependence one may expect not more than a dozen
of {\color{\Pcol}\PJgy} observed. 

%with additional time allocated
%various nuclear effects etc.

The standard equipment would not allow to study production of {\color{black}\Pcgci} or 
{\color{black}\Pcgh}, given the expected rates.  

% ---------------------------------------------------------------------------------------

\subsubsection{A-dependence measurement}
\label{sec:existadep}

The \SigPN{} cross-section will be derived from the A-dependence of \PJgy{} cross-section,
measured on various light and heavy targets. 
At the first stage of Hall~D only a hydrogen target will be used. The best option
to study the A-dependence of the \PJgy{} cross-section is to use MAD+HRS. 
Recoil detection is not important for this measurement. 
Such a measurement can be done at one end point. In order to estimate the energy dependence of
\SigPN{} several end points should be used. 

The event rates were evaluated for the conditions as follows: 
\begin{list}{{\color{black}--}}
                                     {\setlength{\itemsep}{0.cm}
                                      \setlength{\leftmargin}{0.6cm}\setlength{\topsep}{0.cm}}
      \item {} the end point was at 11 GeV; 
      \item {} the liquid hydrogen and deuterium targets were 15~cm thick;
      \item {} the solid targets were 7.7\% of radiation length thick;  
      \item {} $\sigma{}_A\approx{}A\cdot{}\sigma{}_N$
\end{list}
\noindent
The results are summarized in Table~\ref{tab:stanadep}.
\begin{table}[h]
\begin{center}
\scalebox{1.0}{
 \begin{tabular}{|l|l||r|r|r|r|r|r|r|r|}
  \hline 
  \hline 
   \multicolumn{2}{|c|}{target}        &  $^1$H     &   $^2$H    &   Be      &   C       &   Al      &   Cu      &    Ag    &    Pb      \\
  \hline 
  \hline 
   {\color{\Pcol}\PJgy}  & $(1-x)^2$   & 160        &   320      &  550      &  360      &  210      &  110      &  80      &   60       \\
  \cline{2-10} 
    /day                 & $(1-x)^0$   &  \multicolumn{8}{|c|}{$\times{}$5.4}              \\
  \hline
  \hline 
 \end{tabular}
 }
\end{center}
\caption{The expected yields of MAD+HRS setup per day on various targets}
\label{tab:stanadep}
\end{table}
\vspace{0.4cm}

In order to accumulate 1000 events per target about 60 running days are required.
Such a measurement should provide a statistical error for \SigPN{} extraction of
about 7\% (see Table~\ref{tab:nuclabs}).

In order to extract \SigPN{} from data one should take into account the Fermi motion
and the energy dependence of $\sigma_{\gamma{}N\rightarrow{}J/\psi{}X}$. 
Such a correction was used by \cite{Anderson:1977hi}. Therefore a measurement of
the energy dependence  of $\sigma_{\gamma{}N\rightarrow{}J/\psi{}X}$ is needed for 
\SigPN{} extraction. It can be done either with the same MAD+HRS setup or
at Hall~D.

% ---------------------------------------------------------------------------------------

\subsection{A dedicated apparatus for \PJgy{} studies}
\label{sec:dedicapp}

As we have concluded in section~\ref{sec:existsumm}, 
the standard equipment at JLab would allow to make a pilot experiment on 
\PJgy{} production, but would not allow to look for rare effects, like hidden color.
In order to fulfill the most challenging part of the program a considerable improvement is
needed.
It would be difficult to improve considerably the prospects for
open charm studies at JLab. However it is possible to make a major improvement
of {\color{\Pcol}\PJgy{}} studies, building a dedicated detector, which:
\begin{list}{{\color{black}--}}
                                     {\setlength{\itemsep}{0.cm}
                                      \setlength{\leftmargin}{0.6cm}\setlength{\topsep}{0.cm}}
      \item {} capable to work at a luminosity of {\color{\Pcol}${\cal L} \sim 10^{36}$};
      \item {} has a high acceptance of {\color{\Pcol}$>$0.2};
      \item {} detects {\color{\Pcol}$\Psi$} and the recoil proton; 
      \item {} detects a wide range of the decay angles: $-0.5<\cos{\theta{}_{CM}}<0.5$.
\end{list}

\subsubsection{ Outline}
\label{sec:dedicoutline}

The momentum and the angular ranges of the recoil proton are similar to those of
the \PJgy{} decay products, but the proton direction is practically uncorrelated with them.
In order to provide a reasonable acceptance, a large acceptance recoil detector should be used. 
Such a detector would not work with the high resolution spectrometers (MAD+HRS), because
of the high luminosity.  
On the other hand, the luminosity at the large acceptance detector of Hall~D
is limited both by the beam tagging and by the detector geometry and types. 

Here we consider a detector operating in an untagged beam of about 1000 times higher rate
than the beam of Hall~D, with an acceptance smaller than the acceptance of the Hall~D
detector (limited in the polar angle), but still not lower than 10\%. 

