\subsection{Probing the $\Omega^-$ and $\Xi$ baryon spectra}

As noted above, studies of  
two and three-strange-quark baryons have great potential to
enhance our understanding of the QCD structure within baryons. 
The ``computational cost'' for predictions using lattice QCD
are greatly influenced by the number of light quarks ($u$ and $d$) present
in the baryon studied. For that reason, studies that extend our knowledge of the properties 
of states with two and three strange quarks should be extremely useful in
deepening insight into how all baryons are assembled from quarks.

The ASU group is leading an experiment which will provide the
largest-ever sample of photoproduced cascade $\Xi$ baryons,
as well as the first photoproduction measurements of $\Omega^-$~\cite{CascProp}.
This ``very strange particle'' search
represents part of the suite of experiments approved to run during 
Run Group A. 
Using the CLAS12 detector, 
our measurements should greatly enhance knowledge of the excitations of these baryons,
which in turn will provide an empirical ``proving ground'' for QCD-based descriptions of baryons with 
varying numbers of heavy quarks. 

\begin{wraptable}{r}{0.4\linewidth}
\caption{``Well-known'' $\Xi$ resonances listed in the PDG summary \cite{Olive:2016xmw}.} \label{tbl:cas1}
%\vspace{2mm}
\centering
\begin{tabular}{|c|c|c|c|}
\hline
State & $J^{P}$ & Width & PDG\\
        &              &(MeV)  & rating  \\
\hline
\hline 
$\Xi(1318)$ & $\frac{1}{2}^+$  &             & **** \tabularnewline
$\Xi(1530)$ & $\frac{3}{2}^+$  & 9.1$\pm$0.5 & **** \tabularnewline
$\Xi(1690)$ & $\frac{1}{2}^-$? & 10$\pm$6    & ***  \tabularnewline
$\Xi(1820)$ & $\frac{3}{2}^-$  & 24$\pm$6    & ***  \tabularnewline
$\Xi(1950)$ & ?                & 60$\pm$20   & ***  \tabularnewline
$\Xi(2030)$ & $\ge\frac{5}{2}$?& 21$\pm$6    & ***  \tabularnewline
\hline
\end{tabular}
\end{wraptable}


While the ``missing resonance'' problem for the nucleon system is much discussed,
the missing resonance problem is even more striking when looking at the $\Xi$ sector.
For example, the Isgur and Capstick relativistic
constituent quark model \cite{Capstick:1986bm} predicts 44 $\Xi$ states with 
masses below 2.5 GeV, yet the PDG \cite{Olive:2016xmw} only lists {\em{six}} cascade
resonances with ratings of three or four stars, as indicated in Table \ref{tbl:cas1}. 
%This large discrepancy is particularly remarkable since 
%QCD-based predictions (lattice or otherwise) for baryons having one or more
%heavy quarks might be expected to be more successful than
%QCD descriptions for the nucleon. 


Looking more closely at the $\Xi$ states, 
photoproduction cross sections for $\Xi$ resonance states 
are observed to be much smaller than for nucleon resonances.
However, the widths of the $\Xi$ excitations are much
narrower than those for the nucleon, which should make them easier to identify \cite{Crede:2017kyh}. 
As seen in Table \ref{tbl:cas1}, 
the well-known cascade resonances also have mass separations that are greater
than the resonance widths, which again should make identification of excited $\Xi$ states far easier
than for the $N^*$ and $\Delta$ states (with widths of
$\sim$150 MeV). 
Even with those advantages, however,  
no new cascade states have been discovered in the last 20 years. 
\begin{wraptable}{r}{0.7\linewidth}
\vspace{2mm}
\caption{PDG values for branching ratios of excited $\Xi$ states \cite{Olive:2016xmw}.} \label{tbl:cas2}
\centering
\begin{tabular}{|c|c|c|c|}
\hline
State & $\Lambda K$ & $\Sigma K$  & $\Xi \pi$\tabularnewline
\hline
\hline 
$\Xi(1530)$ &      &      & 100 \% \tabularnewline
$\Xi(1690)$ & seen & seen & seen   \tabularnewline
$\Xi(1820)$ & large & small & small  \tabularnewline
$\Xi(1950)$ & seen & seen? & seen \tabularnewline
$\Xi(2030)$ & 20\% & 80\%  & small  \tabularnewline
\hline
\end{tabular}
\end{wraptable}
The 1989
discovery of $\Xi(1690)$ \cite{Adamovich:1997ud} was plagued by  backgrounds
from a $\Sigma^-(C,Cu)\rightarrow \Xi^- \pi^+$ inclusive reaction.
The large solid angle of the CLAS12 detector (discussed
further in the next subsection) will permit using 
exclusive reactions 
to markedly reduce backgrounds.
Moreover, the CLAS12 detector will simultaneously measure $\Xi^*$
decay modes, allowing 
for the determination of 
branching ratios that are, as shown in Table \ref{tbl:cas2}, 
not well determined for most of the three and four star
$\Xi^*$ states~\cite{Olive:2016xmw}.
Of particular interest is the apparent suppression of the excited
cascades going to $\Xi \pi$. For the $\Xi(1530)$, the branch to
$\Xi \pi$ is given in the PDG as 100\%, but for all other cascades, 
the observed decay branches are merely characterized as
``small'' or ``seen''.
Measuring the $\Xi^*$ branching ratios for  states that decouple from 
$\Xi \pi$ can help shed light on why the 
$\Xi^*$ have such narrow widths. 

