Search

We derive helicity amplitudes for the fully charmed tetraquark states decays into vector meson pair under two types of models, where the one is from quark model and the other one is from heavy quark effective theory. The angular distributions have been given by the cascade decays $T_{4c}\to J/\psi(D_{(s)}^*)+J/\psi(\bar{D}_{(s)}^*)$ along with $J/\psi\to \mu^++\mu^-$ or $D_{(s)}^*\to D_{(s)}+\pi$, showing that spin-0 and spin-2 states can be distinguished. If we assume quantum entanglement as a fundamental principle, there is a strict constraint formula for helicity amplitudes. These findings will assist in experimentally differentiating various spin-parity states, determining decay widths and hunting for unobserved structures, thereby shedding light on the internal properties of double $J/\psi$ exotic states., Comment: 15 pages, 10 figures, and 3 tables. Comments and suggestions are welcome

We explore various $\Lambda_c$ states, including $\Lambda_c$, $\Lambda_c(2595)$, $\Lambda_c(2940)$, and the predicted $(\bar{D}N)$ hadronic molecular states, in photoproduction and electroproduction to estimate their yields at EicC and EIC. Assuming $\Lambda_c(2940)$ as either a hadronic molecular state or a three-quark state, our analysis demonstrates that its production rates are of the same order of magnitude, posing challenges in identifying its underlying structure. After considering the integral luminosity, the yields of $\Lambda_c$ excited states reach $10^6$ to $10^7$ at EicC and EIC. The $(\bar{D}N)$ molecular states with both isospin $I = 0$ and $I = 1$ are also studied, with yields reaching $10^5$, making them likely to be detectable at these facilities., Comment: 8 pages, 8 figures, 4 tables

Exotic hadrons beyond the conventional quark model have been discovered in the past two decades. Investigations of these states can lead to deep understanding of nonperturbative dynamics of the strong interaction. In this concise review, we focus on the productions of exotic hadrons in $pp$, $p\bar p$, and nuclear collisions. Experimental observations of light nuclei and hypernuclei, as prototypes of hadronic molecules, in heavy ion collisions will also be briefly discussed., Comment: 17 pages, 16 figures. This review is dedicated to Professor Wenqing Shen on the occasion to celebrate his 80th birthday. All authors contributed equally to this work

The low-energy $J/\psi N$ scattering is important for various reasons: it is related to the hidden-charm $P_c$ pentaquark states, provides insights into the role of gluons in nucleon structures, and is relevant to the $J/\psi$ properties in nuclear medium. The scattering can happen through two distinct mechanisms: the coupled-channel mechanism via open-charm meson-baryon intermediate states, and the soft-gluon exchange mechanism. We investigate the $J/\psi N$ $S$-wave scattering length through both mechanisms, and find that the soft-gluon exchange mechanism leads to a scattering length at least one order of magnitude larger than that from the coupled-channel mechanism and thus is the predominant one. The findings can be verified by lattice calculations and will enhance our understanding of the scattering processes breaking the Okubo-Zweig-Iizuka rule.

Strong empirical and phenomenological indications exist for large sea-quark admixtures in the low-lying excited baryons. Investigating the low-lying excited baryon $\Sigma^*(1/2^-)$ is important to determine the nature of the low-lying excited baryons. We review the experimental and theoretical progress on the studies of the $\Sigma^*(1/2^-)$. Although several candidates have received intensive discussions, such as $\Sigma(1620)$ and $\Sigma(1480)$, their existence needs further confirmation. Following the prediction of the unquenched quark models for the $\Sigma^*(1/2^-)$, many theoretical works suggested the existence of these states in various processes. Future experimental measurements could shed light on the existence of the low-lying excited $\Sigma^*(1/2^-)$ state., Comment: 9 pages, 2 figures, the version of publication in Chinese Physics Letters

We extend our previous study of the interactions of $\bar{D}^{(*)} \Lambda_c - \bar{D}^{(*)}\Sigma_c^{(*)}$ within an analytic, unitary, coupled-channel approach by including the $J/\psi p$ channel and performing fits to the $J/\psi p$ invariant mass distributions in the $\Lambda_b^0 \to J/\psi p K^-$ decay by the LHCb Collaboration. We take into account the contributions of $t$-channel pseudoscalar and vector meson exchanges and $u$-channel baryon exchanges in this work, and a series of bound states and resonances with different spin-parities are dynamically generated. According to the results, four states have a significant impact on the physical observables, with two having a spin-parity of $1/2^-$ and the other two having $3/2^-$. These states can be associated with the LHCb hidden-charm pentaquarks. We further provide the coupling strength between each pole and different channels, which provides some insights on how to search for them in future experiments. Moreover, we also search for poles in higher partial waves up to $J=7/2$ and find indications for the existence of several states with larger widths., Comment: 9 pages