\noindent Let us consider a detector consisting of:
\begin{list}{{\color{black}--}}
                                     {\setlength{\itemsep}{0.cm}
                                      \setlength{\leftmargin}{0.6cm}\setlength{\topsep}{0.cm}}
      \item {} A calorimeter for detecting \Pepem{}: the energy and the coordinates are measured. 
      \item {} A scintillator or lucite hodoscope in front of the calorimeter.
      \item {} Protons are detected/identified using the calorimeter and a scintillator
               detector behind it.
      \item {} Tracking would be of a big help in order to reduce the accidental rate
               (in a long target) and reconstruct the proton tracks;
      \item {} A magnetic field should be used, mainly in order to remove the low energy
               electrons.
\end{list}
\vspace{0.3cm}

The limitations on the luminosity that such a detector can take in 
electron on photon beams are driven by:
%High rate of electromagnetic background in {\color{\Pcol}\Pem} and {\color{\Pcol}\Pgg} beams.
%The limitations on the possible luminosity are driven by:
\begin{list}{{\color{black}$\bullet$}}
                                     {\setlength{\itemsep}{0.2cm}
                                      \setlength{\leftmargin}{0.1cm}\setlength{\topsep}{0.15cm}}
   \item {} The detectors:
        \begin{list}{{\color{black}$-$}}
                                     {\setlength{\itemsep}{0.cm}
                                      \setlength{\leftmargin}{0.3cm}\setlength{\topsep}{0.cm}}
             \item {} the maximum allowed energy flow/s/module in the calorimeter;
             \item {} the maximum allowed charged particle flux/s/cm$^2$ in the tracking detectors;
             \item {} the maximum allowed occupancy in the tracking detectors;
             \item {} the maximum allowed charged particle flux/s/module in the trigger hodoscope;
        \end{list}
   \item {} The trigger rate should be {\color{\Pcol}$<2\cdot{}10^{4}$}/s.
   \item {} The accidental coincidence:
        \begin{list}{{\color{black}$-$}}
                                     {\setlength{\itemsep}{0.cm}
                                      \setlength{\leftmargin}{0.3cm}\setlength{\topsep}{0.cm}}
             \item {} CEBAF defines a minimum resolution time of {\color{\Pcol}2ns};
             \item {} Track reconstruction with an extended target would provide a factor of {\color{\Pcol}$>$10}
                      improvement.
        \end{list}
\end{list}
\vspace{0.3cm}

A successful experiment at Cornell~\cite{Gittelman:1975ix} used 2 arrays of a lead-glass calorimeter
at a distance of 150cm from the target. The low energy background was removed with a help of a dipole magnet
providing a field integral of 0.85~kGs$\cdot$m. Using a dipole field makes a dead zone along a central band, normal
to the field, thus reducing the acceptance. We preferred to consider a solenoidal field and a detector homogeneous
in the azimuthal angle. The strength of the field should be selected on the base of the low energy background
suppression.

\begin{figure}[htb]
\begin{center}
\scalebox{0.55}{
  \rotatebox{-90}{
    \includegraphics{pictures/jpsi_setup_1_nocolor.epsi}
   }
}
\end{center}
\caption{General layout of the dedicated detector proposed for the \PJgy{} studies.}
\label{fig:setup}
\end{figure}

\begin{figure}[htb]
\begin{center}
\scalebox{0.4}{
  \rotatebox{-90}{
    \includegraphics{pictures/jpsi_det_calor_nocolor.epsi}
   }
}
\scalebox{0.4}{
  \rotatebox{-90}{
    \includegraphics{pictures/jpsi_det_hodos_nocolor.epsi}
   }
}
\end{center}
\caption{
%        Layout of the dedicated detector proposed for the \PJgy{} studies.
%        On the top picture a general layout is shown, while on the two bottom
        A frontal look on 
        one quadrant of the calorimeter (left picture) and one quadrant of the hodoscope (right picture).
        }
\label{fig:setupdet}
\end{figure}

A sketch of the detector is presented on Fig.~\ref{fig:setup}. The experiment uses
a mixed beam. A radiator of 6\% radiation length is positioned at about 130cm from the 
target center. A shielding 80~cm long downstream of the radiator helps to absorb
the particles coming from the radiator at high angles. Various targets should be used -
liquid hydrogen (about 10~cm long), liquid deuterium and solid targets.   
The target is positioned in a solenoidal magnetic field. The acceptance of the detector
in the polar angle $\theta$ ranges from 10$^\circ$ to 30$^\circ$, which covers
the decay angles in the \PJgy{} CM frame of $0.5<\cos{\theta{}_{CM}}<0.5$. The magnetic
field fills most of the volume up to the calorimeter, 150~cm downstream of the target.
 The ring-shaped tracking detectors are positioned between the target and the calorimeter. 
For proton identification, a thick scintillator hodoscope (not shown on Fig.~\ref{fig:setup}) 
can be installed downstream of the calorimeter. The choice of the detectors is discussed
in the next sections.

% ---------------------------------------------------------------------------------------

\subsubsection{The choice of the magnetic field}
\label{sec:dedicmagn}

The field would play two roles. The first and the most important is to contain the
low energy charged background to the central area close to the beam, at angles 
below 10$^\circ$. The second role is to help measuring the track momenta, in particular
for the recoil protons. The field was optimized using GEANT~\cite{GEANT321} simulation,
which simulated the electron beam interaction in the radiator and in the target
and tracked the particles through the setup. The energy fluxes through the detector
planes were estimated. In order to check the accuracy of GEANT simulation 
of the energy flux, we compared the results of simulations with a measurement done in Hall~A.
The measurement was done with a 1.833~GeV beam on a 15~cm liquid hydrogen target,
at 11$^\circ$ using a lead-glass calorimeter module. The measured energy flux was about 25\%
lower than predicted by GEANT. This agreement is sufficiently good. \\

The results of the calculations of the energy flux at the face of the calorimeter
are shown on Fig.~\ref{fig:energyflux}. The optimal field is about 2~T. Higher fields
practically would not help to reduce the energy flux, but would help the momentum
measurements.

