computations for a loosely bound $D\bar{D}^{*}$ composite showed that such
similarities were highly unlikely Bignamini:2009sk . Also, in the deuson
picture, the $X(3872)$ is primarily a $D^{0}\bar{D}^{*0}$ bound state.
Searches for other near-threshold $D\bar{D}^{*}$ combinations, such as mostly
$D^{+}D^{*-}$, or $D^{0}D^{*-}$ states, with the same $J^{PC}=1^{++}$ quantum
numbers, came up empty Aubert:2004zr ; Choi:2011fc . Another problem with the
deuson idea is the large rate for $X(3872)\rightarrow\gamma\psi(2S)$ reported
by BaBar Aubert:2008ae and LHCb Aaij:2014ala (see Eq. 6), which is expected
for the $2^{3}{\rm P}_{1}$ charmonium state but counter to predictions for
molecules Swanson:2003tb ; Dong:2009uf .

At present, and as pointed out in ref. Braaten:2007dw , it seems likely that
the $X(3872)$ is a quantum mechanical mixture of a tightly bound $c\bar{c}$
core in $2^{3}{\rm P}_{1}$ configuration and a molecule-like $D\bar{D}^{*}$
combination. This idea was verified by detailed computations in refs.
Coito:2012vf and Takeuchi:2014rsa ; the latter found that the bulk of the
$D\bar{D}^{*}$ binding comes from the coupling between the $c\bar{c}$ core and
the $D\bar{D}^{*}$ components, and not much comes from the mutual attraction
between the $D$ and the $\bar{D}^{*}$, which is the key feature of deuson
models. In this picture for the $X(3872)$, its prompt production in high
energy hadron collisions and radiative decays to the $\psi^{\prime}$ proceed
via the $c\bar{c}$ core component of the $X(3872)$ and, thus, have
characteristics that are similar to those of the $\chi_{c1}^{\prime}$.

The bulk of the huge theoretical literature on non-standard hadrons is on
molecular models Pakvasa:2003ea ; Braaten:2004rw ; Voloshin:2003nt ;
Fleming:2007rp ; Zhu:2007wz ; Gamermann:2009fv ; Molina:2009ct ; Zhang:2009bv
; Sun:2012sy ; Wang:2013cya ; Polosa:2015tra ; Karliner:2016ith . In these,
binding is provided by pion- and other light-meson-exchange forces. Since the
binding provided by these forces is not expected to be very large, molecular
states are expected to be near the masses of their constituent hadrons and
have appropriate S-wave $J^{PC}$ quantum numbers. This is the case for the
$Z_{b}(10610)$ and the $Z_{b}(10650)$, which are within a few MeV of the
$B\bar{B}^{*}$ and $B^{*}\bar{B}^{*}$ thresholds, respectively, and applies
reasonably well to the $Z_{c}(3900)$ and $Z_{c}(4020)$, which are $\simeq 10$
MeV above the $D\bar{D}^{*}$ and $D^{*}\bar{D}^{*}$ thresholds, respectively.
However, the interpretation of these states as molecules is controversial.
Peaks at masses that are slightly above threshold are dangerously similar to
expectations for kinematically induced cusps Bugg:2011jr ; Blitz:2015nra ;
Swanson:2015bsa (see Fig. 8b and related text). Anomalous triangle
singularities are another mechanism that can produce above-threshold peaks
that are not related to a physical resonance Chen:2013coa . Moreover, unlike
the $X(3872)$, no evidence for these states have been found in lattice QCD
calculations Prelovsek:2013xba ; Prelovsek:2014swa ; Lee:2014bea ;
Ikeda:2016zwx . On the other hand, detailed studies of the BESIII’s
$Z_{c}(3900)\rightarrow J/\psi\pi$ and $D\bar{D}^{*}$ signals Guo:2014iya and
Belle’s corresponding $Z_{b}$ signals Guo:2016bjq ; Pilloni:2016obd ;
Albaladejo:2015lob show that the observed peaks can be identified as virtual
states with associated poles in the complex scattering $t$-matrices.

