The spectrum of hadrons is important for understanding the confinement of quantum chromodynamics. Many new puzzles arose since 2003 due to the abundance of experimental discoveries with the $XYZ$ structures in the heavy quarkonium mass region being the outstanding examples. Hadronic resonances correspond to poles of the $S$-matrix, which has other types of singularities such as the triangle singularity due to the simultaneous on-shellness of three intermediate particles. Here we briefly discuss a few possible manifestations of triangle singularities in the $XYZ$ physics, paying particular attention to the formalism that can be used to analyze the data for charged $Z_c$ structures in the $ψπ$ distributions of the reaction $e^+e^-\to ψπ^+π^-$.
We study in the framework of a constituent quark model the possible contributions of molecular structures to the XYZ charmonium like states. We analyze simultaneously the $c\bar{c}$ structures and the possible molecular components in a formalism which allows us to treat channels below and above thresholds. The only molecular state found in the $1^{++}$ sector correspond to the X(3872). Molecular resonances also appear with other quantum numbers. So, the so called Y(3940) and the X(3915) are suggested to be $J^{PC}=0^{++}$ charmonium states. In the $J^{PC}=1^{--}$ sector we also found significa…
Exclusive production of charmonium-like XYZ states in hadron-hadron ultraperipheral collisions(UPCs) and electron-proton scattering is studied employing effective Lagrangian method. Total cross sections and rapidity distributions of charmonium-like XYZ states are obtained in hadron-hadron UPCs and electron-proton scattering process. These predictions can be applied to estimate the observed event number of exclusive charmonium-like XYZ states in hadron-hadron UPCs and electron-proton scattering. The results indicate that it is significant to search $X(3872)$ and $Z^+_c(3900)$ in pA UPCs and Ele…
In the past decade, many new charmonium (or charmonium-like) and bottomonium (or bottomonium-like) states were observed experimentally. I will review these XYZ states which do not fit into the quark model spectrum easily.
With its unique data samples at energies of 3.8--4.6 GeV, the BESIII experiment made a significant contribution to the study of charmonium and charmonium-like states, i.e., the XYZ states. We review the results for observations of the Zc(3900) and Zc(4020) states, the X(3872) in e+e- annihilation, and charmonium psi(1^3D_2) state, as well as measurements of the cross-sections of omega chi_cJ and eta J/psi, and the search for e+e- to gamma chi_cJ and gamma Y(4140). We also present data from BESIII that may further strengthen the study of the XYZ and conventional charmonium states, and discuss p…
In order to test different models proposed for some states discovered recently in the charmonium mass range that do not fit into the pattern predicted by the conventional quark model, we derive predictions for the spectrum within the hadro-charmonium picture, the tetraquark picture as well as the hadronic molecular approach. We exploit heavy quark spin symmetry for the hadro-charmonium and hadronic molecule scenarios. The patterns that emerge from the different models turn out to be quite distinct. For example, only within the hadro-charmonium picture a pseudoscalar state emerges that is light…
The molecular assignments to the three $P_c$ states and the similar production mechanism between the $Λ_b\to P_c+K$ and $B\to XYZ+K$ convince us the $B$ decaying to a charmonium state plus light mesons could be the appropriate production process to search for the charmoniumlike molecular tetraquarks. In this work, we systematically study the interactions between a charmed (charmed-strange) meson and an anti-charmed (anti-charm-strange) meson, which include the $D^{(*)}\bar{D}^{(*)}$, $\bar{D}^{(*)}\bar{D}_1$, $D^{(*)}\bar{D}_2^*$, $D_s^{(*)}\bar{D}_s^{(*)}$, ${D}_s^{(*)}\bar{D}_{s0}^*$, $D_s^{…
Charmonium, the spectroscopy of c\bar{c} mesons, has recently enjoyed a renaissance with the discovery of several missing states and a number of unexpected charmonium-like resonances. The discovery of these new states has been made possible by the extremely large data samples made available by the B-factories at the Stanford Linear Accelerator Center and at KEK in Japan, and at the CESR e^+e^- collider at Cornell. Conventional c\bar{c} states are well described by quark potential models. However, many of these newly discovered charmonium-like mesons do not seem to fit into the conventional c\b…
We propose novel triangle relations, not the well-known triangle singularity, for better understanding of the exotic XYZ states. Nine XYZ resonances, X(3872), Y(4230), Zc(3900), X(4012), Y(4360/4390), Zc(4020), X(4274), Y(4660), and Zcs(3985) have been classified into triples to construct three triangles based on the assumption that they are all tetra-quark states. We also suggest some channels deserving search for with high priority based on this hypothesis, as well as predictions of a few production/decay rates of these channels. We hope further experimental studies of the XYZ states will be…
Within the framework of nonrelativistic quantum chromodynamics, we study the production of $C=+$ charmonium states $H$ in $e^+e^-\to γ~+~H$ at BESIII with $H=η_c(nS)$ (n=1, 2, 3, and 4), $χ_{cJ}(nP)$ (n=1, 2, and 3), and $^1D_2(nD)$ (n=1 and 2). The radiative and relativistic corrections are calculated to next-to-leading order for $S$ and $P$ wave states. We then argue that the search for $C=+$ $XYZ$ states such as $X(3872)$, $X(3940)$, $X(4160)$, and $X(4350)$ in $e^+e^-\to γ~+~H$ at BESIII may help clarify the nature of these states. BESIII can search $XYZ$ states through two body process $e…
Monte Carlo simulations for charmonium(-like) states at the planned PANDA experiment are presented, in particular the search for the $h_c'$, the search for the $^3F_4$ state and the search for the rare decay Y(4260)$\rightarrow$$e^+$$e^-$.