As for the $\Omega$ situation,
as indicated in Table \ref{tbl:Omega}, only four 
$\Omega$ states have been seen: the ground state,
one three-star excited $\Omega$ baryon state, 
and two additional excited states with two-star ratings.
Photoproduction reactions for $\Omega^-$ and its
excited states have yet to be measured;
a SLAC experiment provided an upper limit for 
$\gamma p \rightarrow \Omega^- X$ of $\sigma_t < 17 $ nb \cite{Hassall:1981fs}
Yet, predictions from Roberts, Afanasev, 
and Shklyar suggest that the 
photoproduced $\Omega^-$ cross section should be about 0.3 nb.

We intend to measure the cross section for the reaction 
$\gamma p \rightarrow \Omega^- K^+ K^+ K^0$. 
Assuming a cross section 
of 0.3 nb, our simulations estimate $\sim$7000
$\Omega^-$ baryons and several million $\Xi$ states
will be observed in 80 days of beam time at high luminosity.
Supplemental to the approved 80 days of high-luminosity data, 
an additional 39 days approved at low-lunimosity should
boost statistics to an equivalent of 100 days at 
high-luminosity. Moreover, 20 additional days allocated
with the torus at reversed polarity will increase
statistics even further.

\vspace{2mm}
\begin{wraptable}{r}{0.4\linewidth}
\caption{Status of known $\Omega^-$ states from the PDG summary \cite{Olive:2016xmw}.} \label{tbl:Omega}
\centering
%\vspace{2mm}
\begin{tabular}{|c|c|c|c|}
\hline
State & $J^{P}$ & Width & PDG\tabularnewline
&  & (MeV) &  rating\tabularnewline
\hline
\hline 
$\Omega^-$       & $\frac{3}{2}^+$ &              & **** \tabularnewline
$\Omega(2250)^-$ & ?               & 55 $\pm$ 18  & ***  \tabularnewline
$\Omega(2380)^-$ & ?               & 26 $\pm$ 23  & **   \tabularnewline
$\Omega(2470)^-$ & ?               & 72 $\pm$ 33  & **   \tabularnewline
\hline
\end{tabular}
\end{wraptable}

%In recognition of the ASU role in the analysis effort towards the measurement
%of multi-strangeness baryon production, 
%PI Dugger has been designated by the CLAS Collaboration as the
%coordinator for $\Omega^-$ and $\Xi$ baryon analyses.
%ASU's leading role in the analysis of multi-strangeness baryon production positions 
%our group well to participate fully in the analysis of data to be obtained. Currently,
%PI Dugger and undergraduate student Eric Bryan are working on the analysis of newly obtained 
%CLAS12 data. 

The information obtained on mass splittings 
within these $\Omega^-$ and $\Xi$ systems will be extremely useful 
in testing lattice QCD and QCD-inspired models of
these baryons.
At present, the only baryonic mass splittings available come from the 
ground state octet and decuplets (e.g. $n$-$p$ splitting or ground state $\Delta$ splitting).
All the data will help address the issue of how quarks and gluons assemble
into the hadrons observed in nature. 
