\section{Energy requirements}

The interesting range of meson masses for the study of gluonic excitations
spans the region from the mass of the $\pi^{0}$ to just below $c\bar c$ 
threshold ($\approx 3 $ $ {\rm{GeV/c^2}}$).  
This range includes conventional ($q\bar q$) mesons 
and glueball and exotic hybrid masses, as predicted by lattice gauge calculations, 
flux tube models and bag models.

Figure \ref{kinlimits} shows the maximum mass of particle X, in the reaction 
$\gamma p \to X p$ as a function of incident photon energy.  As can be seen
from this plot, it is possible to produce particles up to $m_X=3$GeV
with photons of 8GeV.  However the photoproduction cross section is zero at
threshold, and somewhat higher energies are needed to produce sufficient
quantities of particle X to make possible a partial-wave analysis.

\begin{figure}[htbp]\centering
\begin{tabular}{cc}
\mbox{\epsfig{file=mxkinem.eps,width=0.45\textwidth,height=0.45\textwidth}} &
\mbox{\epsfig{file=tmin.eps,width=0.45\textwidth,height=0.45\textwidth}} \\
\end{tabular}
\caption{Kinematic limits on production properties
for several choices of beam energy.
(left) Maximum mass for particle X as a function of incident
photon energy in the reaction $\gamma p \to X p$.
(right) The minimum value of $|t|$ as a function of the mass of
particle X in the reaction $\gamma p \to X p$ 
for various values of incident photon energies. \label{kinlimits} }
\end{figure}


Another important consideration in choice of energy is the effect of
the minimum square of the momentum transfer, $|t_{min}|$
from incoming photon to outgoing meson required in the reaction
 $\gamma p \to X p$.  The dependence of $|t_{min}|$ on the mass
of X is shown in Figure \ref{kinlimits} for various incident photon
energies.

The effect of $|t_{min}|$ can be illustrated in the production rate
of mesons in peripheral processes.  Figure \ref{allmasses} shows the
mass spectrum of the meson system $X$ in the reaction
$\gamma p \to X p$.  Resonances with equal cross-sections are
assumed but weighted by $dN/dt = e^{-8 \cdot |t|}$.  Resonance
widths were all chosen to be 100 ${\rm{MeV/c^2}} $ with masses of 
1.0, 1.5, 2.0 and 2.5  ${\rm{GeV/c^2}}$ for
incident photon energies of 6,  8,  10, and 12  GeV.
Clearly, photon beam energies of $ \approx $ 12 GeV are required if 
the mass region up to 3 ${\rm{GeV/c^2}}$ is to be studied.

\begin{figure}[htbp]\centering
\begin{tabular}{cc}
\mbox{\epsfig{file=gammape6mass2.eps,width=0.5\textwidth,height=0.5\textwidth}} &
\mbox{\epsfig{file=gammape8mass2.eps,width=0.5\textwidth,height=0.5\textwidth}} \\
\mbox{\epsfig{file=gammape10mass2.eps,width=0.5\textwidth,height=0.5\textwidth}} &
\mbox{\epsfig{file=gammape12mass2.eps,width=0.5\textwidth,height=0.5\textwidth}} 
\end{tabular}
\caption{ Plots of the mass distribution of 4 produced resonances in
the reaction $\gamma p \to X p$ taking into account the
$t_{min}$ effect for an incident photon energy of
6 GeV (upper left), 8 GeV (upper right),
10 GeV (lower left) and 12 GeV (lower right).
(see the text for details).  
\label{allmasses}
}
\end{figure}

Higher energies are also needed to minimize the effect of the overlap of 
produced baryon resonances with meson resonances. This is illustrated
by the Dalitz plot boundaries of Figure \ref{dal1} for the reactions
$\gamma p \to \pi \pi p$ and
$\gamma p \to \eta \eta p$ for various incident photon energies.  As the
incident energy is increased from 4 to 8 to 12 GeV, the effect of overlap
of produced mesons with produced baryon resonances ($N^*$ or $\Delta$)
becomes less important.


\begin{figure}[htbp]\centering
\begin{tabular}{cc}
\mbox{\epsfig{file=dalpipi.eps,width=0.45\textwidth,height=0.45\textwidth}} &
\mbox{\epsfig{file=daletaeta.eps,width=0.45\textwidth,height=0.45\textwidth}} \\
\end{tabular}
\caption{Dalitz plot boundaries for the reaction $\gamma p \to \pi \pi p$
(left) and  $\gamma p \to \eta \eta p$ (right)
for incident photon energies of 4, 8 and 12 GeV. \label{dal1} }
\end{figure}

\pagebreak

