Charmonium-like States Research Articles

Deciphering the charged heavy quarkoniumlike states in chiral effective field theory

We generalize the framework of chiral effective field theory to study the interactions of the isovector $D^\ast\bar{D}^{(\ast)}$ and $B^\ast\bar{B}^{(\ast)}$ systems up to the next-to-leading order, in which the long-, mid-, and short-range force contributions as well as the $S$-$D$ wave mixing are incorporated. Based on the Lippmann-Schwinger equation, we fit the invariant mass distributions of the elastic channels measured by the BESIII and Belle Collaborations. Our results indicate that the four charged charmoniumlike and bottomoniumlike states $Z_c(3900)$, $Z_c(4020)$ and $Z_b(10610)$, $Z_b(10650)$ can be well identified as the $D\bar{D}^{\ast},D^\ast\bar{D}^{\ast}$ and $B\bar{B}^{\ast},B^\ast\bar{B}^{\ast}$ molecular resonances. The bound state explanations are vetoed in our framework. Our study favors the $Z_c$ and $Z_b$ states are the twin partners under the heavy quark symmetry.

Looking for a vector charmoniumlike state Y in e+e−→D¯D1(2420)+c.c.

Inspired by the first observation of a vector charmonium-like state $Y(4626)$ decaying to a meson pair $D_{s}^{+}D_{s1}(2536)^{-}$, which could be viewed as a $P$-wave scalar-scalar $[cs][\bar{c}\bar{s}]$ tetraquark state, we predict a potential vector charmonium-like state $Y$ with $P$-wave scalar-scalar $[cq][\bar{c}\bar{q}]$ configuration. The corresponding mass spectrum of $Y$ state is calculated to be $4.33^{+0.16}_{-0.23}~\mbox{GeV}$ in the framework of QCD sum rules. We suggest that the predicted $Y$ state could be looked for in an open-charm $e^{+}e^{-}\rightarrow\bar{D}D_{1}(2420)+c.c.$ process.

Study on the possible molecular state composed of within the Bethe-Salpeter framework * * Supported by the National Natural Science Foundation of China (11375128, 11675082, 11735010, 11975165)

Recently, a vector charmonium-like state was observed in the portal of . This intrigues an active discussion on the structure of the resonance because it has obvious significance for gaining a better understanding on its hadronic structure that contains suitable inner constituents. Therefore, this observation concerns the general theoretical framework about possible structures of exotic states. Since the mass of is slightly above the production threshold of whereas it is below that of with the same quark contents as that of , it is natural to conjecture that is a molecular state of , as suggested in the literature. Confirming or negating this allegation would shed light on the goal we are concerned with. We calculate the mass spectrum of a system composed of a vector meson and an axial vector i.e., within the framework of the Bethe-Salpeter equations. Our numerical results show that the dimensionless parameter in the form factor, which is phenomenologically introduced to every vertex, is far beyond the reasonable range for inducing even a very small binding energy . It implies that the system cannot exist in the nature as a hadronic molecule in this model. Therefore, we may not be able to assume the resonance to be a bound state of and instead, it could be attributed to something else, such as a tetraquark.

Study of the process e+e−→π0π0J/ψ and neutral charmoniumlike state Zc(3900)0

Cross sections of the process $e^+e^-\to\pi^0\pi^0 J/\psi$ at center-of-mass energies between 3.808 and 4.600 GeV are measured with high precision by using 12.4 $fb^{-1}$ of data samples collected with the BESIII detector operating at the BEPCII collider facility. A fit to the measured energy-dependent cross sections confirms the existence of the charmonium-like state $Y(4220)$. The mass and width of the $Y(4220)$ are determined to be $(4220.4\pm2.4\pm2.3)$ ${\rm MeV}/c^{2}$ and $(46.2\pm4.7\pm2.1)$ MeV, respectively, where the first uncertainties are statistical and the second systematic. The mass and width are consistent with those measured in the process $e^+e^-\to\pi^+\pi^- J/\psi$. The neutral charmonium-like state $Z_c(3900)^0$ is observed prominently in the $\pi^0 J/\psi$ invariant-mass spectrum, and, for the first time, an amplitude analysis is performed to study its properties. The spin-parity of $Z_c(3900)^0$ is determined to be $J^{P}=1^{+}$, and the pole position is $(3893.1\pm2.2\pm3.0)-i(22.2\pm2.6\pm7.0)$ ${\rm MeV}/c^2$, which is consistent with previous studies of electrically charged $Z_c(3900)^\pm$. In addition, cross sections of $e^+e^-\to\pi^0 Z_c(3900)^0\to \pi^0\pi^0 J/\psi$ are extracted, and the corresponding lineshape is found to agree with that of the $Y(4220)$.

