
\subsection{Probing the $\Omega^-$ and $\Xi$ baryon spectra with CLAS12}

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. 


\subsubsection{The CLAS12 detector}

A brief overview of the CLAS12 detector to be used for the $\Omega^-$ and $\Xi$ measurements
is provided here to provide context for the preliminary ASU results discussed in the next subsection.
While the CLAS12 detector is designed primarily to measure deeply exclusive scattering
using electron beams,
a forward tagger has been installed
within CLAS12 that enables quasi-real photon experiments with $q^2$ as low as 0.01 GeV$^2$.
The ASU efforts in Hall B make use of this forward tagger to perform
photoproduction measurements for the $\Xi$ and $\Omega$ from
the cryogenic hydrogen target within the CLAS12 detector. 
In addition to the presence of the forward tagger, 
another key experimental consideration for using CLAS12 for our studies is that, at present,
the particle identification for kaons should be better than that expected for
the current configuration of 
the GlueX detector in Hall D. 
This superior particle identification for CLAS12 is the primary motivation for our
use of that detector in the search for $\Omega^-$ and $\Xi$ baryons states.
With the availability of both tagged photons and good kaon identification, 
Hall B is well-suited for the measurements we propose to make. 

As seen in Fig. \ref{fig:clas12}, CLAS12
is composed of two main detector arrays: the Central Detector (CD) and the
Forward Detector (FD).
The FD covers the range of 5$^{\circ}$ to 40$^{\circ}$ in polar angle, whereas the CD
covers the polar angles from 40$^{\circ}$ to 135$^{\circ}$. 
The FD is expected to provide separation of identified
$K^{\pm}$ and $\pi^{\pm}$ having momenta less than 3 GeV/c, 
and separation of protons and $K^{\pm}$
with momenta less than 4.5 GeV/c --
the key capability required for this experiment noted above.



\begin{wrapfigure}[]{R}{0.6\textwidth}
\vspace{-10pt}
\begin{center}
\includegraphics[width=\linewidth]{clas12-design.eps}
\end{center}
\vspace{-13pt}
\caption{Schematic diagram for CLAS12. The labeled subsystems
are described in the text. 
\newline
}
{\label{fig:clas12}}
\end{wrapfigure}


A cryogenic target cell is located at the center of the cylindrically-symmetric CD.
Surrounding  the cryogenic target cell
is a Silicon Vertex Tracker (SVT) yielding 1 mrad angular resolution in azimuthal angle
and 15 mrad in polar angle for charged tracks, as well as providing vertex resolution 
better than 2 mm.
Outside the SVT is the cylindrically-symmetric Central Time-of-Flight system (CTOF).
The CTOF scintillator array has a timing resolution of 50 ps.
The Central Electromagnetic Calorimeter forms the next cylindrical layer, consisting of
a scintillating-fiber/tungsten-powder array.
These detectors are housed within a 5-T superconducting solenoid
magnet of aperture 0.78 m. The original
CLAS superconducting toroidal magnet has been repurposed for CLAS12, with
the same six-sector azimuthal symmetry as the original detector.

Downstream of the SVT are the High Threshold Cherenkov Counters and the
Forward Tagger (FT) arrays.
Electrons that scatter with angles
between 2.5$^{\circ}$ and 4.5$^{\circ}$ are detected in the FT, 
enabling quasi-real photon experiments such as those we will undertake in this work. 
Beyond the FT are three regions
of drift chambers, forming  the Forward Tracking Chamber (FTC).
The chambers are arranged in a fashion similar to the original CLAS design, 
with Region 1 drift chambers located
before the torus magnet, Region 2 within the torus magnet, and Region 3 behind the torus.
Ultimately, the spatial resolution for this chamber package
is expected to be a factor of 3 better than the original CLAS system.
Downstream of the FTC are the Low Threshold Cherenkov Counters (LTCC),
which are modified versions
of the original CLAS Cherenkov counters with the same external geometry. 
As with the LTCC, the
Forward Time-of-Flight (FTOF) system has the same geometry as the original CLAS system,
but has been upgraded to obtain 80-ps timing resolution. The detector furthest downstream
is the Forward Electromagnetic Calorimeter, an array retained and repurposed
from the original CLAS detector.

\subsubsection{ASU preliminary analysis of Spring 2018 CLAS12 data}

During the Spring 2018 (2/6/2018 through 5/6/2018), 
the first physics runs were taken at JLab with
the CLAS12 detector. For that running period, 
over 3.8$\times 10^7$ triggers were accumulated at
incident electron energies of 2.2, 6.8 and 10.4 GeV, with 
the lower energy runs used for commissioning the detector. 