\begin{figure}[htb]
\begin{center}
\scalebox{0.5}{
  \rotatebox{-90}{
    \includegraphics{pictures/jpsi_bg_cal_1_nocolor.epsi}
   }
}
\end{center}
\caption{The GEANT simulation of the energy flow on the calorimeter face
         through a $4\times{}4$~cm$^2$ area for 1$\mu{}$A electron beam. 
         On the left
         plot the average flux over the calorimeter surface is presented, depending
         on the field in the solenoid. 
         The flux was calculated
         in two cases - for a mixed beam of electrons and photons and for a pure photon beam.
         On the right plot the flux dependence on
         the distance from the beam for various values of the field is shown.
        }
\label{fig:energyflux}
\end{figure}

% ---------------------------------------------------------------------------------------

\subsubsection{Calorimeter}
\label{sec:dediccalor}

Lead-glass calorimeters have been widely used for high flux environment. They have a typical
energy resolution of about $\sigma{}(E)/E~\approx{}~0.06/\sqrt{E}+0.01$, where energy
is measured in GeV,  and a position resolution
of several mm, depending on the lateral size of the module. Lead-glass calorimeters detect Cherenkov
light and are not sensitive to low energy background which is below the Cherenkov threshold.
The minimal lateral size of a module, defined by the Moli\`ere radius, is typically about 4~cm. \\

The maximum energy flow which a calorimeter can stand was defined as the flow
causing a shift of the pedestal corresponding to about 1\% of the minimal energy to be measured. 
Assuming the minimal energy of 2~GeV and a gate of 100~ns on the ADC, one obtains
the maximal flow allowed of 2$\times{}10^5$GeV/s/module. 
At Hall~A, various tests of lead-glass calorimeter prototypes have been made and it was found
that indeed at the conditions given the calorimeter was operating normally.

Since we have to minimize the energy flow per module, we are also considering 
a smaller size calorimeter modules, built from
a heavier material than lead-glass, for the central part of the array. At the moment the most
attractive candidate is PbWO$_4$ crystal with Moli\`ere radius of 2.2~cm - about 1/2 of the typical
lead-glass. This allows to build modules of about 2$\times$2~cm$^2$. 
The energy resolution is 2-3 times better than the lead-glass resolution. 
Since the PbWO$_4$ crystal scintillates it may be more sensitive to the low energy flux.
The behavior of the crystal in the environment of a high luminosity experiment
should be studied experimentally.\\

Let us assume that the size of the modules at the low angles is $2\times{}2$cm$^2$.
From the Fig.~\ref{fig:energyflux} we see that at a 2~T magnetic field at a radius of 27~cm,
or $\theta{}=10^\circ$, the flux through such a module should be about $3\cdot{}10^4$GeV/s at 1$\mu{}A$,
which is about 15\% of the limit. With no field the flux would be about $1.5\cdot{}10^6$GeV/s,
which is about 7 times higher than the limit. At the radius of about 45~cm the flux drops by
a factor of 4-5. Therefore the small PbWO$_4$ modules should cover a ring between the radii
27 and 45~cm. The outer area can be covered with lead-glass modules of $4\times{}4$cm$^2$.\\

The full number of modules needed for the detector depicted on Fig.~\ref{fig:setupdet}
is 1136 of lead-glass and 1028 of PbWO$_4$.\\

The calorimeter described will be able operate at the beam currents up to $\sim{}6\mu$A.  


% ---------------------------------------------------------------------------------------

\subsubsection{Tracking detectors}
\label{sec:dedictrack}

So far, the best detector for the experiment discussed is GEM (Gas Electron Multiplier)
detector~\cite{Sauli:1997qp,Bachmann:1999tj,Bachmann:1999ru}. This detector
was invented at CERN in about 1996, as an improvement of the MSGC (Micro Strip Gas Chamber)
and its technology is quickly maturing. The parameters are:
\begin{list}{{\color{black}--}}
                                     {\setlength{\itemsep}{0.1cm}
                                      \setlength{\leftmargin}{0.6cm}\setlength{\topsep}{0.cm}}
      \item {} It stands high particle densities {\color{\Fcol}$\sim{}10^{7}$/cm$^2$/s}.
      \item {} A small pitch of 200-400$\mu{}$m helps to keep the occupancy acceptable. 
      \item {} Fast signals allow a short gate of about 30~ns.
      \item {} It has a very good spatial resolution of {\color{\Fcol}$\approx{} 40-60\mu{}$m}.
      \item {} At the moment relatively large 30$\times$30cm$^2$ detectors are being built
               for the experiments COMPASS and HERA-B. The latter should operate at a flux of
               about $0.25\times{}10^{7}$/cm$^2$/s. 
      \item {} Complex detector shapes can be naturally arranged.
      \item {} Two projections readout is possible.
      \item {} It is thin in radiation lengths (below 0.3\% per 2 coordinates).
\end{list}
\vspace{0.3cm}

The momentum resolution which a set of GEM detectors would provide was simulated.
5 GEM double coordinate planes (in the shape of rings) were distributed in the space of 
40-120~cm from the target center. The readout stripes were nearly radial, at the $10^\circ$
stereo angle. At the minimal radius of the ring, the spatial resolution assumed was 
40$\mu{}$m in $\phi$ direction, while increasing linearly with the radius. 

In a field of 2~T the trajectory of a particle with the transverse momentum of 1~GeV/c is bent 
with a curvature of 150~cm.
The momentum resolution calculated is as follows:

\vspace{0.2cm}
 \begin{tabular}{lll}
  P GeV/c & $\theta$ & $\sigma{}(P)/P$ \\
  2.      & $30^\circ$ & 1.3\% \\
  5.      & $20^\circ$ & 3.3\% \\
  9.5     & $10^\circ$ & 6.7\% \\
 \end{tabular}
\vspace{0.3cm}

The charged particle flux was simulated in the same was as the energy flow for the calorimeter
described in section~\ref{sec:dediccalor}. At the lowest radius in the detector plane
closest to the target the calculated flux of $\sim{}5\times{}10^6$/s/cm$^2$ at 1$\mu$A is close to 
the limit. 