The $J^{P}=1^{+}$ $Z(4430)$ (now with a mass near $4478$ MeV) has been
proposed as a radial excitation of the $Z_{c}(3900)$, comprised of a molecule-
like $D\bar{D}^{*}(2S)$ configuration Barnes:2014csa ; Ma:2014zua , where the
$D^{*}(2S)$ is the radial excitation of the $D^{*}$. Although the existence of
the $D^{*}(2S)$ has not been firmly established, the BaBar group reported a
strong candidate for this state in the $D^{+}\pi^{-}$ and $D^{*+}\pi^{-}$
invariant mass distributions in inclusive $e^{+}e^{-}\rightarrow
D^{(*)+}\pi^{-}\ X$ reactions at $E_{\rm cm}=10.58$ GeV delAmoSanchez:2010vq ;
LHCb subsequently reported observations of $D^{(*)}\pi$ invariant mass
structures with peak and width values similar to BaBar’s that were produced in
high energy $pp$ collisions Aaij:2013sza . The averages of the BaBar and LHCb
mass and width measurements for this state, which is called the
$D^{*}_{J}(2600)$, are $2622\pm 12$ MeV and $104\pm 20$ MeV, respectively
Olive:2016xmw . If we assume $D^{*}(2S)=D^{*}_{J}(2600)$, the
$D\bar{D}^{*}(2S)$ “threshold” is at $\simeq 4490$ MeV, and $\simeq 12$ MeV
above the $Z(4430)$ mass. This association with a radially excited $D^{*}$
meson may account for the observed preference for the $Z(4430)$ to decay to
$\psi(2S)\pi$ over $J/\psi\pi$ (recall that $\psi^{\prime}$=$\psi(2S)$). The
large $D^{*}_{J}(2600)$ width could also explain the large $Z(4430)$ width,
although for such a broad constituent, it is not clear whether the molecular
formalism still applies. Also, unlike the $Z(4430)$ state, the $Z_{c}(3900)$
state is not produced in $B\to Z\,K$ decays Chilikin:2014bkk , which casts
doubt on any model in which these two states have essentially the same
internal structure, differing only by a radial excitation.

Molecules are not likely explanations for most of the other hidden-charm non-
standard mesons. For example, when the $Y(4260)$ was first reported by BaBar
with a mass of $4259^{+8}_{-10}$ MeV, its interpretation as a
$D\bar{D}_{1}(2420)$ molecule with a binding energy of $\simeq 25$ MeV might
have been plausible Wang:2013cya . But recent high-statistics measurements by
BESIII have shown that single resonance fits to the $Y(4260)$ were naïve and
the peak is, in fact, best fit by two resonances (see Fig. 38) with masses
$4220\pm 4$ MeV and $4320\pm 13$ MeV Wang:2013cya . This implies that the
required $D\bar{D}_{1}(2420)$ binding energy for the lower-mass peak would be
much higher, at $\simeq 65$ MeV, while the higher-mass state would be unbound
by $\simeq 35$ MeV, making a molecular interpretation for either component of
this peak implausible.

The only relevant two-particle threshold with $J^{PC}=0^{++}$ S-wave quantum
numbers that is near the $X(3915)$ meson is the $D_{s}^{+}D_{s}^{-}$ threshold
at $3937$ MeV. However, since three-pseudoscalar-meson couplings are forbidden
by parity plus rotation invariance, $\pi$-meson exchange forces, which provide
the bulk of the binding for the deuteron, are not applicable. Thus, there is
no plausible deuson-like model that can account for the nature of the
$X(3915)$. Likewise, before the LHCb group established the $J^{PC}$ of the
$X(4140)$ resonance as $1^{++}$, there were a number of suggestions that it
was an S-wave $D^{*+}_{s}D^{*-}_{s}$ molecule ($2m_{D^{*-}_{s}}=4224$ MeV).
But an S-wave $D^{*+}_{s}D^{*-}_{s}$ system can only have $J^{PC}=0^{++}$ or
$2^{++}$ (since $C=(-1)^{L+S}$) Bondar:2016hva . The LHCb measurement
Aaij:2016iza rules out this possibility and, in addition, they reported three
additional candidates for $c\bar{c}s\bar{s}$ states: the $X(4274)$, $X(4500)$
and $X(4700)$. None of these are close to the thresholds of any S-wave
combinations of $D_{s}$ excitations that would reproduce their measured
quantum numbers.

