The GlueX experiment, currently under construction and scheduled to start running in Hall~D at Jefferson Lab in 2015, will provide the data necessary to construct quantitative tests of non-perturbative QCD by studying the spectrum of light-quark mesons. The primary goal of the GlueX experiment is to search for and study the spectrum of so-called hybrid mesons that are formed by exciting the gluonic field that couples the quarks. QCD-based calculations predict the existence of hybrid meson states, including several that have exotic quantum numbers that cannot be formed from a simple quark/anti-quark pair. To achieve its goal, GlueX must systematically study all possible decay modes of conventional and hybrid mesons, including those with kaons. The addition of a Cherenkov-based particle identification system utilizing the BaBar DIRC (Detection of Internally Reflected Cherenkov) components will dramatically increase the number of potential hybrid decay modes that GlueX can access and will reduce the experimental backgrounds from misidentified particles in each mode. This enhanced capability will be crucial in order for the GlueX experiment to realize its full discovery potential.
In this section we motivate the \gx{} experiment and discuss the importance of
kaon identification in the context of the \gx{} physics program. The subsequent
section discusses the baseline \gx{} design and run plan. Both of these sections
are largely reproduced from Refs.~\cite{pac39,pac40}, documents that were
developed jointly by the \gx{}~Collaboration.
\subsection{The GlueX experiment}
\label{Sec:Experiment}
A long-standing goal of hadron physics has been to understand how the quark
and gluonic degrees of freedom that are present in the fundamental QCD Lagrangian
manifest themselves in the spectrum of hadrons. Of particular interest is how the
gluon-gluon interactions might give rise to physical states with gluonic excitations.
One class of such states is the hybrid meson,
which can be naively thought of as a quark anti-quark pair coupled to a valence
gluon ($q\bar{q}g$). Recent lattice QCD calculations~\cite{Dudek:2011bn} predict a rich spectrum
of hybrid mesons. A subset of these hybrids has an exotic experimental signature:
angular momentum ($J$), parity ($P$), and charge conjugation ($C$) that cannot be
created from just a quark-antiquark pair. The primary goal of the \gx~experiment in
Hall~D is to search for and study these mesons.
Our understanding of how gluonic excitations manifest themselves within QCD
is maturing thanks to recent results from lattice QCD. This numerical approach
to QCD considers the theory on a finite, discrete grid of points in a manner that
would become exact if the lattice spacing were taken to zero and the spatial extent
of the calculation, {\it i.e.,} the ``box size,"
was made large. In practice, rather fine spacings and large boxes are used so that
the systematic effect of this approximation should be small. The main limitation of
these calculations at present is the poor scaling of the numerical algorithms
with decreasing quark mass. In practice most contemporary calculations use a
range of artificially heavy light quarks and attempt to observe a trend as the light
quark mass is reduced toward the physical value. Trial calculations at the physical
quark mass have begun, and regular usage is anticipated within a few years.
The spectrum of eigenstates of QCD can be extracted from correlation functions
of the type $\langle 0 | \mathcal{O}_f(t) \mathcal{O}_i^\dag(0) | 0 \rangle$, where
the $\mathcal{O}^\dag$ are composite QCD operators capable of interpolating a
meson or baryon state from the vacuum. The time-evolution of the Euclidean
correlator indicates the mass spectrum ($e^{-m_\mathfrak{n} t}$) and information
about quark-gluon substructure can be inferred from matrix-elements
$\langle \mathfrak{n} | \mathcal{O}^\dag |0 \rangle$. In a series of recent
papers~\cite{Dudek:2009qf,Dudek:2010wm,Dudek:2011tt,Edwards:2011jj},
the Hadron Spectrum Collaboration has explored the spectrum of mesons and
baryons using a large basis of composite QCD interpolating fields, extracting a
spectrum of states of determined $J^{P(C)}$, including states of high internal excitation.
As shown in Fig.~\ref{fig:lqcd_meson}, these calculations show a clear and detailed spectrum of exotic
$J^{PC}$ mesons, with a lightest $1^{-+}$ state lying a few hundred MeV below a $0^{+-}$
and two $2^{+-}$ states. Through analysis of the matrix elements
$\langle \mathfrak{n} | \mathcal{O}^\dag |0 \rangle$ for a range of different quark-gluon
constructions, $\mathcal{O}$, we can infer \cite{Dudek:2011bn} that although the bulk of the
non-exotic $J^{PC}$ spectrum has the expected systematics of a $q\bar{q}$ bound
state system, some states are only interpolated strongly by operators featuring non-trivial
gluonic constructions. One may interpret these states as non-exotic hybrid mesons, and by combining them with
the spectrum of exotics, it is possible to isolate the lightest hybrid supermultiplet of $(0,1,2)^{-+}$ and $1^{--}$ states at a mass
roughly 1.3 GeV heavier than the $\rho$ meson. The form of the operator that has the strongest overlap
onto these states has an $S$-wave $q\bar{q}$ pair in a color octet configuration and
an exotic gluonic field in a color octet with $J_g^{P_gC_g}=1^{+-}$, a \emph{chromomagnetic}
configuration. The heavier $(0,2)^{+-}$ states, along with some positive parity
non-exotic states, appear to correspond to a $P$-wave coupling of the $q\bar{q}$ pair
to the same chromomagnetic gluonic excitation.