As of this writing, the first pass of calibrated cooking has yet to be
started for the Spring 2018 data. 
Thus far, a handful of runs processed for calibration purposes
are also available for collaboration members to analyze. The Very Strange Group
analyzed a single run from the 6.8 GeV data for an initial glance at the data.
From that early look, Fig.~\ref{fig:pidFTOFLogy} shows  the measured mass 
for charged tracks hitting the forward time-of-flight array (FTOF). 
Even though the calibrations were still being made at that point,
charged kaons are already visible between the pion and proton 
peaks. 
The particle identification (PID) scheme will be further optimized 
when the current cooking has completed, but
for the preliminary analyses discussed next, pions were defined
as having a mass between zero and 0.45 GeV, and protons were taken in the mass
range between 0.65 and 1.2 GeV. 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%  pidFTOFLogy.eps from lc7 at   %%%
%%%/home/vs/c12/myAnaStage2/pid.eps%%% 
%%%     using makePics3(127)       %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{wrapfigure}[]{r}{0.5\textwidth}
\vspace{-20pt}
\begin{center}
\includegraphics[width=\linewidth]{pidFTOFLogy.eps}
\end{center}
\vspace{-17pt}
\caption{Initial PID previous to full calibration for events hitting the FTOF.
\newline
\vspace{-7pt}
}
{\label{fig:pidFTOFLogy}}
\end{wrapfigure}

Owing to the large cross section and large beam symmetry of photoproduced $\rho^0$
mesons, the PI performed a beam asymmetry measurement for the reaction 
$\gamma_v  p \rightarrow p  \rho^0$, where $\rho^0 \rightarrow \pi^+ \pi^-$ and 
$\gamma_v$ represents the nearly-real virtual photon.  
For the identification of the $\rho^0$ meson, the missing mass from 
the reaction $\gamma_v  p \rightarrow p  \pi^+  \pi^- X$, where
$X$ is the missing particle was chosen such that -0.02 $<$ Mass$^2$($X$)/GeV $<$ 0.0 
(The center of the squared missing-mass is shifted slightly towards the negative at the 
moment). The $\rho^0$ mesons were then binned in a single 100 MeV wide bin 
in $\gamma_v$ energy with center at 2.5 GeV, three $|t|$ bins with centers ranging
from 0.1 to 0.4 GeV$^2$, and 18 bins in the angular variable $\Psi$, where
$\Psi$ is the azimuthal direction of the resulting $\pi^+$ as seen in the $\rho^0$
rest frame with the $x$-axis defined along the polarization direction (defined below). 
An example of the $\rho^0$ mass for $|t| = 0.15$ GeV$^2$ integrated 
over all $\Psi$ angles and fit to a Breit-Wigner-plus-zero-order polynomial 
is given in Fig.~\ref{fig:pipiMass}. 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%      pipiMass.eps from lc7 at       %%%
%%%/home/vs/c12/myAnaStage2/pipiMass.eps%%% 
%%%     using fitRhoForProp18(1,1)      %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{wrapfigure}[]{r}{0.5\textwidth}
\vspace{-15pt}
\begin{center}
\includegraphics[width=\linewidth,trim={0 0.2cm 0 0.5cm},clip]{pipiMassT2E1.eps}
\end{center}
\vspace{-20pt}
\caption{Mass of the $\pi^+  \pi^-$ system for $E_{\gamma} = 2.5$~GeV and $ |t| = 2.5$ GeV$^2$
\vspace{-5pt}
}
{\label{fig:pipiMass}}
\end{wrapfigure}

Unlike the case for the real photons in the GlueX experiment, the determination 
of the polarization for virtual photons in CLAS12 does not require a dedicated device. 
For the determination of the photon polarization using CLAS12, 
knowledge of the 4-vectors of the incident and scattered electron is sufficient to determine 
the virtual photon polarization. The polarization direction
is orthogonal to the scattering plane with the longitudinal component being negligible
for nearly-real photons. The value of the virtual polarization $\varepsilon$ is given by
\begin{equation*}{
\varepsilon = \left[1 + 2\left(\frac{Q^2+\nu^2}{Q^2}\right)\tan^2{\left(\frac{\theta_{e_F}}{2}\right)} \right]^{-1},
}
\end{equation*}
where $-Q^2$ is the squared-mass of the virtual photon, $\nu$ is the energy of the virtual
photon, and $\theta_{e_F}$ is the scattering angle of the scattered electron relative to 
the incident electron. 