The occupancy predicted is about 3\%. 
%In a pure photon beam the rate would go down by a factor of $\sim{}5$.\\

In total, about 3.5~m$^2$ of GEM detectors is needed, which would have about 20k 
of readout channels. \\

The detector described will be able to operate at the beam currents up to 
$\sim{}2\mu$A.  
 
% ---------------------------------------------------------------------------------------

\subsubsection{Hodoscope}
\label{sec:dedichodos}

The main purpose of the hodoscope is to provide the best timing possible. Another
task - to suppress the events caused by high energy photons should be
performed well by the tracking detectors. The trigger
will be based mainly on the calorimeter signals above a certain threshold. However,
the calorimeters existing or being built at JLab at the moment provide a time resolution
not better than 4-5~ns due to the type of PMT used. The hodoscope should be as highly
segmented as possible in order to provide an acceptable occupancy. It is preferable
to use a lucite Cherenkov counter instead of a scintillator counter in order
to reduce the response to low energy particles. Such a hodoscope is being built
for Real Compton experiment at Hall~A. The time resolution of 1~ns can be achieved.
The expected occupancy of the hodoscope shown on Fig.~\ref{fig:setupdet} with 180 elements
is $\sim$10\%
within a 30~ns time window and about 1.\% with the 2~ns minimal time resolution
of CEBAF, at 1$\mu$A.\\

The detector described will be able operate at the beam currents up to 
$\sim{}2\mu$A.  
  
 
% ---------------------------------------------------------------------------------------

\subsubsection{Acceptance and event rates}
\label{sec:dedicaccep}

The acceptance of the detector was calculated using GEANT simulation. 
For the event rate evaluation it is assumed that the
detector is running with a mixed untagged beam of 0.5$\mu$A at 11~GeV, with a 6\%~RL radiator,
on a 10~cm liquid hydrogen target. 

In order to minimize the errors of the evaluation, the results of the Cornell
experiment~\cite{Gittelman:1975ix} were used, scaled for the difference in
the integrated luminosity and the acceptances (see Table~\ref{tab:dediccorn}).
The end point of the Cornell experiment
was at 11.8~GeV, while the end point at JLab would be 11.0~GeV. Assuming the \PJgy{} cross-section
energy dependence of Eq.~(\ref{eq:gluonexch}), with $n_g=2$, and that the JLab experiment
has the same integrated luminosity as the Cornell experiment,
the \PJgy{} production yield at JLab would be 50\% of the Cornell. If $n_g=0$ in Eq.~(\ref{eq:gluonexch}),
the yield would be 70\% of the Cornell. We assume a correction factor for the JLab to Cornell ratio of 0.5. 

\vspace{0.3cm}
\begin{table}[htb]
\begin{center}
  
 \begin{tabular}{|l|l|r|r|}
  \hline
 \hline
 \multicolumn{4}{|c|}{Estimates of the rates relative to the Cornell experiment} \\ 
 \hline
  \multicolumn{2}{|l|}{meaning     }                                  & Cornell, 1975            & JLab proposal \\
  \hline
  \multicolumn{2}{|l|}{Duty cycle  }                                  & 0.07                     & 1.  \\
  \multicolumn{2}{|l|}{End point, GeV}                                & 11.8                     & 11. \\
  \multicolumn{2}{|l|}{Beam        }                                  & {\color{\Pcol}\Pgg{}}    &  {\color{\Pcol}\Pem{}}    \\%
  \multicolumn{2}{|l|}{{\color{\Pcol}\Pem{}} beam current, radiator}  & -                        & 0.5$\mu$A, 0.06 \\
  \multicolumn{2}{|l|}{N equivalent quanta, average, s$^{-1}$}        & 3.3$\times{}10^{9}$      & 1.9$\times{}10^{11}$ \\
  \multicolumn{2}{|l|}{Target          }                              & 2.9 g/cm$^2$ Be          & 0.7 g/cm$^2$ LH  \\
  \multicolumn{2}{|l|}{Days of running }                              & 11.4                     & 90$\times$0.7={\color{\Fcol}63} \\
  \multicolumn{2}{|l|}{Acceptance      }                              & $\approx{}0.03$          & {\color{\Fcol}$\approx{}0.3$} \\
  \multicolumn{2}{|l|}{End point correction factor}                   & 1.                       & 0.5 \\
  \multicolumn{2}{|l|}{Relative \PJgy{} yield     }                   & 1.                       & {\color{\Fcol}380} \\
  \multicolumn{2}{|l|}{Relative mass resolution   }                   & 1.                       & {\color{\Fcol}0.5} \\
  \multicolumn{2}{|l|}{{\color{\Pcol}\PJgy{}} / BG}                   & 500/100                  & {\color{\Fcol}$\sim{} 2\cdot{}10^{5}/2\cdot{}10^{4}$} \\
  \multicolumn{2}{|l|}{Magnetic field  }                              & 0.85kGs$\cdot$m dipole   & 20kGs solenoid \\
  \multicolumn{2}{|l|}{$\cal L$, $\gamma$p, in spill, cm$^{-2}$s$^{-1}$, E$_{\gamma}>$5~GeV}
                                                                      & $7.0\times{}10^{34}$     & {\color{\Fcol}$6.3\times{}10^{34}$}  \\
  \multicolumn{2}{|l|}{Recoil detected?           }                   & no                       & {\color{\Fcol}yes} \\
  \multicolumn{2}{|l|}{Full kinematics            }                   & no                       & {\color{\Fcol}yes} \\
 \hline
 \multicolumn{4}{|c|}{Direct estimates of the rates} \\ 
 \hline
  model                              & meaning                        &   \multicolumn{2}{|c|}{JLab proposal}  \\
 \hline
  $\frac{d\sigma}{dx}\propto(1-x)^2$ & events/90days                  &   \multicolumn{2}{|c|}{\color{\Fcol}$6\cdot{}10^4$}  \\
                             & days required{\color{black}}           &   \multicolumn{2}{|c|}{\color{\Fcol}10}  \\
  \hline
  $\frac{d\sigma}{dx}\propto(1-x)^0$ & events/90days                  &   \multicolumn{2}{|c|}{\color{\Fcol}$3\cdot{}10^5$}  \\
                             & days required{\color{black}}           &   \multicolumn{2}{|c|}{\color{\Fcol}0.2}  \\
 \hline
 \hline
 \end{tabular}
\end{center}
\caption{Comparison of the proposed experiment at JLab and the experiment at Cornell. The ``number of days'' needed
         is defined in the caption for Table~\ref{tab:existspecres}.}
\label{tab:dediccorn}
\end{table}
\vspace{0.3cm}
 