Exotic hadrons at BESIII

The BESIII experiment at the electron positron collider BEPCII is successfully operating since 2008 and has collected large data samples in the taucharm mass region. Selected recent results on XYZ studies at BESIII are reported. Thanks to the data samples of about 12 fb −1, useful for this kind of studies, BESIII Collaboration continues the exploration of these intriguing charmonium-like states.

Spectroscopy of hidden-charm tetraquarks in diquark model

A nonrelativistic model is used to study hidden-charm tetraquarks within a diquark–antidiquark configuration. Using the perturbation theory, we estimate the masses of the heavy tetraquarks with hidden charm. Our present analysis suggests the charmonium-like states: X(3860), X(3872), $$Z_c(3943)$$ , X(4140), $$Z_c(4430)$$ and X(4700) can be accommodated in tetraquark picture. We particularly find that the $$ Z_c(4430) $$ may be treated as the first radial excitation of X(3872).

Properties of Zc(3900) tetraquark in a cold nuclear matter

The study of medium effects on properties of particles embedded in nuclear matter is of great importance for understanding the nature and internal quark-gluon organization as well as exact determination of the quantum numbers, especially of the exotic states. In this context, we study the physical properties of one of the famous charmonium-like states, $Z_c(3900)$, in a cold dense matter. We investigate the possible shifts in the mass and current-meson coupling of the $Z_c(3900)$ state due to the dense medium at saturation density, $ \rho^{sat} $, by means of the in-medium sum rules. We also estimate the vector self-energy of this state at saturation nuclear matter density. We discuss the behavior of the spectroscopic parameters of this state with respect to the density up to a high density corresponding to the core of neutron stars, $\rho\approx 5\rho^{sat}$. Both the mass and current-coupling of this state show nonlinear behavior and decrease with respect to the density of the medium: the mass reaches roughly $30\%$ of its vacuum value at $ \rho=5\rho^{sat} $, while the current-coupling approaches zero at $ \rho\approx2.1\rho^{sat} $, when the central values of the auxiliary and other input parameters are used.

Future Physics Programme of BESIII * * Supported in part by National Key Basic Research Program of China (2015CB856700); National Natural Science Foundation of China (NSFC) (11335008, 11425524, 11625523, 11635010, 11735014, 11822506, 11935018); the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP); Joint Large-Scale Scientific Facility Funds of the NSFC

There has recently been a dramatic renewal of interest in hadron spectroscopy and charm physics. This renaissance has been driven in part by the discovery of a plethora of charmonium-like XYZ states at BESIII and B factories, and the observation of an intriguing proton-antiproton threshold enhancement and the possibly related X(1835) meson state at BESIII, as well as the threshold measurements of charm mesons and charm baryons. We present a detailed survey of the important topics in tau-charm physics and hadron physics that can be further explored at BESIII during the remaining operation period of BEPCII. This survey will help in the optimization of the data-taking plan over the coming years, and provides physics motivation for the possible upgrade of BEPCII to higher luminosity.

Possibility of charmoniumlike state X(3915) as χc0(2P) state

In this work, we seriously discuss whether $X(3915)$ can be treated as a $\chi_{c0}(2P)$ state. Based on an unquenched quark model, we give the mass spectrum of the $\chi_{cJ}(2P)$ states, where there are no free input parameters in our calculation. Our result shows that the mass gap between $\chi_{c0}(2P)$ and $\chi_{c2}(2P)$ can reach 13 MeV, which can reproduce the mass difference between $Z(3930)$ and $X(3915)$. Additionally, the calculated masses of $\chi_{c0}(2P)$ and $\chi_{c2}(2P)$ are consistent with experimental values of $X(3915)$ and $Z(3930)$, respectively. Besides, giving the mass spectrum analysis to support $X(3915)$ as $\chi_{c0}(2P)$, we also calculate the width of $\chi_{c0}(2P)$ with the same framework, which is also consistent with the experimental data of $X(3915)$. Thus, the possibility of charmoniumlike state $X(3915)$ as $\chi_{c0}(2P)$ state is further enforced.

The New Results from Multi-quark Exotic States Searches at D0 Experiment

Recent results from a search for multi-quark exotic states at D0 experiment (FNAL, USA) are presented. This includes the new data for possible tetraquark state X(5568) decaying to , in the channels with semileptonic decays of mesons. Also, result from the J/ψπ system analysis and an evidence for exotic charged charmoniumlike state Zc(3900) in semiinclusive weak decays of B-flavored hadrons are presented as well.