Some authors have suggested that the narrow $P_{c}(4450)$ pentaquark might be
an S-wave, $J^{P}=3/2^{-}$ molecule comprised of a $\Sigma_{c}$ baryon and a
$\bar{D}^{*}$ meson, with a binding energy of $\simeq 13$ MeV Karliner:2015ina
; Roca:2015dva . This, taken alone, might be a reasonable suggestion. However,
if the $P_{c}(4450)$ is $3/2^{-},$ the LHCb data indicate that the
$P_{c}(4380)$ should be $5/2^{+}$ Aaij:2015tga . The lightest meson-baryon
combinations that can produce spin $5/2$ in an S-wave are $p\chi_{c2}$ (for
which $\pi$-exchange forces are not allowed) and $\Sigma_{c}^{*}\bar{D}^{*}$,
with mass thresholds that are 115 and 145 MeV above the $P_{c}(4380)$ mass,
respectively. Moreover, the $\sim 200$ MeV width of the lower-mass
$P_{c}(4380)$ state makes it pretty short-lived for a molecular state with $c$
and $\bar{c}$ spatially separated into two different confining volumes,
resulting in a small overlap of its wave function with the $J/\psi$ state that
is produced in its decay Karliner:2016via . These thresholds are also too high
to provide a plausible molecular explanation for the case where the
$J^{P}=5/2^{\pm}$ assignment is associated with the heavier and narrower
$P_{c}(4450)$ peak. This is not only the case for a bound molecule
interpretation, but also for cusp or triangle anomaly mechanisms, which
require S-wave interactions to make significant contributions Bayar:2016ftu .

Thus, a reasonable conclusion is that while molecule models have relevance for
some of the observed candidates, they are not the whole story.

####  VIII.1.2 Diquarks

QCD, which explains the existence of $q\bar{q}$ mesons and $qqq$ baryons, also
predicts that the short-distance color force between two quarks in an $S=0$
diquark antitriplet state (see Fig. 6b) is attractive and one-half the
strength of the attraction between a quark and antiquark in a standard meson.
Therefore, diquarks and diantiquarks are expected to play a strong role in
shaping the spectroscopy of multi-quark hadrons, when pairs of quarks exist
inside the confinement volume Jaffe:1976ig .

In 2004, Maiani et. al Maiani:2004vq proposed that the $X(3872)$ is formed
from a symmetric combination of an $S=0$ and $S=1$ diquark and diantiquark in
a relative S-wave:
$[cq]_{S=0}[\bar{c}\bar{q}]_{S=1}+[cq]_{S=1}[\bar{c}\bar{q}]_{S=0}$, with
$q=u$ or $d$. This implies the existence of two nearly degenerate neutral
states, $X_{h}$ and $X_{l}$, that are mixtures of $X_{u}=[cu][\bar{c}\bar{u}]$
and $X_{d}=[cd][\bar{c}\bar{d}]$, with a mass difference:

$\displaystyle M(X_{h})-M(X_{l})$ $\displaystyle=$ $\displaystyle
2(m_{d}-m_{u})/\cos 2\theta$ (20) $\displaystyle=$ $\displaystyle(7\pm
2)~{}{\rm MeV}/\cos 2\theta,$

where $\theta$ is the mixing angle. Here, an unequal mixture of the two states
(i.e., $\theta\neq 45^{0}$) would generate isospin violation in $X_{h}$ and
$X_{l}$ decays. Tetraquarks made out of diquarks must be compact due to the
confinement of color, which naturally can explain the large $X(3872)$ prompt
production rate at hadron colliders. However, this model predicted the
existence of three additional states: two $0^{++}$ states with lower mass
values and a $2^{++}$ state at a higher mass. The production of two neutral
$X(3872)$ states differing in mass by an amount consistent with the Eq. 20
prediction was ruled for high energy $p\bar{p}$ production by CDF
Aaltonen:2009vj and for production in $B$ meson decays by BaBar Aubert:2008gu
and Belle Choi:2011fc . Compelling candidates for the predicted $0^{++}$ and
$2^{++}$ states have yet to be identified. Similar to the case for molecular
models, the significant $X(3872)\to\gamma\psi(2S)$ rate relative to the
$X(3872)\to\gamma J/\psi(1S)$ decays is not naturally explained by the
tetraquark model, unless it also includes mixing with the $\chi_{c1}(2{\rm
P})$ charmonium state or dynamical effects Brodsky:2014xia discussed below.
Moreover, unlike molecular models, the tetraquark picture does not offer
natural explanations for the $X(3872)$ mass coincidence with the
$D^{0}\bar{D}^{*0}$ threshold, or its very narrow width. The latter led to
hybridized-tetraquark model, which explains the near-threshold states as an
interplay between bound molecules and compact tetraquark states
Esposito:2016itg .