The beam current of 0.5$\mu$A was selected in order to equalize the \PJgy{}p luminosity
with the ``in-spill'' luminosity of the Cornell experiment. In these conditions 
the experiment at JLab should be able to accumulate about 400 times higher statistics
than at Cornell. The gains
come from the duty cycle of CEBAF, from the detector acceptance and the duration of running.\\

The direct estimate of the \PJgy{} yield, done in in the same way as described for the ``standard spectrometers''
(see section~\ref{sec:existspec}), gave $\sim{}0.6-3\cdot{}10^{5}$ particles for a 90 day run, depending on the production model,
comparable to the yield obtained by scaling from the Cornell experiment. The direct estimate results
are presented on Fig.~\ref{fig:expresdec}, along with the estimates for HRS+MAD spectrometers
on the open charm studies. \\

\begin{figure}[htb]
\begin{center}
   \scalebox{0.75}{
%    \rotatebox{-90}{
        \includegraphics{pictures/brodsky_crossec_proj_cal_nocolor.epsi}
%    }
   }
\end{center}
\caption{Expected results for the \PJgy{} cross-section measurements with 
         the dedicated setup and for open charm with MAD+HRS spectrometers.
         The theoretical curves were normalized to the existing measurements
         at 11 and 13~GeV. On the top of the plots the thresholds of various
         charm channels are shown.
        }
\label{fig:expresdec}
\end{figure}

The advantages with respect to the Cornell experiment are summarized:
\vspace{0.3cm}
\begin{list}{{\color{black}$-$}}
                                     {\setlength{\itemsep}{0.1cm}
                                      \setlength{\leftmargin}{0.6cm}\setlength{\topsep}{0.cm}}
      \item {} higher statistics (about $\times{}400$);
      \item {} the better energy and mass resolution ($\times 3$) and also the full kinematic information
               on the event should reduce the background; 
      \item {} the full kinematic information will exclude the inelastic processes,
               which could contribute about 30\% to the Cornell sample;
      \item {} the {\color{\Pcol}\Pgg{}} energy can be reconstructed with a resolution
               of about 1\% - at least 2 times better than at Cornell.
\end{list}
\vspace{0.3cm}

\subsubsection{Feasibility of the experiment}
\label{sec:feasibility}

The experiment discussed, running with a pure photon beam, must be feasible
as an extrapolation from the successful Cornell experiment at the same luminosity.
Since building a pure photon beam may pose a problem in the environments of halls A or C,
one should consider using a mixed beam. 

The influence of the electron component of the beam should be considered.
The simulation shows that the low energy particles from the electron beam do not create an unacceptable
load on the detectors up to the beam current of $\sim{}2\mu$A. However, the high energy particles
may affect the trigger or add a considerable background to the mass spectra. Two types of 
processes were evaluated for 0.5$\mu$A:

\vspace{0.3cm}
\begin{list}{{\color{black}$\bullet$}}
                                     {\setlength{\itemsep}{0.1cm}
                                      \setlength{\leftmargin}{0.6cm}\setlength{\topsep}{0.cm}}
      \item {} The {\color{\Pcol}\Pem{}} beam produces additionally
               about $2.5\cdot{}10^4$/s scattered {\color{\Pcol}\Pem{}} at E$>$1.5GeV in $10^{\circ}<\theta{}<30^{\circ}$.  
               The accidental coincidence rate should be still under control. 
      \item {} The pion rate from the {\color{\Pcol}\Pem{}} beam should be about 2 times higher
               than in Cornell experiment, where it made no visible contribution to the background.
\end{list}
\vspace{0.3cm}

We conclude that the electron component of the beam should not increase the background in
any dramatic way.\\

We used a conservative limit of 0.5$\mu$A for the beam current. It is likely that the experiment would
be able to use up to 2$\mu$A.

\subsubsection{Other items of the physics program}
\label{sec:ntargets}

The experiment discussed can run with nuclear targets. 
It is capable of detecting
reactions of the type $D(\gamma,J/\psi~p)n$ or $^3He(\gamma,J/\psi 2p)n$ in order to look
for the hidden color effects. In particular, the latter reaction is of interest, since
both nucleons struck are protons and detectable by the apparatus. In the former reaction
the neutron momentum has to be reconstructed from kinematical constraints.

The detector can run with solid targets in order 
to measure the A-dependence of the cross-section. The optimal thickness of the targets
depends on the background they create. In the worst case, it should scale like the radiation length
of the material, and the ratio between the charm yields on hydrogen and lead would be about 10.
In 5 days the experiment would be able to accumulate about 10$^3$ \PJgy{} particles on one
heavy target, and about 20 days should be enough for the A-dependence measurements.
 