Charmonium resonances with JPC=1−− and 3−− from D¯D scattering on the lattice

We present a lattice QCD study of charmonium resonances and bound states with $J^{PC}=1^{--}$ and $3^{--}$ near the open-charm threshold, taking into account their strong transitions to $\bar DD$. Vector charmonia are the most abundant in the experimentally established charmonium spectrum, while recently LHCb reported also the first discovery of a charmonium with likely spin three. The $\bar DD$ scattering amplitudes for partial waves $l=1$ and $l=3$ are extracted on the lattice by means of the L\"uscher formalism, using multiple volumes and inertial frames. Parameterizations of the scattering amplitudes provide masses and widths of the resonances, as well as the masses of bound states. CLS ensembles with 2+1 dynamical flavors of non-perturbatively $O(a)$ improved Wilson quarks are employed with $m_\pi\simeq 280$ MeV, a single lattice spacing of $a\simeq0.086$ fm and two lattice spatial extents of $L=24$ and $32$. Two values of the charm quark mass are considered to examine the influence of the position of the $\bar{D}D$ threshold on the hadron masses. For the lighter charm quark mass we find the vector resonance $\psi(3770)$ with mass $m=3780(7)$ MeV and coupling $g=16.0(^{+2.1}_{-0.2})$ (related to the width), both consistent with their experimental values. The vector $\psi(2S)$ appears as a bound state with $m=3666(10)$ MeV. The charmonium resonance with $J^{PC}=3^{--}$ is found at $m=3831(^{+10}_{-16})$ MeV, consistent with the $X(3842)$ recently discovered by LHCb. At our heavier charm-quark mass the $\psi(2S)$ as well as the $\psi(3770)$ are bound states and the $X(3842)$ remains a resonance. We stress that all quoted uncertainties are only statistical, while lattice spacing effects and the approach to the physical point still need to be explored. This study of conventional charmonia sets the stage for more challenging future studies of unconventional charmonium-like states.

D -wave charmonia

Inspired by the recent observations of the vector charmonium-like states at BES III Collaboration and $\psi(3842)$ at LHCb Collaboration, we comb the $D$ wave charmonium state in the present work. We first evaluate the possibility of $Y(4320)$ as $\psi(3^3D_1)$ by investigating its open charm decays in quark-pair creation model and we find the width of $Y(4320)$ can be reproduced in a reasonable parameter range. Moreover, we take $\psi(3770)$, $\psi(4160)$ and $Y(4320)$ as the scale of $1D$, $2D$ and $3D$ charmonia to estimate the open charm decays of other $D$ wave charmonia. The total and partial widths of $D$ wave charmonium states have been predicted, which could be tested by further measurements at LHCb and Belle II Collaborations.

Zc(4430) and Zc(4200) as triangle singularities

$Z_c(4430)$ discovered by the Belle and confirmed by the LHCb in $\bar{B}^0\to\psi(2S)K^-\pi^+$ is generally considered to be a charged charmonium-like state that includes minimally two quarks and two antiquarks. $Z_c(4200)$ found in $\bar{B}^0\to J/\psi K^-\pi^+$ 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 include only experimentally well-established hadrons. Applying this idea to $\Lambda_b^0\to J/\psi p\pi^-$, we also identify triangle singularities that behave like $Z_c(4200)$, but no triangle diagram is available for $Z_c(4430)$. This is consistent with the LHCb's finding that their description of the $\Lambda_b^0\to J/\psi p\pi^-$ data is significantly improved by including a $Z_c(4200)$ contribution while $Z_c(4430)$ seems to hardly contribute. Even though the proposed mechanisms have uncertainty in the absolute strengths which are currently difficult to estimate, they are certainly a compelling alternative to tetraquark-based interpretations of $Z_c(4430)$ and $Z_c(4200)$.

Properties of Zc±(3900) produced in pp¯ collisions

We study the production of the exotic charged charmonium-like state $Z_c^{\pm}(3900)$ in $p \bar p$ collisions through the sequential process $\psi(4260) \rightarrow Z_c^{\pm}(3900) \pi^{\mp}$, $Z_c^{\pm}(3900) \rightarrow J/\psi \pi^{\pm}$. Using the subsample of candidates originating from semi-inclusive weak decays of $b$-flavored hadrons, we measure the invariant mass and natural width to be $M=3902.6^{+5.2}_{-5.0}{\rm \thinspace (stat)}^{+3.3}_{-1.4}{\rm \thinspace (syst)}$ MeV and $\Gamma=32 ^{+28}_{-21}{\rm \thinspace (stat)} ^{+26}_{-7}{\rm \thinspace (syst)}$ MeV, respectively. We search for prompt production of the $Z_c^{\pm}(3900)$ through the same sequential process. No significant signal is observed, and we set an upper limit of 0.66 at the 95\% credibility level on the ratio of prompt production to the production via $b$-hadron decays. The study is based on $10.4~\rm{fb^{-1}}$ of $p \overline p $ collision data collected by the D0 experiment at the Fermilab Tevatron collider.