Ascribed as $\rho\rho$ and $K^* \bar{K}^*$ molecular states, respectively, iso-scalar $f_0(1500)$ and $f_0(1710)$ states are expected to have iso-vector partners, potentially identified as $a_0(1450)$ and $a_0(1710)$. The predicted dominant decay modes for these two $a_0$ resonances are $a_0(1450) \to \omega\pi\pi$ and $a_0(1710) \to \omega\pi\pi,\,\phi\pi\pi$. We estimate cross sections for two-photon production of these four resonances within the hadronic molecular picture, and demonstrate that SuperKEKB's luminosity is sufficient for their observation and more precise parameter measurements.

We investigate the possibility of deuteron-like $\Sigma_c^*\bar{\Sigma}$ bound states within the one-boson-exchange model and systematically analyze the effects of the contact-range $\delta^{3}(\vec{r}\,)$ potential, the tensor term from the vector-meson exchange, and nonlocal potentials due to the dependence on the sum of the initial and final state center-of-mass momenta. We find that the pion-exchange potential including the $\delta^{3}(\vec{r}\,)$ term and the tensor term of the $\rho$-exchange potential exhibit comparable magnitudes but opposite signs for any $S$-wave baryon-antibaryon systems. For the $\Sigma_c^*\bar{\Sigma}$ system, it is most likely to form bound states with mass around 3.7 GeV in the $I(J^P)=0(2^-)$ and $1(2^-)$ channels., Comment: 22 pages, 11 figures

The primary objective of this study is to investigate hadronic molecules of $K^*\bar K_1(1270)$ using a one-boson-exchange model, which incorporates exchanges of vector and pseudoscalar mesons in the $t$-channel, as well as the pion exchange in the $u$-channel. Additionally, careful consideration is given to the three-body effects resulting from the on-shell pion originating from $K_1(1270)\to K^*\pi$. Then the BESIII data of the $J/\psi\to\phi\eta\eta'$ process is fitted using the $K^*\bar K_1(1270)$ scattering amplitude with $J^{PC}=0^{--}$ or $1^{--}$. The analysis reveals that both the $J^{PC}=0^{--}$ and $1^{--}$ assumptions for $K^*\bar K_1(1270)$ scattering provide good descriptions of the data, with similar fit qualities. Notably, the parameters obtained from the best fits indicate the existence of $K^*\bar K_1(1270)$ bound states, denoted by $\phi(2100)$ and $\phi_0(2100)$ for the $1^{--}$ and $0^{--}$ states, respectively. The current experimental data, including the $\eta$ polar angular distribution, cannot distinguish which $K^*\bar K_1(1270)$ bound state contributes to the $J/\psi\to\phi\eta\eta'$ process, or if both are involved. Therefore, we propose further explorations of this process, as well as other processes, in upcoming experiments with many more $J/\psi$ events to disentangle the different possibilities., Comment: 11pages, 8figures and 1 table

Two-pole structures refer to the fact that two dynamically generated states are located close to each other between two coupled channels and have a mass difference smaller than the sum of their widths. Thus, the two poles overlap in the invariant mass distribution of their decay products, creating the impression that only one state exists. This phenomenon was first noticed for the $\Lambda(1405)$ and the $K_1(1270)$, and then for several other states. This report explicitly shows how the two-pole structures emerge from the underlying universal chiral dynamics describing the coupled-channel interactions between a heavy matter particle and a pseudo-Nambu-Goldstone boson. Furthermore, we predict similar two-pole structures in other systems dictated by chiral symmetry, such as the isospin $1/2$ $\bar{K}\Sigma_c-\pi\Xi'_c$ coupled channel, awaiting experimental discoveries., Comment: 6 pages, 2 figures; presentation given by Li-Sheng Geng at MENU2023