We discuss analytical properties of partial waves derived from projection of a 4-legged amplitude with crossed-channel exchanges in the kinematic region of the direct channel that corresponds to the XYZ peaks in charmonium and bottomonium. We show that in general partial waves can develop anomalous branch points in the vicinity of the direct channel physical region. In a specific case, when these branch points lie on the opposite side of the unitary cut they pinch the integration contour in a dispersion relation and if the pinch happens close to threshold, the normal threshold cusp is enhanced…
Charmonium(-like) or bottomonium(-like) states, which are incompatible with predictions from a static quark anti-quark potential model, are often refered to as XYZ states. In this lecture, some peculiar properties of states such as the X(3872), the Y(4260), or the Zc(3900) are explained. Such properties are utmost proximity to a threshold, overpopulation of states, or possibly binding in the regime of string breaking. Among decays, the surprising observation of isospin violation, and using radiative decays for the observation of a D-wave state is discussed. A second part of the lecture present…
I discuss the nature of the new charm and charmonium like states observed in the last few years and measurements that can test these assignments. In particular it appears that the X(3943) is the eta_c''(3^1S_0) which can be tested by looking for it in gamma gamma to D\bar{D}^*, the Y(3943) is the chi_{c1}'(2^3P_1) which can be tested by looking for it in D\bar{D} and D\bar{D}^*, the Z(3930) is the chi_{c2}'(2^3P_2) which can be confirmed by looking for it in D\bar{D}^*. If the X(3872) is confirmed to have J^{PC}=1^{++} it is almost certainly a multiquark state while if its J^{PC} is found to b…
Through the spin rearrangement scheme in the heavy quark limit, we have performed a comprehensive investigation of the decay pattern and production mechanism of the hidden beauty di-meson states, which are either composed of a P-wave bottom meson and an S-wave bottom meson or two S-wave bottom mesons. We further extend the corresponding formula to discuss the decay behavior of some charmonium-like states by combining the experimental information with our numerical results. The typical ratios presented in this work can be measured by future experiments like BESIII, Belle, LHCb and the forthcomi…
$Z_c(4430)$ discovered by the Belle and confirmed by the LHCb in $\bar{B}^0\toψ(2S)K^-π^+$ is generally considered to be a charged charmonium-like state that includes minimally two quarks and two antiquarks. $Z_c(4200)$ found in $\bar{B}^0\to J/ψK^-π^+$ by the Belle is also a good candidate of a charged charmonium-like state. We demonstrate that kinematical singularities in triangle loop diagrams induce a resonance-like behavior that can consistently explain the properties (mass, width, and Argand plot) of $Z_c(4430)$ and $Z_c(4200)$ from the experimental analyses. The triangle diagrams includ…
We investigate the processes $e^+e^-$$\to$$γJ/ψϕ$, $γJ/ψω$ and $π^0 J/ψη$ to search for the charmnium-like states with hidden $s\bar{s}$, such as $Y(4140)$, $Y(4274)$, $X(4350)$ and $X(3915)$. These processes will receive contributions from the charmed-strange meson rescatterings. When the center-of-mass energies of the $e^+e^-$ scatterings are taken around the $D_{s0}(2317)D_s^{*}$, $D_{s1}(2460)D_s$ or $D_{s1}(2460)D_s^{*}$ threshold, the anomalous triangle singularities can be present in the rescattering amplitudes, which implies a non-resonance explanation about the resonance-like structur…
This paper summarizes what we have done so far to explain charged charmonium/bottomonium-like structures using a hadronic triangle diagram which we call the initial single chiral particle emission mechanism. We discuss processes like $A\to A'+P+P'$ in which two chiral particles $P$ and $P'$ are emitted from $A$. In the intermediate we consider a hadronic one-loop diagram in which $D^{(*)}/D_s^{(*)}/B^{(*)}/B_s^{(*)}$ are included to explain some enhancements experimentally observed. Using this mechanism we explain some of the exotic enhancements and predict a couple of enhancement structures.