Diquark interpretations have been proposed to explain most of the observed
states. For example, in this model, the $Y(4260)$ is a symmetric
$[cq]_{S=0}[\bar{c}\bar{q}]_{S=1}$ diquark-diantiquark combination, like the
$X(3872)$, but in a relative P-wave Maiani:2014aja . The $\simeq 350$ MeV mass
difference between the two states is consistent with the typical mass penalty
that is associated with the addition of one unit of orbital angular momentum
(see, e.g., Table 3) and the strong $Y(4260)\rightarrow\gamma X(3872)$
transition reported by BESIII Ablikim:2013dyn would be an allowed electric
dipole transition between the two related states Chen:2015dig . Likewise the
$Z_{c}(3900)$ can be naturally accommodated as the antisymmetric, S-wave
$[cq]_{S=0}[\bar{c}\bar{q}^{\prime}]_{S=1}$ diquark-diantiquark combination,
and the $Z(4430)$ as its first radial excitation. The diquark picture also can
explain states that molecular models have trouble with, such as the $X(3915)$
Lebed:2016yvr and the four states seen decaying to $J/\psi\phi$ Chen:2016oma ;
Maiani:2016wlq , and provide a common origin for the $P_{c}(4380)$ and
$P_{c}(4450)$ pentaquarks that can accommodate their opposite parities
Maiani:2015vwa ; Lebed:2015tna .

These successes can be attributed to a larger number of degrees of freedom in
strong color binding as compared to weak, Yukawa-type exchange forces. Orbital
excitations between colored objects can reach higher spin states at lower
masses. Slight changes in free parameters that describe the strength of the
color forces, can shift predicted masses to any value, while molecular models
can only accommodate structures near hadron-hadron mass thresholds. However,
the free parameters of diquark models are usually readjusted when moving from
the description of one exotic hadron system to another, resulting in no single
unified diquark model that can describe all of the observed states at once.
The universal prediction of large prompt production rates for tightly bound
tetraquarks and pentaquarks at hadron colliders are in some conflict with the
reality that to date, only the $X(3872)$ and $X(4140)$ states have been seen
in this production mode Bondar:2016hva .

One big problem with the diquark picture is that, since the strong radial
color force between the diquark and the diantiquark is universal, it has the
same strength for $q,q^{\prime}=u,d,s$ independently of their flavor or spin
state. Therefore, every successful application of the idea to an
experimentally observed state carries with it predictions for a large number
of related states that typically are not seen, as was the case for the
original diquark-diantiquark interpretation of the $X(3872)$ discussed above.
Another problem is that in this picture, diquark separations are comparable to
the diquark sizes, and there is nothing in the model to prevent fast fall-
apart widths to individually confined mesons and baryons, thereby precluding
the existence of narrow states.

Brodsky, Hwang and Lebed Brodsky:2014xia address these problems with a scheme
that creates separation between diquarks, severely restricts the number of
observed states, and suppresses the superfluous ones. Their basic idea, which
they call dynamical diquarks, is that at production, the diquark and
diantiquark move rapidly apart, a motion that is opposed by the increasingly
stronger confinement force. By the time the motion stops, the diquark
diantiquark separation is large and there is no substantial overlap between
the quarks in one and the antiquarks in the other. Hadronization of diquarks
separated dynamically by this production mechanism depends on the overlap of
the tails of the quark and antiquark wave-functions and only occurs if this
overlap is well matched to an accessible configuration of final-state hadrons.
In this way the process has a complex and intricate dependence on the
production mechanism and decay final states that suppresses all the unwanted
states. But this comes at the cost of stripping the dynamical diquark picture
of virtually all of its ability to predict the existence of additional states.

Baryons with heavy quarks are an interesting testing ground for diquark
models. For example, in heavy-light-light quark baryons, spin couplings of the
heavy quark are expected to be suppressed by its heavy mass creating favorable
conditions for formation of a light diquark, $[qq]Q$. Since a good diquark
would be in the same color state as $\bar{q}$, meson-like radial and orbital-
angular-momentum excitation spectrum is expected for such a system. The known
excitations of charmed and beauty baryons follow these predictions. For
example, the LHCb has recently observed five narrow $\Omega_{c}$ excitations
Aaij:2017nav , that lie in the mass range of 1P and 2S states predicted in
diquark models Ebert:2011kk ; Karliner:2017kfm . Their masses extend to just
below $m_{\Xi}+m_{D}$, which is the threshold for decays that leave the $ss$
diquark intact. Therefore, their strong decays to $\Xi_{c}^{+}K^{-}$ requires
the disintegration of the $ss$ diquark, which can explain their narrow widths
(0.8-8.7 MeV) in spite of the fact that there is no OZI suppression.