A search for {\color{\Pcol}\Pcgh}$\rightarrow$\Pgg\Pgg{} could hardly be successful
since the background in \Pgg\Pgg{} is about 10 times higher than in \Pep\Pem{} 
combinations~\cite{Gittelman:1975ix} and, taking the branching ratio into account, one
may expect a signal to background ratio of $\sim{}10^{-3}$, if the {\color{\Pcol}\Pcgh}
cross-section is similar to that of \PJgy{}. A search for {\color{\Pcol}\Pcgci}
seems more promising down to cross-sections of $\sim{}0.01$~nb.

% ---------------------------------------------------------------------------------------

\subsection{Summary on the experimental options}
\label{sec:options}

Summarizing the experimental options discussed we select the most promising
ones, namely Hall~D, HRS+MAD of Hall A and the dedicated, calorimeter-based  experiment called here ``ECAL''
for brevity. These three options provide the resolutions on the key physics variables as shown in Table~\ref{tab:resolut}. 


\vspace{0.2cm}
\begin{table}[htb]
\begin{center}
 \begin{tabular}{|l|l|l|l|l|}
 \hline
  setup                & \scalebox{1.0}{$\sigma{}(M)/M$} & \scalebox{1.0}{$\sigma{}(E_{\Psi})/E_{\Psi}$} 
              & \scalebox{1.0}{$\sigma{}(E_{\gamma})/E_{\gamma}$} & \scalebox{1.0}{$\sigma{}t (GeV/c)^2$}  \\
 \hline
  \scalebox{1.0}{Hall D, tagged beam}    & 0.010  & 0.004  &  0.001 &  0.03  \\  
  \scalebox{1.0}{HRS+{\color{black}MAD}} & 0.002  & 0.001  &  0.002 &  0.014 \\  
  \scalebox{1.0}{ECAL}                   & 0.035  & 0.007  &  0.01  &  0.11  \\  
 \hline
 \end{tabular}
\end{center}
\caption{Experimental resolutions of the possible charm experiments at JLab}
\label{tab:resolut}
\end{table}
\vspace{0.2cm}

\begin{table}[htb]
\begin{center}
 \begin{tabular}{|l|l|r|r||r|r|r|r|}
 \hline
 \hline
  process & setup & recoil & BG/sig & \multicolumn{2}{|c|}{$d\sigma{}/dt\propto(1-x)^2$} & \multicolumn{2}{|c|}{$d\sigma{}/dt\propto(1-x)^0$}  \\ 
 \cline{5-8}
          &       &        &        &  events/        & days         &  events/        & days      \\
          &       &        &        &  90 days        & needed       &  90 days        & needed    \\
 \hline
 \hline
  \multicolumn{8}{|c|}{\scalebox{1.0}{{\small{\color{\Pcol} \Pgg{}p $\rightarrow$\PJgy{}p}}}} \\ 
 \hline
   \scalebox{1.0}{{\color{\Pcol}\PJgy$\rightarrow$}\Pepem{}}          & \scalebox{1.0}{ECAL}     & {\color{\Fcol}yes}  & 0.10     & 0.6$\cdot{}10^5$ & {\color{\Fcol}10}  & 3.0$\cdot{}10^5$ & {\color{\Fcol}0.2} \\
   \scalebox{1.0}{{\color{\Pcol}\PJgy$\rightarrow$}\Pmll} 
                 & \scalebox{1.0}{HRS+MAD}  & {\color{black}no}   & $<$0.02  & 2.4$\cdot{}10^3$ & {\color{\Fcol}190} & 2.8$\cdot{}10^4$ & {\color{\Fcol}45}  \\
   \scalebox{1.0}{{\color{\Pcol}\PJgy$\rightarrow$}\Pmll}         & \scalebox{1.0}{D} tag    & {\color{\Fcol}yes}  & 0.07     & 2.6$\cdot{}10^2$ & {\color{\Fcol}640} & 2.1$\cdot{}10^3$ & {\color{\Fcol}40} \\
 \hline
 \hline
  \multicolumn{8}{|c|}{\scalebox{1.0}{{\color{\Pcol} \Pgg{}p $\rightarrow$\PcgLp{}\PaDz{}}}} \\
 \hline
   \scalebox{1.0}{{\color{\Pcol} \PaDz$\rightarrow$\PKp{}\Pgpm{}}}    & \scalebox{1.0}{HRS+MAD}  & {\color{black}no}   & 0.05     & 2.9$\cdot{}10^3$ & -                  & 2.9$\cdot{}10^4$ & -                  \\
   \scalebox{1.0}{{\color{\Pcol} \PaDz$\rightarrow$\PKp{}\Pgpm{}}}    & \scalebox{1.0}{D} tag    & {\color{\Fcol}yes}  & 0.25     & 5.4$\cdot{}10^2$ & -                  & 3.4$\cdot{}10^3$ & -                  \\
 \hline
 \hline
 \end{tabular}
\end{center}
\caption{Comparison of the experimental options to study charm at JLab. The background to signal ratio was estimated for 11~GeV
        photons. The last column shows the number of days of data taking needed to achieve an average relative statistical accuracy
        of the cross-section measurement of 10\%, in an energy range of 0.4~GeV above the threshold. This estimate has not been done 
        for open charm since the background is at the moment uncertain. 
        }
\label{tab:options}
\end{table}
\vspace{0.2cm}
The expected particle rates and background estimates are presented on Table~\ref{tab:options}.\\

In the open charm sector Hall~D and HRS+MAD would be able to do the measurement, depending on
the background levels. Hall~D 4$\pi$ acceptance and tagged beam could help to
reduce the background considerably. However the HRS+MAD mass resolution would be better. At the moment
it is not clear which option is more advantageous. \\

For \PJgy{} studies, the best option is the dedicated experiment (ECAL). With ECAL all the program
can be accomplished including the search for rare phenomena like hidden color. Nevertheless,
pilot measurement of the ``elastic production'' cross-section might be done with Hall~D
and A-dependence can be measured with HRS+MAD.  


