\vspace{-5pt}
\subsection{Exotic hadrons}
\vspace{-5pt}

%Improving our understanding of quark confinement
%in hadrons requires deepening our insight into the 
%gluonic fields within those particles.  
%Exploration of the spectrum and properties of exotic hybrid mesons 
%has emerged as a key path forward for exploring quark
%confinement. Indeed, that topic 
%was a major motivation for the upgrade of JLab,
%and is specifically mentioned multiple times 
%in the 2015 NSAC Long-Range Plan \cite{Geesaman:2015fha}.

To deepen understanding of how confinement arises, ASU is working 
with the GlueX Collaboration in Hall D to search for 
exotic hybrids  with masses up to $2.5$~GeV.
Exotic hadrons (``exotics") are classified as one of three types: glueballs,
 tetraquarks, and hybrids. 
Glueballs are states that completely lack valence
quarks. The lightest glueballs should have $J^{PC} = 0^{++}$ or $2^{++}$,
and are expected to mix with constituent quark states with the same quantum
numbers. 
Tetraquarks are comprised of two $q \overline{q}$ states, 
and are the product of two $SU$(3) octets that 
can be represented as
\begin{equation*}
\bf{8} \otimes \bf{8} = \bf{27} \oplus \bf{10} \oplus \bf{\overline{10}} \oplus \bf{8_1} \oplus \bf{8_2} \oplus \bf{1}.
\end{equation*}
Hybrid states in a constituent $q \overline{q} g$ model 
are built from the usual $q \overline{q}$ constituent-quark representation 
with the promotion of one or more gluons from virtual to real.
For a hybrid state, a  $q \overline{q}$ colored state interacts with real
constituent colored gluon(s) to form an overall colorless state. 
In contrast to glueballs and tetraquarks,  
hybrids are only expected to exist in nonets similar to those
for the constituent quark model. 
Exotics, however, can have quantum numbers $J^{PC}$ that differ from those of hadrons 
constructed with the simple constituent quark model. 
Finding particles with exotic quantum numbers $J^{PC}$ 
serves as the ``smoking gun'' for determining if a state is exotic. 

Some guidance in the search for hybrid states has come from lattice QCD predictions. For example,
a lattice calculation performed by the Hadron Spectrum Collaboration (HSC) in 2013~\cite{Dudek:2013yja} 
found hybrid states  in supermultiplets with  
$J^{PC}$ = $0^{+-}$, $1^{-+}$, $2^{+-}$, and $1^{--}$. 
This HSC model description suggests that
those hybrids have the structure 
($\bf{[q\overline{q}]_{8_c} \otimes G_{8_c}}$).  
States of particular importance for the search of hybrids have the exotic quantum 
numbers of
$J^{PC} = 0^{+-}, 1^{-+}, 2^{+-}$.

Table ~\ref{tbl:exotic} shows several possible decays of exotic mesons of interest for the GlueX experiment.
Currently, there are two exotic $J^{PC} = 1^{-+}$ states ($\pi_1(1400)$ and $\pi_1(1600)$) 
listed by the Particle Data Group \cite{Zyla:2020zbs}. 
For the $\pi_1(1400)$, the decay modes that have been seen
are $\eta \pi^0$ and $\eta \pi^-$, while for $\pi_1(1600)$ the decays seen
are $b_1 \pi$, $\eta^{\prime} \pi^-$ and $f_1 \pi$.
The interpretation of the $\pi_1(1400)$ as a hybrid is problematic \cite{Chung:2002fz,Iddir:2000yb,Close:1987aw}. 
A hybrid meson ($q \overline{q} g$) state
can either have an angular excitation between the quark+anti-quark system and the gluon 
(said to be ``gluon excited'') or
the excitation can be exclusively between the quark and anti-quark (``quark excited''). 
For the gluonic angular-excitation, within
the $q \overline{q} g$ constituent model,
a decay of a hybrid into two fundamental mesons is suppressed. 
This would make the 
$\pi(1400) \rightarrow \eta \pi$ decay unlikely in the gluon-excited case. 
However, a quark excitation can proceed into two fundamental mesons, 
though the branch into the $\eta$-singlet
is favored over the $\eta$-octet. 
Since no search for $\pi(1400) \rightarrow \eta^{\prime} \pi$ 
has been successful, there is some doubt that the $\pi_1(1400)$ is a hybrid. 
Instead, some have
suggested that the $\pi_1(1400)$ is a tetraquark state \cite{Chung:2002fz,Iddir:2000yb,Close:1987aw}.