A similar calculation for isoscalar states uses both $u\bar{u} + d\bar{d}$ and $s\bar{s}$
constructions and is able to extract both the spectrum of states and also their hidden
flavor mixing. (See Fig.~\ref{fig:lqcd_meson}.) The basic experimental pattern of significant
mixing in the $0^{-+}$ and $1^{++}$
channels and small mixing elsewhere is reproduced, and for the first time, we are able to say
something about the degree of mixing for exotic-$J^{PC}$ states. In order to
probe this mixing experimentally, it is essential to be able to reconstruct decays to both strange and non-strange
final state hadrons.
\begin{figure*}
\begin{center}
\includegraphics[width=\linewidth]{figures/lqcd_meson_spec}
\caption{\label{fig:lqcd_meson}A compilation of recent lattice QCD computations for both the
isoscalar and isovector light mesons from Ref.~\cite{Dudek:2011bn}, including
$\ell\bar{\ell}$ $\left(|\ell\bar{\ell}\rangle\equiv (|u\bar{u}\rangle+|d\bar{d}\rangle)/\sqrt{2}\right)$ and
$s\bar{s}$ mixing angles (indicated in degrees). The dynamical computation is
carried out with two flavors of quarks, light ($\ell$) and strange ($s$). The $s$ quark
mass parameter is tuned to match physical $s\bar{s}$ masses, while the light quark mass parameters are
heavier, giving a pion mass of 396~MeV. The black brackets with upward ellipses represent regions of the spectrum
where present techniques make it difficult to extract additional states.
The dotted boxes indicate states that are interpreted as the lightest
hybrid multiplet -- the extraction of clear $0^{-+}$ states in this region is difficult in practice.}
\end{center}
\end{figure*}
\subsection{The importance of kaon identification}
\label{Sec:KaonMotivation}
The primary goal of the \gx~experiment is to conduct a definitive mapping of states in the light
meson sector, with an emphasis on searching for exotic mesons. Ideally, we would like to produce
the experimental analogue of the lattice QCD spectrum pictured in Fig.~\ref{fig:lqcd_meson}, enabling
a direct test of our understanding of gluonic excitations in QCD. In order to achieve this, one must be
able to reconstruct strange final states, as observing decay patterns of mesons has been one of the
primary mechanisms of inferring quark flavor content. An example of this can be seen by examining
the two lightest isoscalar $2^{++}$ mesons in the lattice QCD calculation in Fig.~\ref{fig:lqcd_meson}.
The two states have nearly pure flavors, with only a small ($11^\circ$) mixing in the $\ell\bar{\ell}$ and
$s\bar{s}$ basis. A natural experimental assignment for these two states are the $f_2(1270)$ and the
$f_2'(1525)$. An experimental study of the branching ratios shows that
$\mathcal{B}(f_2(1270)\to K K)/\mathcal{B}(f_2(1270)\to \pi\pi)\approx 0.05$ and
$\mathcal{B}(f_2'(1525)\to \pi\pi)/\mathcal{B}(f_2'(1525)\to K K) \approx 0.009$~\cite{Beringer:1900zz},
which support the prediction of an $f_2(1270)$ ($f_2'(1525)$) with a dominant $\ell\bar{\ell}$ ($s\bar{s}$)
component. By studying both strange and non-strange decay modes of mesons, \gx~hopes to provide
similarly valuable experimental data to aid in the interpretation of the hybrid spectrum.
%%%%%%%%%%%%%%%%%
\subsubsection{Exotic $s\bar{s}$ states}
%%%%%%%%%%%%%%%%%
While most experimental efforts to date have focused on the lightest isovector exotic meson, the
$J^{PC}=1^{-+}$ $\pi_1(1600)$, lattice QCD clearly predicts a rich spectrum of both isovector and
isoscalar exotics, the latter of which may have mixed $\ell\bar{\ell}$ and $s\bar{s}$ flavor content.
A compilation of the ``ground state" exotic hybrids is listed in Table~\ref{tab:exotic_modes}, along with
theoretical estimates for masses, widths, and key decay modes. It is expected that initial searches
with the baseline \gx~hardware will target primarily the $\pi_1$ state. Searches for the $\eta_1$, $h_0$, and $b_2$ may be
statistically challenging, depending on the masses of these states and the production cross sections.