%\subsubsection{Running plan}
%\label{sec:dedicaccep}

\newpage
\clearpage

\section{Conclusions}

Charm production near threshold has remarkable sensitivity to new
physics, not only the target proton or nuclei, but also the charm
system itself.  All of the valence quarks of the target are forced to
act as a coherent compact state in order that all of the available
energy be focused into heavy flavor production. In the case of nuclear
targets, charm production in the subthreshold regime is sensitive to
hidden-color non-nucleonic correlated states, Fock components which
must occur according to QCD evolution equations.  The unpublished data
from SLAC on $J/\psi$ production near threshold appears to be
remarkably flat, indicating that such high correlated mechanisms may
indeed be relevant.  We have also noted that the production of
charmonium states of even and odd $C$ can selectively reveal different
coherent mechanisms at threshold.  On the other hand the production of
charm states at low relative velocity in the target allows the study
of the QCD van der Waals interaction and the production of exotic
charm resonances or bound states, such as the penta-quark or nuclear
bound quarkonium.

This physics program can be partly fulfilled with the standard JLab
equipment, while the full program, including a search for the rare phenomena
like hidden color requires building a dedicated setup. A general layout
of such a setup has been discussed and it has been argued that this setup
would be adequate to the task.


% ---------------------------------------------------------------------------------------

\section*{ Acknowledgements }

We thank S.~Brodsky, P.~Hoyer, D.~Kharzeev, M.~Strikman and E.~Tomasi-Gustafsson for their help to shape up
this program for charm studies at JLab. 
We are grateful to all who took part in the discussions and helped in writing
down this proposal.

\clearpage

\begin{thebibliography}{99}
\setlength{\itemsep}{0pt}

%\newcommand{\wwwspires}{http://www.slac.stanford.edu/spires/find/hep/www}

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%     ???????????????
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% -- THEORY

%\cite{Brodsky:1980pb}
\bibitem{Brodsky:1980pb}
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%\cite{Frixione:1994dg}
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% -- EXPERIMENT --

%\cite{Camerini:1975cy}
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U.~Camerini {\it et al.},
%``Photoproduction Of The Psi Particles,''
Phys.\ Rev.\ Lett.\  {\bf 35}, 483 (1975).
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%\cite{Gittelman:1975ix}
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B.~Gittelman, K.~M.~Hanson, D.~Larson, E.~Loh, A.~Silverman and G.~Theodosiou,
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%\cite{Knapp:1975nf}
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%\cite{Anderson:1977hi}
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R.~L.~Anderson {\it et al.},
%``A Measurement Of The A-Dependence Of Psi Photoproduction,''
Phys.\ Rev.\ Lett.\  {\bf 38}, 263 (1977).
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%\cite{Anderson:1976sd}
\bibitem{Anderson:1976sd}
R.~L.~Anderson,
%``Excess Muons And New Results In Psi Photoproduction,''
SLAC-PUB-1741
{\it Invited talk presented at Int. Conf. on Production of Particles with New Quantum Numbers, Wisconsin U., Madison, Apr 22-24, 1976}.

%\cite{Aston:1980fk}
\bibitem{Aston:1980fk}
D.~Aston {\it et al.},
%``Photoproduction Of Charmed D Mesons At Gamma Energies Of 40-Gev To 70-Gev,''
Phys.\ Lett.\  {\bf B94}, 113 (1980).
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%\cite{Binkley:1982kv}
\bibitem{Binkley:1982kv}
M.~Binkley {\it et al.},
%``J / Psi Photoproduction From 60-Gev/C To 300-Gev/C,''
Phys.\ Rev.\ Lett.\  {\bf 48}, 73 (1982).
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%\cite{Abe:1983pe}
\bibitem{Abe:1983pe}
K.~Abe {\it et al.},
%``Charm Photoproduction Cross-Section At 20-Gev,''
Phys.\ Rev.\ Lett.\  {\bf 51}, 156 (1983).
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%\href{\wwwspires?j=PRLTA\%2c51\%2c156}{SPIRES}

%\cite{Abe:1984ck}
\bibitem{Abe:1984ck}
K.~Abe {\it et al.}  [SLAC Hybrid Facility Photon Collaboration],
%``Charm Photoproduction At 20-Gev,''
Phys.\ Rev.\  {\bf D30}, 1 (1984).
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%\href{\wwwspires?j=PHRVA\%2cD30\%2c1}{SPIRES}

%\cite{Denby:1984az}
\bibitem{Denby:1984az}
B.~H.~Denby {\it et al.},
%``Inelastic And Elastic Photoproduction Of J / Psi (3097),''
Phys.\ Rev.\ Lett.\  {\bf 52}, 795 (1984).
%%CITATION = PRLTA,52,795;%%
%\href{\wwwspires?j=PRLTA\%2c52\%2c795}{SPIRES}

%\cite{Sokoloff:1986bu}
\bibitem{Sokoloff:1986bu}
M.~D.~Sokoloff {\it et al.}  [Fermilab Tagged Photon Spectrometer
                  Collaboration],
%``An Experimental Study Of The A-Dependence Of J / Psi Photoproduction,''
Phys.\ Rev.\ Lett.\  {\bf 57}, 3003 (1986).
%%CITATION = PRLTA,57,3003;%%
%\href{\wwwspires?j=PRLTA\%2c57\%2c3003}{SPIRES}