\begin{table}[h]
\vspace{5mm}
\caption{
Possible decay modes of exotic hybrids that will be explored by GlueX.
} \label{tbl:exotic}
\centering
\begin{tabular}{|c|c|c|c|c|}
\hline
Hybrid &                 & Reachable with           & Reachable with  		& Challenging even  \\
 meson         & $J^{PC}$  & limited running &  longer running            & with longer running  \\
\hline
$b_0$ & $0^{+-}$ &   --- & ---   & $\pi(1300) \pi$, $h_1 \pi$,  \\
          &                &  &  &  $f_1 \pi$, $b_1 \pi$ \\
$h_0$ & $0^{+-}$  & --- & $b_1 \pi$ & $h_1 \eta$ \\
$h^{\prime}_0$ & $0^{+-}$  & ---  & $K_1(1270) K$  & $K(1460) K$, $h_1 \eta$ \\
\hline
$\pi_1$ & $1^{-+}$  & $\pi \rho$ & $\pi b_1$, $\pi f_1$, $\pi \eta^{\prime}$ & $\eta a_1$ \\
$\eta_1$ & $1^{-+}$  & $\eta f_2$, $a_2 \pi$ & $\eta f_1$, $\eta \eta^{\prime}$ & $\pi(1300) \pi$, $a_1 \pi$  \\
$\eta^{\prime}_1$ & $1^{-+}$  & $K^{*}K$ & $K_1(1270) K$, $K_1(1410) K$, & --- \\
                            &                 &                   & $K^{*}_2 K$, $\eta \eta^{\prime}$ &  \\
\hline
$b_2$ & $2^{+-}$  & $\omega \pi$, $a_2 \pi$, $\rho \eta$ & ---  & $f_1 \rho$, $a_1 \pi$, $h_1 \pi$, $b_1 \eta$ \\
$h_2$ & $2^{+-}$  & $\rho \pi$ & $b_1 \pi$, $\omega \eta$ & $f_1 \omega$ \\
$h^{\prime}_2$ & $2^{+-}$  & --- & $K_1(1270) K$, $K_1(1410) K$  & $f_1 \phi$ \\
                         &                  &     &  $K^{*}_2 K$, $\phi \eta$         &                  \\
\hline
\end{tabular}
%\vspace{-5mm}
\end{table}


In addition to the $\pi_1$ exotic states, there should be corresponding isospin $I$ = 0
nonet members if the $\pi_1$ is a hybrid. 
Establishing these isoscalar members for the nonets is important 
in order to verify these exotics as being hybrids. 
The tetraquark state with $J^{PC} = 1^{-+}$ excludes the presence of an isosinglet, and is
fully contained within the $\bf{20}$-plet ($\bf{10} \oplus \bf{\overline{10}}$).
Thus, identifying an isosinglet state with $J^{PC} = 1^{-+}$ 
excludes that state as being a tetraquark. 

%%In contrast to the approach taken by the CLAS Collaboration, 
%the GlueX Collaboration does not consider any particular physics reaction or observable 
%as being reserved for analysis by any particular university group or subset of collaboration members.
%Instead, the GlueX Collaboration considers every physics reaction available for
%%analysis by anyone in the collaboration. 
%%Thus, in Hall D, the ASU group will continue to contribute to the
%%analyses of GlueX data in a way that maximizes our utility to the collaboration while
%%paying special attention to the reactions of primary interest for the group.
%%In addition to our keen interest in the search for exotics, 
%%we also have the parallel interest in ``very strange'' particles as noted in the previous section.
%%Final states detected in GlueX containing multiple final-state
%%kaons thus are of particular interest to ASU, since 
%%analyses of those states provide a possible path to extend our
%%CLAS12 $\Omega$ and cascade studies to the dataset obtained in Hall D.
%%Thus, by concentrating our Hall D analysis efforts on multi-kaon final states,
%%we not only participate in the effort to harvest important physics on exotics there,  
%%but also maintain the possibility of a synergy
%%between our Hall B and Hall D efforts looking for very strange hadrons.

