Charged Charmonium-like State Research Articles

Experimental Road to a Charming Family of Tetraquarks...and Beyond

Abstract Discovery of the X(3872) meson in 2003 ignited intense interest in exotic (neither $q\bar{q}$ nor $qqq$) hadrons, but a $c\bar{c}$ interpretation of this state was difficult to exclude. An unequivocal exotic was discovered in the $Z_c(3900)^+$ meson—a charged charmonium-like state. A variety of models of exotic structure have been advanced but consensus is elusive. The grand lesson from heavy quarkonia was that heavy quarks bring clarity. Thus, the recently reported triplet of all-charm tetraquark candidates—$X(6600)$, $X(6900)$, and $X(7100)$—decaying to $J/\psi\,J/\psi$ is a great boon, promising important insights. We review some history of exotics, chronicle the road to prospective all-charm tetraquarks, discuss in some detail the divergent modeling of $J/\psi\,J/\psi$ structures, and offer some inferences about them. These states form a Regge trajectory and appear to be a family of radial excitations. A reported, but unexplained, threshold excess could hint at a fourth family member. We close with a brief look at a step beyond: all-bottom tetraquarks.

Correlation of the hidden-charm molecular tetraquarks and the charmoniumlike structures existing in the B→XYZ+K process

The molecular assignments to the three ${P}_{c}$ states and the similar production mechanism between the ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{P}_{c}+K$ and $B\ensuremath{\rightarrow}XYZ+K$ 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 anticharmed (anticharm-strange) meson, which include the ${D}^{(*)}{\overline{D}}^{(*)}$, ${\overline{D}}^{(*)}{\overline{D}}_{1}$, ${D}^{(*)}{\overline{D}}_{2}^{*}$, ${D}_{s}^{(*)}{\overline{D}}_{s}^{(*)}$, ${D}_{s}^{(*)}{\overline{D}}_{s0}^{*}$, ${D}_{s}^{(*)}{\overline{D}}_{s1}^{\ensuremath{'}}$, ${D}_{s}^{(*)}{\overline{D}}_{s1}$, ${D}_{s}^{(*)}{\overline{D}}_{s2}^{*}$ systems. After adopting the one-boson-exchange effective potentials, our numerical results indicate that, on one hand, there can exist a serial of isoscalar charmoniumlike $\mathcal{D}\overline{\mathcal{D}}$ and ${\mathcal{D}}_{s}{\overline{\mathcal{D}}}_{s}$ molecular states, on the other hand, we can fully exclude the charged charmoniumlike states as the isovector charmoniumlike molecules. Meanwhile, we discuss the two-body hidden-charm decay channels for the obtained $\mathcal{D}\overline{\mathcal{D}}$ and ${\mathcal{D}}_{s}{\overline{\mathcal{D}}}_{s}$ molecules, especially the ${D}^{*}{\overline{D}}^{*}$ molecular tetraquarks. By analyzing the experimental data collected from the $B\ensuremath{\rightarrow}XYZ+K$ and the mass spectrum and two-body hidden-charm decay channels for the obtained $\mathcal{D}\overline{\mathcal{D}}$ and ${\mathcal{D}}_{s}{\overline{\mathcal{D}}}_{s}$ molecules, we find several possible hints of the existence of the charmoniumlike molecular tetraquarks, i.e., a peculiar characteristic mass spectrum of the isoscalar ${D}^{*}{\overline{D}}^{*}$ molecular systems can be applied to identify the charmoniumlike molecule. We look forward to the future experiments like the LHCb, Belle II, and BESIII Collaborations can test our results with more precise experimental data.

Search for the reaction e+e−→χcJπ+π− and a charmoniumlike structure decaying to χcJπ± between 4.18 and 4.60 GeV

We search for the process $e^{+}e^{-}\rightarrow \pi ^{+}\pi ^{-} \chi_{cJ}$ ($J=0,1,2$) and for a charged charmonium-like state in the $\pi ^{\pm} \chi_{cJ}$ subsystem. The search uses data sets collected with the BESIII detector at the BEPCII storage ring at center-of-mass energies between 4.18 GeV and 4.60 GeV. No significant $\pi ^{+}\pi ^{-} \chi_{cJ}$ signals are observed at any center-of-mass energy, and thus upper limits are provided which also serve as limits for a possible charmonium-like structure in the invariant $\pi ^{\pm} \chi_{cJ}$ mass.