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%sigmaRhoT1E1.png taken presentation%%%
%%%      Was created on lc7 at        %%%
%%%    /home/vs/c12/myAnaStage2/      %%%
%%%      using sigmaRho(1,1)          %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{wrapfigure}[]{R}{0.6\textwidth}
\vspace{-13pt}
\begin{center}
\includegraphics[width=\linewidth,trim={0 0.2cm 0 0.4cm},clip]{sigmaRhoT2E1.png}
\end{center}
\vspace{-19pt}
\caption{The $\Psi$ distribution for the reaction 
$\gamma_v  p \rightarrow p  \rho^0$, where $\rho^0 \rightarrow \pi^+ \pi^-$ 
at $|t| = 0.25$~GeV and a fit to $A[1 - B \cos(2\Psi - 2\Psi_0)]$,
where $A$, $B$ and $\Psi_0$ were variables of the fit. 
\newline
\newline
\vspace{-2pt}
}
{\label{fig:sigmaRhoT1E1}}
\end{wrapfigure}

For each of the three values of $|t|$ used, we created 18 bins in the $\Psi$ variable 
to obtain the $\Psi$ distribution of the $\rho^0$ yields. These yields were 
then fit to the function $A[1 - B \cos(2\Psi - 2\Psi_0)]$, where $A$, $B$ and $\Psi_0$
were varied. To extract
the beam asymmetry ($\Sigma$), the value of $B$ from the fitting routine was divided by the 
polarization $P$, which yields $\Sigma$. For all  $|t|$-bins, $\Psi_0$
was within 1.16 standard deviations of the expected value ($\Psi_0 = 0$). An example  
of the $\Sigma$ extraction from a $\Psi$-distribution is provided n Fig.~\ref{fig:sigmaRhoT1E1}.

Once the beam asymmetry $\Sigma$ was determined for each $|t|$-bin, 
a plot of $\Sigma$ versus $|t|$ was produced. The energy and $|t|$ ranges we 
chose for this analysis permit a comparison
to existing world data. In 1970 DESY reported beam asymmetries using two
counter-wire telescopes~\cite{Criegee:1969qg}, while in 1972 SLAC published
 $\rho^0$ beam asymmetries using a bubble chamber \cite{Ballam:1971yd}. 
A comparison of the preliminary CLAS12 $\rho^0$ asymmetries compared
to SLAC and DESY is shown in Fig.~\ref{fig:clas12RhoSigma}.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%     rhoAssy.eps from lc7 at        %%%
%%%/home/vs/c12/myAnaStage2/rhoAssy.eps%%% 
%%%         using showSig.C            %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{wrapfigure}[]{r}{0.6\textwidth}
\vspace{-17pt}
\begin{center}
\includegraphics[width=\linewidth,trim={0 0.0cm 0 0.5cm},clip]{rhoAssy.eps}
\end{center}
\vspace{-19pt}
\caption{Beam asymmetry $\Sigma$ for $\rho^0$ photoproduction on the proton. 
Black filled squares are from the ASU preliminary analysis
of CLAS12 data from a single run, while red
filled triangles are from SLAC~\cite{Ballam:1971yd} and blue open circles
represent results from DESY~\cite{Criegee:1969qg}. 
\newline
\vspace{-13pt}
}
{\label{fig:clas12RhoSigma}}
\end{wrapfigure}

Our preliminary $\Sigma$
results from a {\em{single CLAS12  run (that was still being calibrated)}}
agree quite well with the previous results. When
calibrated full statistics are available for all Spring 2018 runs, our CLAS12 results
for $\Sigma$ for 
$\gamma_v  p \rightarrow p  \rho^0$, where $\rho^0 \rightarrow \pi^+ \pi^-$, 
will cover a wider range in $|t|$ with smaller bin widths and
smaller statistical uncertainties than the few published data.

Though we are not primarily interested in the 
physics associated with $\rho^0$ photoproduction, 
this $\rho^0$ analysis may lead to CLAS12's first physics publication. 
We are acting quickly and opportunistically
with respect to this reaction observable. If the analysis of the 
fully cooked Spring 2018 data goes as smoothly as the
single run used thus far, 
ASU could complete the analysis of $\rho^0$ beam asymmetries 
early in the requested grant period. 
Regardless, these $\rho^0$ results confirm that ASU is fully capable of carrying out the
analyses for the proposed $\Omega^-$ and $\Xi$ baryons studies outlined above.