In doubly-heavy baryons, the heavy quark pair is likely to form a diquark,
$[QQ]q$, acting like an effective heavy antiquark. Using an approach based on
this idea, Karliner and Rosner Karliner:2014gca predicted with good precision
the mass of the $\Xi_{cc}^{++}$ baryon, that was recently observed by LHCb
Aaij:2017ueg . They have extended this model to predict that the mass of the
lightest $1^{+}$ $[bb][\bar{u}\bar{d}]$ tetraquark system would be well below
the threshold for decays to $B^{-}\bar{B}^{0}\gamma$, and therefore be stable
under strong and electromagnetic decays (see also refs. Eichten:2017ffp ). The
similar $[bc][\bar{u}\bar{d}]$ tetraquark state is also likely to be stable,
while $[bc][\bar{u}\bar{d}]$ may be right below, or right above the
$D^{0}D^{*+}$ threshold. Almost the same predictions for these states were
obtained a year earlier by Francis et al. employing LQCD calculations with
diquark interpolators Francis:2016hui . Therefore, these are now perhaps the
most firm theoretical predictions offering hope for unambiguously establishing
the existence of diquark tetraquarks in not too distant future.

####  VIII.1.3 QCD hybrids

The existence of hybrid states is among the most intriguing predictions of
QCD. The most striking experimental signature for QCD hybrids is the possible
existence of mesons with exotic quantum numbers. However, since all the states
discussed in this report have non-exotic quantum numbers, there is no smoking
gun candidate for a hybrid state. The state that has been most strongly
promoted as a candidate for a $c\bar{c}$-gluon charmonium hybrid is the
$1^{--}$ $Y(4260)$ Zhu:2005hp ; Close:2005iz ; Kou:2005gt . However, this
assignment is not unique, and this state is also considered to be a good QCD
tetraquark candidate. Charmonium hybrids are expected to have strong decays to
S-wave $D^{(*)}\bar{D}^{**}$ final states, where $D^{**}$ designates the
P-wave charmed mesons described in Table 3. For the $Y(4260)$, the only
possible accessible final state of this type would be
$D^{*}\bar{D}_{0}^{*}(2400)$, where the $D_{0}^{*}(2400)$ is a $0^{++}$ $D\pi$
resonance with mass and width $M=2318\pm 29$ MeV and $\Gamma=267\pm 40$ MeV.
In principle, a high-statistics study of $Y(4260)\rightarrow D^{*}\bar{D}\pi$
might see evidence for a $D^{*}\bar{D}^{*}_{0}$ final state but, since it is a
broad S-wave state, it would probably be difficult to distinguish from a non-
resonant background. As mentioned in Section V.3, the latest lattice QCD study
of charmonium states has a lowest-mass $1^{--}$ hybrid candidate at $M=4285\pm
14$ MeV Liu:2012ze . This is $\simeq 65$ MeV above the recent BESIII
measurement of the $Y(4260)$ mass ($4220\pm 4$ MeV). However, given that the
LQCD calculations are missing simulations of couplings to the available decay
channels, this difference should probably be considered small.