%\cite{Barate:1987fq}
\bibitem{Barate:1987fq}
R.~Barate {\it et al.}  [NA14 Collaboration],
%``Measurement Of J / Psi And Psi-Prime Real Photoproduction On Li-6 At A Mean Energy Of 90-Gev,''
Z.\ Phys.\  {\bf C33}, 505 (1987).
%%CITATION = ZEPYA,C33,505;%%
%\href{\wwwspires?j=ZEPYA\%2cC33\%2c505}{SPIRES}

%\cite{Adamovich:1987gx}
\bibitem{Adamovich:1987gx}
M.~I.~Adamovich {\it et al.}  [Photon Emulsion Collaboration],
%``Cross-Sections And Some Features Of Charm Photoproduction At Gamma Energies Of 20-Gev To 70-Gev,''
Phys.\ Lett.\  {\bf B187}, 437 (1987).
%%CITATION = PHLTA,B187,437;%%
%\href{\wwwspires?j=PHLTA\%2cB187\%2c437}{SPIRES}

%\cite{Anjos:1990be}
\bibitem{Anjos:1990be}
J.~C.~Anjos {\it et al.}  [Tagged Photon Spectrometer Collaboration],
%``Photon - Gluon Fusion Analysis Of Charm Photoproduction,''
Phys.\ Rev.\ Lett.\  {\bf 65} (1990) 2503.
%%CITATION = PRLTA,65,2503;%%
%\href{\wwwspires?j=PRLTA\%2c65\%2c2503}{SPIRES}

%\cite{Alvarez:1993yb}
\bibitem{Alvarez:1993yb}
M.~P.~Alvarez {\it et al.}  [NA14/2 Collaboration],
%``Study of charm photoproduction mechanisms,''
Z.\ Phys.\  {\bf C60}, 53 (1993).
%%CITATION = ZEPYA,C60,53;%%
%\href{\wwwspires?j=ZEPYA\%2cC60\%2c53}{SPIRES}

%\cite{Frabetti:1993ux}
\bibitem{Frabetti:1993ux}
P.~L.~Frabetti {\it et al.}  [E687 Collaboration],
%``A Measurement of elastic J / psi photoproduction cross-section at fermilab E687,''
Phys.\ Lett.\  {\bf B316}, 197 (1993).
%%CITATION = PHLTA,B316,197;%%
%\href{\wwwspires?j=PHLTA\%2cB316\%2c197}{SPIRES}

%\cite{Adloff:2000vm}
\bibitem{Adloff:2000vm}
C.~Adloff {\it et al.}  [H1 Collaboration],
%``Elastic photoproduction of J/psi and Upsilon mesons at HERA,''
hep-ex/0003020.
%%CITATION = HEP-EX 0003020;%%
%\href{\wwwspires?eprint=HEP-EX/0003020}{SPIRES}

%\cite{Theodosiou:1976fn}
\bibitem{Theodosiou:1976fn}
G.~Theodosiou, B.~Gittelman, K.~M.~Hanson, D.~Larson, E.~Loh and A.~Silverman,
%``Search For Heavy Narrow Resonances Produced By Photons With Energies Up To 11.8-Gev,''
Phys.\ Rev.\ Lett.\  {\bf 37}, 126 (1976).
%%CITATION = PRLTA,37,126;%%
%\href{\wwwspires?j=PRLTA\%2c37\%2c126}{SPIRES}

%\cite{Lemoigne:1982jc}
\bibitem{Lemoigne:1982jc}
Y.~Lemoigne {\it et al.},
%``Measurement Of Hadronic Production Of The Chi 1++ (3507) And The Chi 2++ (3553) Through Their Radiative Decay To J / Psi,''
Phys.\ Lett.\  {\bf B113}, 509 (1982).
%%CITATION = PHLTA,B113,509;%%
%\href{\wwwspires?j=PHLTA\%2cB113\%2c509}{SPIRES}

%\cite{HallD:1999}
\bibitem{HallD:1999}
R.~Clark {\it et al.}  [Hall D Collaboration],
%``Photoproduction of Gluonic Excitations and Unusual Nesons'',
Design Report, 1999.

% -- GEM -------

%\cite{Sauli:1997qp}
%\cite{Bachmann:1999tj}
%\cite{Bachmann:1999ru}

%\cite{Sauli:1997qp}
\bibitem{Sauli:1997qp}
F.~Sauli,
%``GEM: A new concept for electron amplification in gas detectors,''
Nucl.\ Instrum.\ Meth.\  {\bf A386} (1997) 531.
%%CITATION = NUIMA,A386,531;%%
%\href{\wwwspires?j=NUIMA\%2cA386\%2c531}{SPIRES}

%\cite{Bachmann:1999tj}
\bibitem{Bachmann:1999tj}
S.~Bachmann, A.~Bressan, L.~Ropelewski, F.~Sauli and D.~Mormann,
%``Recent progress in GEM manufacturing and operation,''
Nucl.\ Instrum.\ Meth.\  {\bf A433}, 464 (1999).
%%CITATION = NUIMA,A433,464;%%
%\href{\wwwspires?j=NUIMA\%2cA433\%2c464}{SPIRES}

%\cite{Bachmann:1999ru}
\bibitem{Bachmann:1999ru}
S.~Bachmann, A.~Bressan, A.~Placci, L.~Ropelewski and F.~Sauli,
%``Optimization of operation and test of large size GEM detectors,''
CERN-EP-99-148
{\it Prepared for 5th International Conference on Position Sensitive Detectors (PSD 5), London, England, 13-17 Sep 1999}.

\bibitem{GEANT321} 
GEANT 3.21 CERN Program Library W5103, CERN 1998 


\end{thebibliography}


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