A number of charmonium- and bottomonium-like meson states have been observed that have properties that do not match well to expectations for the simple quark-antiquark substructure suggested by the constituent quark model. Some of them are electrically charged and decay to final states containing hidden charmonum or bottomonium mesons and, thus, must contain at least four quarks. Common properties of these so-called XYZ mesons are partial widths for decays to hidden quarkonium states plus light hadrons that are much larger than corresponding partial widths for established quarkonium mesons. I …
The masses of tetraquark states of all $qc\bar q \bar c$ and $cc\bar c \bar c$ quark configurations are evaluated in a constituent quark model, where the Cornell-like potential and one-gluon exchange spin-spin coupling are employed. All model parameters are predetermined by comparing the theoretical and experimental masses of light, charmed and bottom mesons. The theoretical predictions of the charmoniumlike tetraquarks are compared with the observed $XYZ$ states, and one tentative assignment is suggested. The work suggests that the $X(6900)$ observed by LHCb is likely to be the first radial e…
Many charmonium-like and bottomonium-like $XYZ$ resonances have been observed by the Belle, Babar, CLEO and BESIII collaborations in the past decade. They are difficult to fit in the conventional quark model and thus are considered as candidates of exotic hadrons, such as multi-quark states, meson molecules, and hybrids. In this talk, we first briefly introduce the method of QCD sum rules and then provide a short review of the mass spectra of the quarkonium-like tetraquark states and the heavy quarkonium hybrids in the QCD sum rules approach. Possible interpretations of the $XYZ$ resonances ar…
We investigate the process $B_c^+\to B_s^0π^+π^0$ via $B\bar{K}^*$ rescattering. The kinematic conditions for triangle singularities are perfectly satisfied in the rescattering diagrams. A resonance-like structure around the $B\bar{K}$ threshold, which we denote as $X(5777)$, is predicted to be present in the invariant mass distribution of $B_s^0 π^+$. Because the relative weak $B\bar{K}$ $(I=1)$ interaction does not support the existence of a dynamically generated hadronic molecule, the $X(5777)$ can be identified as a pure kinematical effect due to the triangle singularity. Its observation m…
We analyze possible singularities in the $J/ψΛ$ invariant mass distribution of the $Ξ^-_{b}~\to~K^- J/ψΛ$ process via triangle loop diagrams. Triangle singularities in the physical region are found in 18 different triangle loop diagrams. Among those with $Ξ^*$-charmonium-$Λ$ intermediate states, the one from the $χ_{c1} Ξ(2120) Λ$ loop, which is located around 4628 MeV, is found the most likely to cause observable effects. One needs $S$- and $P$-waves in $χ_{c1} Λ$ and $J/ψΛ$ systems, respectively, when the quantum numbers of these systems are $1/2^+$ or $3/2^+$. When the quantum numbers of th…
We review how quark models are able to describe the phenomenology of the charm meson sector. The spectroscopy and decays of charmonium and open charm mesons are described in a particular quark model and compared with the data and the results of other existing models in the literature. A quite reasonable global description of the heavy meson spectra is reached. A new assignment of the $ψ(4415)$ resonance as a 3D state leaving aside the 4S state to the X(4360) is tested through the analysis of the resonance structure in $e^{+}e^{-}$ exclusive reactions around the $ψ(4415)$ energy region. We make…
There have been numerous developments in hadron spectroscopy over the past year. In this brief review I focus on two general areas. In the first I give an update on hadrons with b-quarks. Their properties are in textbook agreement with QCD motivated constituent quark models. The second topic is the Charmonium-like $XYZ$ states above open charm threshold that continue to be discovered. Many of these do not seem to be described as conventional c\bar{c} states and may be hadronic molecules, Tetraquarks, or Charmonium Hybrids. The first topic is an example of how well we seem to understand hadrons…