####  VIII.1.4 Hadrocharmonium

In the hadrocharmonium model, the strong preference for the $Y(4260)$
($Y(4360)$) meson to decay to $\pi^{+}\pi^{-}J/\psi$
($\pi^{+}\pi^{-}\psi^{\prime}$) over the fall-apart $D^{(*)}\bar{D}^{(*)}$
modes is accommodated by a meson structure that contains a color-singlet
charmonium-state core surrounded by a light quark excitation Dubynskiy:2008mq
. In the case of the $Y(4260)$ ($Y(4360)$), this core state was taken to be
the $J/\psi$ ($\psi^{\prime}$). Since the $J/\psi$ ($\psi^{\prime}$) state is
present in its constituents, the $Y(4260)$ ($Y(4360)$) naturally prefers to
decay to final states that include it. However this model had trouble with
BESIII observations of substantial rates for $Y(4260)$ and $Y(4360)$ decays to
$\pi^{+}\pi^{-}h_{c}$ final states Ablikim:2013wzq . In the $J/\psi$ and
$\psi^{\prime}$, the $c$\- and $\bar{c}$-quarks are in a spin-triplet state,
while in the $h_{c}$ they are in a spin-singlet. By themselves, the triplet
and singlet cores cannot mix and a hadrocharmonium state should have strong
rates for decays to one of them, but not both. In an attempt to fix this
problem, the model was revised to include two hadrocharmonium states, one with
a spin-triplet core and one with a spin-singlet core, and these two states
mix, producing the observed $Y(4260)$ and $Y(4360)$, which now can both decay
to singlet and triplet states with relative rates determined by the
(unspecified) mixing angle Li:2013ssa . But, subsequent to the appearance of
this modification to the model, the BESIII group found that in the two
resonance $Y(4260)\rightarrow\pi^{+}\pi^{-}J/\psi$ structure shown in Fig. 38
Ablikim:2016qzw , both resonant components have strong decay rates to
$\pi^{+}\pi^{-}J/\psi$, while the latest BESIII $\pi^{+}\pi^{-}h_{c}$ cross
section measurements BESIII:2016adj , shown in Fig. 39, find a strong
$\pi^{+}\pi^{-}h_{c}$ decay rate for the lower mass resonant component, but no
signal for the higher mass component. Even with the above-described mixing,
the hadrocharmonium model will have a hard time reproducing this decay
pattern.

####  VIII.1.5 Kinematically induced resonance-like peaks

As mentioned above in the discussion of molecular models, some authors have
suggested that the $Z_{c}$ and $Z_{b}$ peaks are due to kinematic effects
caused by the nearby $D^{(*)}\bar{D}^{*}$ and $B^{(*)}\bar{B}^{*}$ mass
thresholds Bugg:2011jr ; Blitz:2015nra ; Swanson:2015bsa ; Chen:2013coa .
Other authors claim that the same data show that the peaks are are associated
with poles in the corresponding $D^{(*)}\bar{D}^{*}$ or $B^{(*)}\bar{B}^{*}$
scattering t-matrix and, therefore, qualify as genuine physical states
Guo:2014iya ; Guo:2016bjq . This seems to be a controversy that only more, and
higher-precision data can resolve. For example, although both mechanisms
produce strong phase motion that can be displayed in Argand plots, the
detailed mass dependence of this phase motion is distinctly different for the
two models. Another suggestion requires the application of sophisticated
coupled-channel data analysis techniques Pilloni:2016obd . However,
distinguishing between the two scenarios with either method will require huge
data samples, with increases over existing data sets by factors that approach
two orders of magnitude. This would require at least a year-long dedicated
BESIII run at energies near the $Y(4260)$ peak and a long period of BelleII
operation at the $\Upsilon(10860)$ peak.

####  VIII.1.6 Comments

At this point, the challenges posed by the observed heavy quarkonium-like
states with unusual properties have not been answered well by any theory for
hadronic states.

In general the successful theoretical work in this area has been reactive
rather than predictive. Different approaches have had some success for some
states but fail or are not applicable to others. This could be because the
non-standard hadrons that are observed are due to a variety of different,
unrelated mechanisms, or that the actual underlying mechanism has not yet been
discovered. The lack of good understanding of the nature of these states,
sheds doubts into our understanding of hadronic structures in general. Open-
flavor thresholds in light hadron spectroscopy are usually right above the
ground states of such systems and whatever mechanisms that are in play for
above-open-flavor-threshold heavy quarkonium-like hadrons are likely having a
strong influence on light hadron spectroscopy.

More theoretical and experimental work is required in all areas of hadron
spectroscopy to overcome this crisis.

###  VIII.2 Experiment

To date, the progress in the field has mainly been driven by experiments.
Although Törnqvist proposed the existence of a $J^{PC}=1^{++}$ state with mass
near the $D\bar{D}^{*}$ threshold ten years before its discovery
Tornqvist:1993ng , the $X(3872)$’s narrow width, close proximity to the
$D^{0}\bar{D}^{*0}$, large isospin violation, and its strong production in
$B$-meson decays and high-energy $p\bar{p}$ collisions were big surprises.
Likewise, the discovery of the $Y(4260)$ as a huge peak in the
$e^{+}e^{-}\rightarrow\pi^{+}\pi^{-}J/\psi$ cross section with no hints of a
corresponding signal in the open charmed meson channel was totally unexpected.
Subsequent discoveries, both in the $c$-quark and $b$-quark sectors, were
similarly unanticipated. New developments in this field have closely tracked
increases in the size and improvements in the quality of the available data
samples plus advances in the sophistication of analysis techniques. The
discovery of the $P_{c}(4380)$ and $P_{c}(4450)$ pentaquarks was possible
because of the unprecedentedly large sample of $\Lambda_{b}$ decays that was
accumulated by the LHCb experiment. Likewise, the two-resonance structure of
the $Y(4260)$ was seen by BESIII only because they had a larger data sample
and better mass resolution than the earlier measurements. The clear
demonstration of BW-amplitude-like phase motion for the $Z(4430)$ meson and
the $P_{c}(4450)$ pentaquark was the result of complex, multidimensional
amplitude analyses.