With increased statistics and kaon identification, the search scope can be broadened to include these
heavier exotic states in addition to the $s\bar{s}$ states: $\eta_1'$, $h_0'$, and $h_2'$. The $\eta_1'$ and
$h_2'$ are particularly interesting because some models predict these states to be relatively narrow, and
that they should decay through well-established kaon resonances.
Observations of various $\pi_1$ states have been reported in the literature for over fifteen
years, with some analyses based on millions of events~\cite{Meyer:2010ku}.
However, it is safe to say that there exists
a fair amount of skepticism regarding the assertion that unambiguous experimental evidence
exists for exotic hybrid mesons. If the scope of exotic searches with \gx~is narrowed to only include
the lightest isovector $\pi_1$ state, the ability for \gx~to comprehensively address the question of
the existence of gluonic excitations in QCD is greatly diminished. On the other hand, clear identification of
all exotic members of the lightest hybrid multiplet, the three exotic $\pi_1^{\pm,0}$ states and the exotic
$\eta_1$ and $\eta_1'$, which can only be done by systematically studying a large number of
strange and non-strange decay modes, would provide unambiguous experimental confirmation of
exotic mesons. A study of decays to kaon final states could demonstrate that the $\eta_1$ candidate
is dominantly $\ell\bar{\ell}$ while the $\eta_1'$ candidate is $s\bar{s}$, as predicted by initial lattice
QCD calculations. Such a discovery would represent a substantial improvement in the experimental
understanding of exotics. In addition, further identification of members of the
$0^{+-}$ and $2^{+-}$ nonets as well as measuring the mass splittings with the $1^{+-}$ states will
validate the lattice QCD inspired phenomenological picture of these states as $P$-wave
couplings of a gluonic field with a color-octet $q\bar{q}$ system.
\begin{table*}\centering
\caption{\label{tab:exotic_modes}
A compilation of exotic quantum number hybrid approximate masses, widths, and decay predictions.
Masses are estimated from dynamical LQCD calculations with $M_\pi = 396~\mathrm{MeV}/c^2$~\cite{Dudek:2011bn}.
The PSS (Page, Swanson and Szczepaniak) and IKP (Isgur, Kokoski and Paton) model widths are from Ref.~\cite{Page:1998gz},
with the IKP calculation based on the model in Ref.~\cite{Isgur:1985vy}. The total widths have a mass
dependence, and Ref.~\cite{Page:1998gz} uses somewhat different mass values than suggested by the most recent
lattice calculations~\cite{Dudek:2011bn}.
Those final states marked with a dagger ($\dagger$) are ideal for experimental exploration
because there are relatively few stable particles in the final state or moderately narrow
intermediate resonances that may reduce combinatoric background.
(We consider $\eta$, $\eta^\prime$, and $\omega$ to be stable final state particles.)}
\begin{tabular}{ccccccc}\hline\hline
& Approximate & $J^{PC}$ & \multicolumn{2}{c}{Total Width (MeV)} &
Relevant Decays & Final States \\
& Mass (MeV) & & PSS & IKP & & \\ \hline
$\pi_{1}$ & 1900 & $1^{-+}$ & $80-170$ & $120$ &
$b_{1}\pi^\dagger$, $\rho\pi^\dagger$, $f_{1}\pi^\dagger$, $a_{1}\eta$, $\eta^\prime\pi^\dagger$ & $\omega\pi\pi^\dagger$, $3\pi^\dagger$, $5\pi$, $\eta 3\pi^\dagger$, $\eta^\prime\pi^\dagger$ \\
$\eta_{1}$ & 2100 & $1^{-+}$ & $60-160$ & $110$ &
$a_{1}\pi$, $f_{1}\eta^\dagger$, $\pi(1300)\pi$ & $4\pi$, $\eta 4\pi$, $\eta\eta\pi\pi^\dagger$ \\
$\eta^{\prime}_{1}$ & 2300 & $1^{-+}$ & $100-220$ & $170$ &
$K_{1}(1400)K^\dagger$, $K_{1}(1270)K^\dagger$, $K^{*}K^\dagger$ & $KK\pi\pi^\dagger$, $KK\pi^\dagger$, $KK\omega^\dagger$ \\ \hline
%
$b_{0}$ & 2400 & $0^{+-}$ & $250-430$ & $670$ &
$\pi(1300)\pi$, $h_{1}\pi$ & $4\pi$ \\
$h_{0}$ & 2400 & $0^{+-}$ & $60-260$ & $90$ &
$b_{1}\pi^\dagger$, $h_{1}\eta$, $K(1460)K$ & $\omega\pi\pi^\dagger$, $\eta3\pi$, $KK\pi\pi$ \\
$h^{\prime}_{0}$ & 2500& $0^{+-}$ & $260-490$ & $430$ &