The past decade witnessed a remarkable proliferation of exotic charmonium-like resonances discovered at accelerators. In particular, the recently observed charged states are clearly not interpretable as q-qbar mesons. Notwithstanding the considerable advances on the experimental side, conflicting theoretical descriptions do not seem to provide a definitive picture about the nature of the so-called XYZ particles. We present here a comprehensive review about this intriguing topic, discussing both those experimental and theoretical aspects which we consider relevant to make further progress in th…
$Z_c(4430)$ discovered in $\bar{B}^0\toψ(2S)K^-π^+$, $Z_c(4200)$ found in $\bar{B}^0\to J/ψK^-π^+$, and $Z_1(4050)$ and $Z_2(4250)$ observed in $\bar{B}^0\toχ_{c1}K^-π^+$ are candidates of charged charmonium-like states. All surviving theoretical models interpreted these candidates as four-quark states, until we recently identified a compelling alternative. We discuss that kinematical singularities in triangle loop diagrams induce a resonance-like behavior that can consistently explain the properties (such as spin-parity, mass, width, and Argand plot) of $Z_c(4430)$, $Z_c(4200)$, $Z_1(4050)$ a…
$Z_1(4050)$ and $Z_2(4250)$ observed in $\bar{B}^0\toχ_{c1}K^-π^+$ by the Belle Collaboration are candidates of charged charmonium-like states that minimally includes two quarks and two antiquarks. While $Z_1(4050)$ and $Z_2(4250)$ have been interpreted as tetraquark states previously, we propose a completely different scenario based on a kinematical effect called the triangle singularity. We demonstrate that the triangle singularities cause in the $χ_{c1}π^+$ invariant mass distribution resonance-like bumps that fit very well the Belle data. If these bumps are simulated by the $Z_1(4050)$ and…
By investigating the very closely lied $D_{s1}\bar{D}_{s}+c.c.$ and $D_{s0}\bar{D}^*_{s}+c.c.$ thresholds at about 4.43 GeV we propose that the $ψ(4415)$ and $ψ(4160)$ can be mixing states between the dynamic generated states of the strong $S$-wave $D_{s1}\bar{D}_{s}+c.c.$ and $D_{s0}\bar{D}^*_{s}+c.c.$ interactions and the quark model states $ψ(4S)$ and $ψ(2D)$. We investigate the $J/ψK\bar{K}$ final states and invariant mass spectrum of $J/ψK$ to demonstrate that nontrivial lineshapes can arise from such a mechanism. This process, which goes through triangle loop transitions, is located in t…
We have analyzed the singularities of a triangle loop integral in detail and derived a formula for an easy evaluation of the triangle singularity on the physical boundary. It is applied to the $Λ_b \rightarrow J/ψK^{-} p$ process via $Λ^*$-charmonium-proton intermediate states. Although the evaluation of absolute rates is not possible, we identify the $χ_{c1}$ and the $ψ(2S)$ as the relatively most relevant states among all possible charmonia up to the $ψ(2S)$. The $Λ(1890)\, χ_{c1}\, p$ loop is very special as its normal threshold and triangle singularities merge at about 4.45 GeV, generating…
Bottomonium-like resonances Zb(10610) and Zb'(10650) are good candidates of hadronic molecules composed of BBbar* (or B*Bbar) and B*Bbar*, respectively. Considering Zb (Zb') as heavy meson molecules, we investigate the decays of Zb(')^+ -> Upsilon (nS) pi^+$ in terms of the heavy meson effective theory. We find that the intermediate B (B*) and Bbar (Bbar*) meson loops and the form factors play a significant role to reproduce the experimental values of the decay widths. We also predict the decay widths of Zc^+ -> J/ψpi^+ and psi(2S) pi^+ for a charmonium-like resonance Zc which has been reporte…
Cross section of the process $e^+ + e^- \to Ξ^0 + \barΞ^0$ in the vicinity of charmonium $ψ(3770)$ and in the charmonium (-like) state including the $D$-meson loop and three-gluon contributions
Institute of Physics, Ministry of Science and Education（阿塞拜疆教育与科学部物理研究所）；Bogoliubov Laboratory of Theoretical Physics, JINR（俄罗斯杜布纳联合核子研究所鲍戈留博夫理论物理实验室）
Triangle and other kinematic singularities are very sensitive to the precise masses and widths of the intervening particles. Therefore, the effect that the heavy-ion collision medium can have on those masses and widths, as captured by finite-temperature field theory and reported in the literature, may erase the singularity from the spectrum if the effect is large enough and the loop completes before the hot gas freezes out. A very timely example is provided by the $Z_{cs}(3985)$ structure recently reported by BES-III in a $(D_s^-D^{*0}+D_s^{*-}D^0)$ spectrum recoiling against a $K^+$. If a new…