There are huge differences in what we know about various candidate states. For
some, like the $X(3872)$ and the $Y(4260)$, we know the quantum numbers and a
number of decay modes, while for others we do not even know their quantum
numbers. Even the ones with a lot of available information have important
pieces of information that are unknown. For example, we still do not know the
natural width of the $X(3872)$ or whether its mass is above or below the
$m_{D^{0}}+m_{D^{*0}}$ mass threshold. We have not seen phase motion for the
$Y(4260)$, or convincing phase motion for the $P_{c}(4380)$. While we learned
a great deal about the nature of the $X(3872)$ from the fact that it is
produced promptly in high energy $p\bar{p}$ and $pp$ collisions, we only have
limited information about prompt hadro-production of other states.

For experimental reasons, most of the states seen so far were first discovered
in decay modes that include a $J/\psi$ or a $\psi^{\prime}$ the final state.
Future experiments that access pairs of open-charm or beauty particles may
uncover a interesting dimensions of this spectroscopy that might give
important clues about the underlying dynamics.

In addition to finding new states, it would be very useful if our level of
knowledge of all of the candidate states could be brought to the same high
level as the currently best known ones. For example, multidimensional
amplitude analyses of $B\rightarrow KJ/\psi\omega$ and $K\chi_{c1}\pi$ are
needed to establish the $J^{PC}$ quantum numbers of the $X(3915)$, and the
$Z(4050)^{+}$ and $Z(4250)^{+}$.

Fortunately there are powerful experiments that are currently running and
producing important and unique results. For example, $B\rightarrow
K\chi_{c1}\pi$ and $KJ/\psi\omega$ are accessible to the LHCb even with their
existing data sample. Their recent discoveries of $J/\psi\phi$ mesons and
$P_{c}$ pentaquarks were based on analyses of their 3 fb-1 Run-I data sample
that was accumulated at $E_{\rm cm}(pp)=7~{}{\rm and}~{}8$ TeV. In Run-II,
which is now underway and will finish in 2018, they will accumulate an
additional 8 fb-1 at $E_{\rm cm}(pp)=13$ TeV. Since the $b$-quark production
cross section at 13 TeV is about twice that at 7 TeV Aaij:2016avz , the Run-II
data set will be equivalent to approximately five times that for Run-I. Thus,
we can anticipate the discovery of additional states and significant
improvements of existing results, including substantial improvements in the
precision of the $Z(4430)$ and $P_{c}$ Argand plots. A LHCb detector upgrade
in 2021 will enable it to accumulate higher luminosities. After that they
expect that the total data sample accumulated by 2030 will be 50 fb-1
(collected at $E_{\rm cm}(pp)=14$ TeV). The LHCb collaboration is also
discussing a major detector/luminosity upgrade after 2030 with an ultimate
goal of 300 fb-1. Even larger integrated luminosities will be collected at the
LHC by the CMS and ATLAS detectors. Therefore, it is expected that these
experiments will also continue to contribute to advances in exotic hadron
spectroscopy in spite of their lack of hadron identification and their more
restrictive triggers.

BESIII is planning long data runs in the Y(4260) peak region during the next
few years, and these should provide sufficient data to support studies of the
phase motion across the $Z_{c}$ peaks in
$Y(4260)\rightarrow\pi^{+}\pi^{-}J/\psi$ and $\pi^{+}\pi^{-}h_{c}$ decay
channels, and enable amplitude analyses of $Y(4260)\rightarrow\pi
D^{(*)}\bar{D}^{*}$ decays. Long-term future BESIII running plans include high
luminosity scans over the $2m_{D}\leq E_{\rm cm}(e^{+}e^{-})\leq
2m_{\Lambda_{c}}+50$ MeV range to completely map out $c$-quark production in
the threshold region in a large assortment of decay channels.