Decoding the nature of Zcs(3985) and establishing the spectrum of charged heavy quarkoniumlike states in chiral effective field theory

We study the newly observed charmoniumlike state $Z_{cs}(3985)$ in the framework of chiral effective field theory. The interaction kernel of the $\bar{D}_sD^\ast/\bar{D}^\ast_sD$ system is calculated up to the next-to-leading order with the explicit chiral dynamics. With the fitted parameters extracted from the $Z_c(3900)$ data as inputs, the mass, width and event distributions of the $Z_{cs}(3985)$ are very consistent with the experimental measurements. Our studies strongly support the $Z_{cs}(3985)$ as the partner of the $Z_c(3900)$ in the SU(3)$_f$ symmetry and the $\bar{D}_sD^\ast/\bar{D}^\ast_sD$ molecular resonance with the same dynamical origin as the other charged heavy quarkoniumlike states. We precisely predict the resonance parameters of the unobserved states in $\bar{D}_s^\ast D^\ast$, $B^\ast_s \bar{B}/B_s\bar{B}^\ast$ and $B_s^\ast\bar{B}^\ast$ systems, and establish a complete spectrum of the charged charmoniumlike and bottomoniumlike states with the $I(J^P)$ quantum numbers $1(1^+)$ and $\frac{1}{2}(1^+)$, respectively.

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.

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.

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 $J^P=1^+$.

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.

Evidence for Zc±(3900) in semi-inclusive decays of b -flavored hadrons

We present evidence for the exotic charged charmonium-like state $Z_c^{\pm}(3900)$ in semi-inclusive weak decays of $b$-flavored hadrons. The signal is correlated with a $J/\psi \pi^+ \pi^-$ system in the invariant mass range 4.2$-$4.7~GeV and includes the sequential process $b$-quark hadron $ \rightarrow Y(4260) +$ anything, $Y(4260) \rightarrow Z_c^{\pm}(3900) \pi^{\mp}$, $Z_c^{\pm}(3900) \rightarrow J/\psi \pi^{\pm}$. 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.

Search for ϒ(1S,2S)→Zc+Zc(′)− and e+e−→Zc+Zc(′)− at s=10.52 , 10.58, and 10.867 GeV

The first search for double charged charmoniumlike state production in ϒ(1S) and ϒ(2S) decays and in e+e− annihilation at s=10.52, 10.58, and 10.867 GeV is conducted using data collected with the Belle detector at the KEKB asymmetric energy electron-positron collider. No significant signals are observed in any of the studied modes, and the 90% credibility level upper limits on their product branching fractions in ϒ(1S) and ϒ(2S) decays [B(ϒ(1S,2S)→Zc+Zc(′)−)×B(Zc+→π++cc¯) (cc¯=J/ψ, χc1(1P), ψ(2S))] and the product of Born cross section and branching fraction for e+e−→Zc+Zc(′)− (σ(e+e−→Zc+Zc(′)−)×B(Zc+→π++cc¯)) at s=10.52, 10.58, and 10.867 GeV are determined. Here, Zc refers to the Zc(3900) and Zc(4200) observed in the πJ/ψ final state, the Zc1(4050) and Zc2(4250) in the πχc1(1P) final state, and the Zc(4050) and Zc(4430) in the πψ(2S) final state.3 MoreReceived 6 May 2018DOI:https://doi.org/10.1103/PhysRevD.97.112004Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsExotic mesonsQuarkoniaParticles & Fields

Interpretation of Y(4390) as an isoscalar partner of Z(4430) from {D^{*}}(2010){bar{D}}_1(2420) interaction

Invoked by the recent observation of Y(4390) at BESIII, which is about 40 MeV below the {D^{*}}(2010){bar{D}}_1(2420) threshold, we investigate possible bound and resonance states from the {D^{*}}(2010){bar{D}}_1(2420) interaction with the one-boson-exchange model in a quasipotential Bethe–Salpeter equation approach. A bound state with quantum number 0^-(1^{-,-}) is produced at 4384 MeV from the {D^{*}}(2010){bar{D}}_1(2420) interaction, which can be related to experimentally observed Y(4390). Another state with quantum number 1^+(1^{+}) is also produced at 4461+i39 MeV from this interaction. Different from the 0^-(1^{-,-}) state, the 1^+(1^{+}) state is a resonance state above the {D^{*}}(2010){bar{D}}_1(2420) threshold. This resonance state can be related to the first observed charged charmonium-like state Z(4430), which has a mass about 4475 MeV measured above the threshold as observed at Belle and LHCb. Our result suggests that Y(4390) is an isoscalar partner of the Z(4430) as a hadronic-molecular state from the {D^{*}}(2010){bar{D}}_1(2420) interaction.