$K(1460)K$, $K_{1}(1270)K^\dagger$, $h_{1}\eta$ & $KK\pi\pi^\dagger$, $\eta3\pi$ \\ \hline
%
$b_{2}$ & 2500 & $2^{+-}$ & $10$ & $250$ &
$a_{2}\pi^\dagger$, $a_{1}\pi$, $h_{1}\pi$ & $4\pi$, $\eta\pi\pi^\dagger$ \\
$h_{2}$ & 2500 & $2^{+-}$ & $10$ & $170$ &
$b_{1}\pi^\dagger$, $\rho\pi^\dagger$ & $\omega\pi\pi^\dagger$, $3\pi^\dagger$ \\
$h^{\prime}_{2}$ & 2600 & $2^{+-}$ & $10-20$ & $80$ &
$K_{1}(1400)K^\dagger$, $K_{1}(1270)K^\dagger$, $K^{*}_{2}K^\dagger$ & $KK\pi\pi^\dagger$, $KK\pi^\dagger$\\
\hline\hline
%
\end{tabular}
\end{table*}
%%%%%%%%%%%%%%%%%
\subsubsection{Non-exotic $s\bar{s}$ mesons}
\label{sec:normalss}
%%%%%%%%%%%%%%%%%
As discussed above, one expects the lowest-mass hybrid multiplet to contain
$(0,1,2)^{-+}$ states and a $1^{--}$ state that all have about the same mass and correspond to an
$S$-wave $q\bar{q}$ pair coupling to the gluonic field in a $P$-wave. For each $J^{PC}$ we
expect an isovector triplet and a pair of isoscalar states in the spectrum. Of the four sets of $J^{PC}$
values for the lightest hybrids, only the $1^{-+}$ is exotic. The other hybrid states will appear as
supernumerary states in the spectrum of conventional mesons. The ability to clearly identify these
states depends on having a thorough and complete understanding of the meson spectrum. Like
searching for exotics, a complete mapping of the spectrum of non-exotic mesons requires the
ability to systematically study many strange and non-strange final states. Other experiments, such
as BESIII or COMPASS, are carefully studying this with very high statistics data samples
and have outstanding capability to cleanly study any possible final state. While the production
mechanism of \gx~is complementary to that of charmonium decay or pion beam production and is
thought to enhance hybrid production, it is essential that the detector capability and statistical
precision of the data set be competitive with other contemporary experiments in order to maximize the collective
experimental knowledge of the meson spectrum.
Given the numerous discoveries of unexpected, apparently non-$q\bar{q}$ states in the charmonium spectrum,
a state that has attracted a lot of attention in the $s\bar{s}$ spectrum is the $Y(2175)$, which is
assumed to be an $s\bar{s}$ vector meson ($1^{--}$). The $Y(2175)$ (also denoted as $\phi(2170)$) has been observed to decay to
$\pi\pi\phi$ and has been produced in both $J/\psi$ decays~\cite{Ablikim:2007ab} and $e^+e^-$
collisions~\cite{Aubert:2006bu,Shen:2009zze}. The state is a proposed analogue of the $Y(4260)$ in
charmonium, a state that is also about 1.2 GeV heavier than the ground state triplet ($J/\psi$)
and has a similar decay mode: $Y(4260)\to\pi\pi J/\psi$~\cite{Aubert:2005rm,Coan:2006rv,He:2006kg,Yuan:2007sj}.
The $Y(4260)$ has no obvious interpretation
in the charmonium spectrum and has been speculated to be a hybrid
meson~\cite{Close:2005iz,Zhu:2005hp,Kou:2005gt,Luo:2005zg}, which, by loose analogy,
leads to the implication that the $Y(2175)$ might also be a hybrid candidate. It should be noted
that the spectrum of $1^{--}$ $s\bar{s}$ mesons is not as well-defined experimentally as the $c\bar{c}$ system;
therefore, it is not clear that the $Y(2175)$ is a supernumerary state. However, \gx~is ideally suited
to study this system. We know that vector mesons are copiously produced in photoproduction; therefore,
with the ability to identify kaons, a precision study of the $1^{--}$ $s\bar{s}$ spectrum can be conducted
with \gx. Some have predicted~\cite{Ding:2007pc} that the potential hybrid nature of the $Y(2175)$ can be explored by studying ratios of branching fractions into various kaonic final states.
In addition, should \gx~be able to conclude that the $Y(2175)$ is in fact a supernumerary
vector meson, then a search can be made for the exotic $1^{-+}$ $s\bar{s}$ member of the multiplet
($\eta_1'$), evidence of which would provide a definitive interpretation of the $Y(2175)$ and likely have
implications on how one interprets charmonium data.