%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%
%As detailed further below, we participated in GlueX analyses of single meson final states
%with the initial data obtained in the Spring 2016 running. 
%The first GlueX physics paper has been published
%for the photon beam asymmetry $\Sigma$ 
%from $\gamma p \rightarrow p \pi^0$ and $\gamma p \rightarrow p \eta$ reactions \cite{AlGhoul:2017nbp}.
%This paper was made possible by the photon beam polarization measurements 
%determined by the ASU group using
%TPOL, described further below.
%No other measurement of the photon beam polarization was available
%since the coherent bremsstrahlung spectral analysis (CBSA) approach
%originally envisioned proved unreliable. 
%PI Dugger, who spearheaded the triplet polarization analysis, 
%served on the three-member GlueX analysis/paper review committee. 

%The collection of physics results we intend to focus on in Hall D
%and those from other analyses by our collaborators in the GlueX Collaboration,
%will clarify the existence of exotic states,
%determine the properties of any such particles found,
%and, in turn, lead to progress in understanding how quarks and gluons assemble into hadrons. 



%\subsubsection{The first physics publication from GlueX}
%
%\begin{wrapfigure}[]{r}{0.59\textwidth}
%\vspace{-10pt}
%\begin{center}
%\includegraphics[width=\linewidth,trim={0 0.2cm 0 0.2cm},clip]{gluexresult1.png}
%\end{center}
%\vspace{-13pt}
%\caption{
%Beam asymmetry $\Sigma$ for $\pi^0$ photoproduction from the proton
%with 8.4 to 9 GeV linearly-polarized photons
%from the first GlueX physics publication~\cite{AlGhoul:2017nbp}.
%\newline
%\vspace{-5pt}
%}
%{\label{fig:gluexresult}}
%\end{wrapfigure}
%As an example of the performance of the GlueX detector, TPOL, and an example of
%ASU's participation in the collaboration, we briefly
%discuss here the first physics publication arising from GlueX analyses. 

%The Spring 2016 running period in Hall D coincided with the 
%JLab accelerator providing its first 12 GeV electron beam.
%A 50-micron-thick diamond was placed in the beamline using a
%goniometer, and polarized photons with a coherent edge energy of 9 GeV were produced.
%Most of the running period was consumed
%by commissioning activities, but 45 data runs with polarized photons had conditions sufficient for physics production.
%From those 45 polarized photon-beam runs, 21 were taken with the polarization
%parallel to the lab floor and 24 with the polarization perpendicular.


%Using this small initial sample of production data,
%the GlueX collaboration was able to obtain photon beam asymmetries $\Sigma$
%for $\pi^0$ and $\eta$ photoproduction from the proton 
%($\pi^0$ results are shown in Fig.~\ref{fig:gluexresult}),
%which included the first $\Sigma$ measurements for $\eta$ photoproduction at 9 GeV.
%The $\pi^0$ results possessed much higher precision than any previous measurement.
%These $\Sigma$ measurements  became the first physics publication for the GlueX Collaboration \cite{AlGhoul:2017nbp}.
%The results would not have been possible without the TPOL work of the ASU group%
%that provided the polarization measurements illustrated above in Fig.~\ref{fig:polPlots}
%since no other approach to determine the beam polarization 
%attempted by the GlueX Collaboration was successful.