And interactions and the charged charmonium-like state Z(4430)**Supported by Major State Basic Research Development Program in China (2014CB845405), National Natural Science Foundation of China (11275235)

The and interactions are studied in a one-boson-exchange model. Isovector bound state solutions with spin parity JP = 1+ are found from the interaction, which may be related to the observed charged charmonium-like state Z(4430). There is no bound state solution found from the interaction.

Quarkonium (-like) states at BELLE

We report the recent results on quarkonium (-like) states by the Belle experiment. A new charged charmonium-like state Zc(4200)+ decaying to J/ψπ+ is observed with a significance of 6.2σ. The mass and width of the Zc(4200)+ are 4196−29−13+31+17 MeV/c2 and 370−70−132+70+70 MeV, respectively; the preferred assignment of the quantum numbers is JP=1+. We also report the first observation of the e+e−→ω[π+π−π0]χbJ(J=1,2) processes at a center-of-mass energy of 10.867 GeV. In the π+π−π0 invariant mass spectrum, significant non-ω signals are also observed.

Z +(4430): Nonexotic interpretation

The possibility of describing the charged charmonium-like state Z+(4430) as the kinematical rescattering effect is examined. This approach makes it possible to avoid the introduction of exotic hadron states in the model, and one describes structures in the ψ(2S)π+ mass spectrum by the presence of the Ds(*)′ resonance in a hidden intermediate state. The resulting model predictions are compared with the results obtained by the LHCb Collaboration.

Charged charmonium-like states in the Belle experiment

The most recent results obtained for charged charmonium-like states in the Belle experiment are presented.

Charged charmoniumlike states at Belle

Results on charged charmoniumlike states observed in B-meson decays at Belle are reviewed. The review also includes the results on these states from other experiments (BABAR and LHCb).

The charged Zc states from rescattering in conventional B decays

In this paper we discuss a possible interpretation of the charged charmonium-like states observed in B decays as a rescattering effect. This approach allows to avoid introduction of exotic hadrons into the theory, while explains the unusual peaking structures 4observed recently in three body B decays. In particular, the peaks in the ψ(2S)π+ mass spectrum are ascribed to the rescattering process with kinematics governed by the presence of conventional radial excitations, the Ds(*)’ resonances, in the hidden intermediate state. Our predictions are compared to the LHCb results.

Systematic study ofZc+family from a multiquark color flux-tube model

Inspired by the present experimental status of charged charmonium-like states $Z_c^+$, the tetraquark states $[cu][\bar{c}\bar{d}]$ are systematically studied in a color flux-tube model with a multi-body confinement potential. The investigation indicates that charged charmonium-like states $Z_c^+(3900)$ or $Z_c^+(3885)$, $Z_c^+(3930)$, $Z_c^+(4020)$ or $Z_c^+(4025)$, $Z_1^+(4050)$, $Z_2^+(4250)$, and $Z_c^+(4200)$ can be uniformly described as tetraquark states $[cu][\bar{c}\bar{d}]$ with the quantum numbers $n^{2S+1}L_J$ and $J^P$ of $1^{3}S_1$ and $1^+$, $2^{3}S_1$ and $1^+$, $1^5S_2$ and $2^+$, $1^3P_1$ and $1^-$, $1^5D_1$ and $1^+$, and $1^3D_1$ and $1^+$, respectively. The predicted lowest charged tetraquark state $[cu][\bar{c}\bar{d}]$ with $0^+$ and $1^1S_0$ has a energy of $3780\pm10$ MeV in the model. The tetraquark states are compact three-dimensional spatial configurations similar to a rugby ball, the higher orbital angular momentum $L$ between the diquark $[cu]$ and antidiquark $[\bar{c}\bar{d}]$, the more prolate of the states. The multibody color flux-tube, a collective degree of freedom, plays an important role in the formation of those charge tetraquark states. However, the two heavier charged states $Z^+_c(4430)$ and $Z^+_c(4475)$ can not be explained as tetraquark states $[cu][\bar{c}\bar{d}]$ in this model approach.