The BelleII experiment will start physics operation in late 2017. The first
year of running will be used to develop experience with machine operations
without either the inner pixel or the silicon-strip vertex detector in place.
Since this configuration has limited capabilities for doing $B$-meson physics,
which is the main motivation for the project, operation at the
$\Upsilon(10860)$ and higher energies for detailed studies of the $Z_{b}$
mesons and searches for possible additional states is planned Bondar:2016hva .
Over the anticipated ten-year operational lifetime of BelleII, a total data
sample of 50 ab-1 will be accumulated, mostly at $E_{\rm
cm}(e^{+}e^{-})=10.58$ GeV. Thus, the final BelleII data sample will be a
factor of 50 larger than the Belle data set. The strengths of BelleII, i.e.
superior photon, $\pi^{0}$, $\omega$ and $\eta^{(^{\prime})}$ detection
capabilities and higher absolute reconstruction efficiencies, are
complementary to those of LHCb. High reconstruction efficiencies are
especially essential for studies of $D^{(*)}_{(s)}\bar{D}^{(*)}_{(s)}$
systems. In addition, the $B$-factory environment provides a unique
opportunity for making precise measurements of inclusive branching fractions
such as $B^{+}\rightarrow K^{+}\,X_{c\bar{c}}$; $X_{c\bar{c}}\rightarrow\,{\rm
anything}$ decays Aubert:2005vi , where $X_{c\bar{c}}$ designates relatively
narrow charmonium-like states such as the $X(3872)$ or $X(3915)$. Inclusive
branching fractions are required input for converting product branching
fraction and total width measurements into decay partial width values, which
are usually the theoretically relevant quantities.

There are several current and future medium-energy experiments designed to
explore non-standard hadrons and to provide information on the properties of
the still enigmatic states complementary to $e^{+}e^{-}$ and hadron collider
experiments.

The $\rm{PANDA}$ experiment Lutz:2009ff at the Facility for Antiproton and Ion
Research in Germany, expected to start data taking in 2022, will study
particles produced in collisions of an intense, nearly monoenergetic beam of
antiprotons with nucleons or nuclei in the c.m. energy range from 2.5 GeV to
5.5 GeV. By performing a mass scan in several steps across the $X(3872)$
resonance, $\rm{PANDA}$ will measure the resonance line shape that is
sensitive to the binding mechanism with an accuracy an order of magnitude
better than currently available. To resolve the nature of the
$D^{*}_{s0}(2317)$, $\rm{PANDA}$ will do precise measurements of its total
width and branching fractions to different decay channels. The $p\bar{p}$
initial state will provide access to possible states with exotic quantum
numbers. Lattice QCD indicates that the lightest exotic $c\overline{c}$ hybrid
with $J^{PC}=1^{-+}$ has a mass that is near 4.2 GeV Liu:2012ze , and will be
accessible at $\rm{PANDA}$.

Discovery and studies of properties of hybrid mesons are the primary goals of
the GlueX Ghoul:2015ifw and CLAS12 Burkert:2008rj photo-production experiments
at the Jefferson National Accelerator Facility. Soon after the discovery of
the LHCb pentaquark candidates, it was suggested Wang:2015jsa ;
Kubarovsky:2015aaa ; Karliner:2015voa ; Blin:2016dlf that photo-production on
a nucleon would be a promising way to search for these states and to study
their properties. Recently, a proposal Meziani:2016lhg to study photo-
production of $J/\psi$ near threshold in search for the $P_{c}$ states was
approved by JLab and designated as a “high-impact” activity.

###  VIII.3 Final remark

The heavy-flavor, non-standard hadrons discussed in this report have severely
challenged existing ideas about the underlying structure of hadrons. The
puzzles that they pose have intrigued theorists in both the particle and
nuclear physics communities, and experimenters at all of the world’s particle
physics accelerator facilities. While they do not challenge QCD as the exact
theory of strong interactions, they expose the phenomenological disconnect
between its Lagrangian and types of structures it can produce at large
distances, with possible implications to strongly coupled theories proposed as
extensions of the Standard Model. Often in the history of physics, puzzles and
their eventual resolution have produced important advances in our
understanding of nature. We hope that this will ultimately be the case for the
issues that are discussed here.

Acknowledgements: This work was supported by the Institute for Basic Science
(Korea) by project code IBS-R016-D1 and by the National Science Foundation
(USA) Award Number 1507572. We would like to thank Steven Gottlieb for reading
the manuscript and providing a number of useful comments.

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