%The dip in the SLAC $\pi^0$ results shown in Fig.~\ref{fig:gluexresult}
%occurs where large corrections were required due to Compton backgrounds.
%In the SLAC article~\cite{Anderson:1971xh}, the authors stated
%``The extracted $\pi^0$ cross section in the dip depends very critically on this
%correction. For example, at 15 GeV and t = -0.5 (GeV/c), two-thirds of the
%observed yield is due to Compton scattering.'' In terms of physics, 
%a large positive value of the beam asymmetry corresponds to the expected case, where
%the $\pi^0$ is created through a $t$-channel process with a vector meson acting as
%a messenger particle. This particular type of exchange results in  a natural parity
%exchange. The dip shown in Fig.~\ref{fig:gluexresult}, however, would correspond to
%a large contribution from a pseudovector meson exchange, like a $b$ or $h$ meson. 
%Such a pseudovector exchange would lead to an unnatural parity exchange. 
%This sensitivity to the reaction mechanism is illustrative
%of how polarization information can be useful in determining, in this case, the type
%of meson being exchanged. Such information is critical for extracting 
%the $J^{PC}$ information required for the classification of a $t$-channel produced 
%meson as being exotic.

%These first results illustrate that progress toward understanding the 
%GlueX detector has been swift, that the triplet polarization approach to 
%measuring the photon beam polarization is sound, 
%and that the partial wave analyses needed in the search for exotics will
%not be hampered by ambiguities in measurements of the photon beam
%polarization. As additional data is obtained in future running periods during
%the proposed award, the searches undertaken in Hall D should proceed
%apace, with ASU both participating in those analyses and providing the beam
%polarization information essential for achieving the physics goals for Hall D. 

%\subsubsection{ASU analysis of GlueX $K^* K$ data}

%To illustrate the types of analysis we can currently perform with GlueX data,
%we discuss here portions of the analysis of multi-kaon states undertaken by
%ASU graduate student Sebastian Cole 
%using GlueX data. 
In ASU's Hall B studies, the group extensively utilized the $\eta$ and
$\eta^{\prime}$ to filter out $I$ = 3/2 resonances from the nucleon
resonance spectrum. For Hall D, we will similarly use
the $\eta_1^{\prime}$ to filter out tetraquark states from the
spectrum of exotic meson states. The $K^\ast \bar{K}$ branch is a prime
candidate for early detection of the $\eta_1^{\prime}$ hybrid.
However, prior to our search for $\eta_1^{\prime} \rightarrow K^\ast \bar{K}$, 
we have decided to map out the lower mass states going $K^\ast \bar{K}$, eventually working
our way towards the expected mass range of the $\eta_1^{\prime}$ hybrid of about 2 GeV. 

%%Since the $K^{*} \rightarrow K \pi$ 100\% of the time, the 
%%detected particles necessary for the reconstruction of the 
%%$\eta_1^{\prime} \rightarrow K^{*} K$ are $K K \pi$. The particular 
%%charge states that Sebastian is pursuing in his search for the 
%%$\eta_1^{\prime}$, is $K^+ K^- \pi^0$. To begin his search, Sebastian 
%%has taken the strategy of making sure that he can construct the well 
%%known $\phi \rightarrow K^+ K^-$ meson state reaction, and then 
%%include an additional $\pi^0$. In Fig.~\ref{fig:seb2d}, Sebastian has 
%%constructed a plot showing the invariant mass of $p K^-$ versus the 
%%invariant mass of $K^+ K^-$. That plot shows strong enhancement bands in
%%the vertical and horizontal directions. Along with the data shown on the 
%%plot, there is a vertical white line at 1.4 GeV and a horizontal one at 
%%2 GeV. These white lines represent analysis cuts performed on the data 
%%in order to extract the $\phi$ and also, as a bonus, the $\Lambda(1520)$. 