Triangle singularities in B¯0→χc1K−π+ relevant to Z1(4050) and Z2(4250)

$Z_1(4050)$ and $Z_2(4250)$ observed in $\bar{B}^0\to\chi_{c1}K^-\pi^+$ 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 $\chi_{c1}\pi^+$ invariant mass distribution resonance-like bumps that fit very well the Belle data. If these bumps are simulated by the $Z_1(4050)$ and $Z_2(4250)$ resonance excitations, the spin-parity of them are predicted to be $1^-$ for $Z_1(4050)$ and $1^+$ or $1^-$ for $Z_2(4250)$. The bump corresponding to $Z_1(4050)$ has a highly asymmetric shape, which the Belle data exactly indicate. We show that the asymmetric shape originates from an interplay between the triangle singularity and the opening of the $X(3872)\pi^+$ channel near the triangle-singularity energy. This characteristic lineshape could be used to discriminate different interpretations of $Z_1(4050)$. An interesting prediction from interpretting $Z_1(4050)$ and $Z_2(4250)$ as the triangle singularities is that similar bumps caused by the same mechanisms possibly appear also in $\bar{B}^0\to J/\psi K^-\pi^+$ data; the already observed $Z_c(4200)$ corresponds to $Z_2(4250)$ of $J^P=1^+$.

Constructing J/ψ family with updated data of charmoniumlike Y states

Based on the updated data of charmoniumlike state $Y(4220)$ reported in the hidden-charm %and open-charm channels of the $e^+e^-$ annihilation, we propose a $4S$-$3D$ mixing scheme to categorize $Y(4220)$ into the $J/\psi$ family. We find that the present experimental data can support this charmonium assignment to $Y(4220)$. Thus, $Y(4220)$ plays a role of a scaling point in constructing higher charmonia above 4 GeV. To further test this scenario, we provide more abundant information on the decay properties of $Y(4220)$, and predict its charmonium partner $\psi(4380)$, whose evidence is found by analyzing the $e^+e^-\to \psi(3686)\pi^+\pi^-$ data from BESIII. If $Y(4220)$ is indeed a charmonium, we must face how to settle the established charmonium $\psi(4415)$ in the $J/\psi$ family. In this work, we may introduce a $5S$-$4D$ mixing scheme, and obtain the information of the resonance parameters and partial open-charm decay widths of $\psi(4415)$, which do not contradict the present experimental data. Additionally, we predict a charmonium partner $\psi(4500)$ of $\psi(4415)$, which can be accessible at future experiments, especially, BESIII and BelleII. The studies presented in this work provide new insights to establish the higher charmonium spectrum.

X(3872) in the molecular model

We discuss methods and approaches for describing molecular states in the spectrum of heavy quarks and investigate various properties of the exotic charmonium-like state X(3872) in detail in the framework of the mesonic molecule model.

The dynamical diquark model: first numerical results

We produce the first numerical predictions of the dynamical diquark model of multiquark exotic hadrons. Using Born-Oppenheimer potentials calculated numerically on the lattice, we solve coupled and uncoupled systems of Schrödinger equations to obtain mass eigenvalues for multiplets of states that are, at this stage, degenerate in spin and isospin. Assuming reasonable values for these fine-structure splittings, we obtain a series of bands of exotic states with a common parity eigenvalue that agree well with the experimentally observed charmoniumlike states, and we predict a number of other unobserved states. In particular, the most suitable fit to known pentaquark states predicts states below the charmonium-plus-nucleon threshold. Finally, we examine the strictest form of Born-Oppenheimer decay selection rules for exotics and, finding them to fail badly, we propose a resolution by relaxing the constraint that exotics must occur as heavy-quark spin-symmetry eigenstates.

Settling the Zc(4600) in the charged charmoniumlike family

Very recently LHCb reported the evidence of a new charged charmonium-like structure in the $J/\psi \pi^-$ invariant mass spectrum near 4600 MeV. In this work we investigate this structure together with three other charged charmonium-like states, the $Z_c(3900)$, $Z_c(4020)$, and $Z_c(4430)$. Our results suggest that the two higher states can be established as the first radial excitations of the two lower ones, all of which have the quantum numbers $J^{PC}=1^{+-}$. We propose to search for more relationship among exotic hadrons in order to better understand them.

Precision measurements of the e+e−→KS0K±π∓ Born cross sections at center-of-mass energies between 3.8 and 4.6 GeV

Using data samples collected by the BESIII detector operating at the BEPCII storage ring, we measure the $e^+e^- \to K_{S}^{0}K^{\pm}\pi^{\mp}$ Born cross sections at center-of-mass energies between 3.8 and 4.6\,GeV, corresponding to a luminosity of about 5.0~fb$^{-1}$. The results are compatible with the BABAR measurements, but with the precision significantly improved. A simple $1/s^n$ dependence for the continuum process can describe the measured cross sections, but a better fit is obtained by an additional resonance near 4.2\,GeV, which could be an excited charmonium or a charmonium-like state.