%\begin{wrapfigure}[]{r}{0.59\textwidth}
%\vspace{-10pt}
%\begin{center}
%\includegraphics[width=\linewidth,trim={0.5cm 0.4cm 1.0cm 1.6cm},clip]{seb2dV3_1.png}
%\end{center}
%\vspace{-13pt}
%\caption{
%Invariant mass of $p K^+$ versus the invariant mass of $K^+ K^-$. The white
%lines denote different cut selections (described in text).
%\newline
%\vspace{-5pt}
%}
%{\label{fig:seb2d}}
%\end{wrapfigure}
%Since the $K^{*} \rightarrow K \pi$ 100\% of the time, the
%detected particles necessary for the reconstruction of the
%$\eta_1^{\prime} \rightarrow K^{*} K$ are $K K \pi$. 
%The particular
%branches that Cole is isolating in his search for the
%$\eta_1^{\prime}$ are $K^+ K^- \pi^0$ and $K^0_s K^{\pm} \pi^{\mp}$.
%To begin his search, he has reconstructed
%the well-known $\phi \rightarrow K^+ K^-$ meson decay, as well
%as the $\Lambda(1520) \rightarrow p K^-$ baryon decay. This work
%will assist in improving pre-DIRC kaon identification in order to search
%for $\eta_1^{\prime}$. Fig.~\ref{fig:seb2d} 
%shows the invariant mass of $p K^-$ versus the invariant mass of
%$K^+ K^-$ 
%%using improvements to the standard GlueX kaon identification and
%%requiring the kinematic fit $\chi^{2}/NDF > 3.5$ on $gamma p \rightarrow p K^+ K^-$
%%events in 
%from the August 2018 reconstruction of Spring 2016 GlueX data. Fig.~\ref{fig:seb2d}
%shows strong enhancement bands $\sim1.02$ GeV in the vertical direction, and $\sim1.52$ GeV and
%$\sim1.8$ GeV in the horizontal direction. (The vertical enhancement at $\sim1.2$ GeV due to
%the misidentification of pions with low opening angles and high momentum as kaons.) 
%Also shown in Fig.~\ref{fig:seb2d} is a vertical white line at 1.4 GeV and a horizontal
%white line at 2 GeV, which indicate the location of cuts on the data  to
%further isolate $\phi(1020)$ and $\Lambda(1520)$.

%%By taking events above the horizontal white line shown in 
%%Fig.~\ref{fig:seb2d}, a plot of the $K^+ K^-$ invariant mass 
%%showing a strong, and fairly clean, $\phi$ signal is created 
%%(Fig.~\ref{fig:sebKpKm}). Likewise, by using events to the 
%%right of the vertical white line, the $\Lambda(1520)$ is 
%%clearly visible in Fig.~\ref{fig:sebPKm}. Now that Sebastian 
%%has finished his study on isolating the 
%%$\phi \rightarrow K^+ K^-$ reaction, he is simply waiting
%%for a $p K^+ K^- \pi^0$ skim of the GlueX data. Once that 
%%$p K^+ K^- \pi^0$ data skim has been obtained, a subset of 
%%$K^{*} \rightarrow K \pi$ candidate events will be identified 
%%and the $\eta_1^{\prime}$ hybrid search will begin. 

%\begin{figure}[h!]
%\vspace{2pt}
%\begin{minipage}[b]{3.4in}
% { \centering
%  \captionsetup{margin=0.5cm}
%  \includegraphics[width=\linewidth,trim={0 0.2cm 0 0.2cm},clip]{sebKpKmV2_1.png}
%  \caption{Invariant mass of $p K^-$. The vertical red line shows
%    the PDG value for the mass of the $\phi$ meson.
%    \newline
%    \vspace{-5pt}
%  }
%  \label{fig:sebKpKm}}
%\end{minipage}%
%\begin{minipage}[b]{3.4in}
% { \centering
%  \captionsetup{margin=0.5cm}
%  \includegraphics[width=\linewidth,trim={0 0.2cm 0 0.2cm},clip]{sebPKmV2_1.png}
%  \caption{Invariant mass of $p K^-$. The vertical red line shows
%    the PDG value for the mass of the $\Lambda(1520)$ baryon.
%    \newline
%    \vspace{-5pt}
%  }
%  \label{fig:sebPKm}}
%\end{minipage}
%\end{figure}
%By taking events above the horizontal white line shown in
%Fig.~\ref{fig:seb2d}, a plot of the $K^+ K^-$ invariant mass
%shows a strong $\phi$ signal, as seen in Fig.~\ref{fig:sebKpKm}. 
%Likewise, by selecting events to the
%right of the vertical white line, the $\Lambda(1520)$ is
%clearly visible in Fig.~\ref{fig:sebPKm}. 

%\begin{figure}[t!]
%\vspace{2pt}
%\begin{subfigure}{0.63\textwidth}
% { \centering
%   \includegraphics[width=\linewidth,trim={0 0.2cm 0 0.2cm},clip]{KpPimInvMass}
%   \vspace{-15pt}
% }
% \caption{} \label{fig:sebKpPim}
%\end{subfigure} 
%\begin{subfigure}{0.37\textwidth}
%  \vspace{10pt}
% { \centering
%   \includegraphics[width=\linewidth,trim={0 0.0cm 0 0.0cm},clip]{E852KStarV3.png}
%  \caption{}  \label{fig:E852KStar}} 
%\end{subfigure}
%  \caption{(a) Invariant mass of $K^+ \pi^-$. The vertical red line indicates
%     the PDG value for the mass of the $K^{*}(892)$. (b) Missing mass spectrum
%     from Ref.~\cite{Adams:2001sk}. The shaded area indicates results where $|t| > 0.1$~GeV$^2$.
%  } 
% \end{figure} 
 
%At the time of this writing,
%we await $p K^+ K^- \pi^0$ and $p K^{\pm} 2\pi^{\mp} \pi^{\pm}$
%skims of the GlueX data from the August reconstruction launches of 2016 and 2017
%data, as well as the first reconstruction launch of 2018 data to occur in Fall 2018, 
%to dig deeper into this search.
%These reconstruction launches are critical for analyses in GlueX due to major
%improvements to GlueX tracking, and energy deposition determination in the CDC
%and FDC, leading to a recovery of approximately 30\% more events than current analysis
%efforts. A subset of the $p K^+ K^- \pi^0$ and $p K^{\pm} 2\pi^{\mp} \pi^{\pm}$ skims
%containing $K^{*} \rightarrow K \pi$ candidate events will be identified
%and the $\eta_1^{\prime}$ hybrid search will begin in earnest.
%In preparation for this newly reconstructed data, Cole has
%begun analyzing $p K_s^{0} K^{+} \pi^{-}$, where $K_s^{0} \rightarrow \pi^{+} \pi^{-}$,
%skims from the initial reconstruction of low and high intensity 2017 data.
%Fig.~\ref{fig:sebKpPim} shows evidence of $K^{*}(892)$ in the high intensity 2017 running of GlueX. 
%The reconstruction of a $K^{*}(892)$ is a necessary step in the search for 
%$\eta_1^{\prime}$ in $K^{*} K_{s}^{0}$.
%While still at a relative early stage of analysis, this spectrum is remarkably 
%similar to prior published data on this channel \cite{Adams:2001sk}, as seen in Fig.~\ref{fig:E852KStar}.

%%The next 12 months is a particularly exciting time for the 
%%exploration of reaction signatures that include kaons. 
%%Recently, the GlueX Collaboration installed a DIRC 
%%(Detection of Internally Reflected Cherenkov) for in-beam 
%%commissioning slated for Fall 2018, with DIRC-included 
%%production runs starting in Fall 2019. The DIRC will greatly 
%%improve the particle identification for kaons needed for the
%%search of the $\eta^{\prime}_1$ hybrid.



%The next 12 months is a particularly exciting time for the
%exploration of reaction signatures that include kaons.
%Recently, the GlueX Collaboration installed a DIRC
%%(Detection of Internally Reflected Cherenkov) 
%for in-beam
%commissioning slated for Fall 2018, with DIRC-included
%production runs starting in Fall 2019. The DIRC will greatly
%improve the particle identification for kaons needed for the
%search of the $\eta^{\prime}_1$ hybrid.