A novel approach is proposed to probe the nature of the double charm tetraquark through the prompt production asymmetry between $T_{\bar{c}\bar{c}}^-$ and $T_{cc}^+$ in $pp$ collisions. When comparing two theoretical pictures, i.e. the compact tetraquark and hadronic molecular pictures, we find that the former one exhibits a significantly larger production asymmetry, enabling the unambiguous determination of the tetraquark's internal structure. Additionally, distinctive differences in the transverse momentum and rapidity distributions of $T_{\bar{c}\bar{c}}^-$ and $T_{cc}^+$ cross sections emerge, particularly at $p_\mathrm{T}\approx 2~\mathrm{GeV}$ and $y\approx \pm 6$ at a center-of-mass energy of 14$~\mathrm{TeV}$. The insignificant asymmetry in hadronic molecular picture is because that hadronic molecules are produced in hadronic phase, where the phase space of their constituents needs to be taken into account rigorously. Our work can be extended to the exploration of other double heavy tetraquark candidates, offering a versatile approach to advance our understanding of exotic hadrons., Comment: 16 pages, 8 figures. Published in: Eur.Phys.J.C 84 (2024) 8, 800

We extend the chiral quark model for $u$, $d$, $c$ and $b$ quarks with vector mesons, which we proposed in the previous analysis, to a model with the $s$ quark. We include the nonet pseudo-scalar and vector mesons together with the singlet scalar meson based on the SU(3)$_L \times$SU(3)$_R$ chiral symmetry combined with the Hidden Local Symmetry, which mediate force among $u$, $d$ and $s$ quarks. We fit the model parameters to the known ground state mesons and baryons. We show that the mass spectra of those hadrons are beautifully reproduced. We predict the masses of missing ground states, one meson and twenty baryons, which will be tested in the future experiment., Comment: 5 pages, 3 figures

In the past two decades, one of the most puzzling phenomena discovered in hadron physics is that a nominal hadronic state can actually correspond to two poles on the complex energy plane. This phenomenon was first noticed for the $\Lambda(1405)$, then for $K_1(1270)$, and to a lesser extent for $D_0^*(2300)$. In this Letter, we show explicitly how the two-pole structures emerge from the underlying universal chiral dynamics describing the coupled-channel interactions between heavy matter particles and pseudo Nambu-Goldstone bosons. In particular, the fact that two poles appear in between the two dominant coupled channels can be attributed to the particular form of the leading order chiral potentials of the Weinberg-Tomozawa form. Their lineshapes overlap with each other because the degeneracy of the two coupled channels is only broken by explicit chiral symmetry breaking of higher order. We predict that for light-quark~(pion) masses heavier than their physical values (e.g., about 200 MeV in the $\Lambda(1405)$ case studied), the lower pole becomes a virtual state, which can be easily verified by future lattice QCD simulations. Furthermore, we anticipate similar two-pole structures in other systems, such as the isopin $1/2$ $\bar{K}\Sigma_c-\pi\Xi'_c$ coupled channel, which await for experimental discoveries., Comment: to appear in PRD as a letter

Based on the high statistical data of the CLAS Collaboration on $\gamma p \to \phi p$ reaction in the center-of-mass energy range of 2.2 GeV to 2.8 GeV, we investigate the possible existence of strange molecular partners of $P_c$ states, i.e., $N^*(2080)$ and $N^*(2270)$ as $K^*\Sigma$ and $K^*\Sigma^*$ molecular states. In addition to the t-channel Pomeron exchange, t-channel meson exchange including pseudo-scalar meson $(\pi,\eta)$, scalar meson $(\sigma, a_0(980), f_0(980))$, axial-vector meson $f_1(1285)$, tensor meson $f_2(1270)$, as well as s- and u-channel proton exchange, including s-channel $N^*(2080)$ and $N^*(2270)$ states can fit the data very well. The fitted coupling constants of these $N^*$ molecular states to $p\phi$ and $\gamma p$ are consistent with the results directly calculated from the relevant hadronic triangle diagrams of the molecular picture., Comment: 17 pages, 9 figures, 4 tables

We propose a chiral quark model including the $\omega$ and $\rho$ meson contributions in addition to the $\pi$ and $\sigma$ meson contributions. We show that the masses of the ground state baryons such as the nucleon, $\Lambda_c$ and $\Lambda_b$ are dramatically improved in the model with the vector mesons compared with the one without them. The study of the tetraquark $T_{cc}$ is also performed in a coupled channel calculation and the resultant mass is much closer to its experimental value than the result without vector meson contribution. This approach can be applied to the future study of multi-quark systems., Comment: 6 pages, 4 figures

The possible hadronic molecules in $D_s^{(*)+}\Xi_c^{(',*)}$ systems with $J^P=1/2^-,3/2^-$ and $5/2^-$ are investigated with interactions described by light meson exchanges. By varying the cutoff in a phenomenologically reasonable range of $1\sim2.5$ GeV, we find ten near-threshold (bound or virtual) states in the single-channel case. After introducing the coupled-channel dynamics of $D_s^{+}\Xi_c$-$D_s^{+}\Xi_c^{'}$-$D_s^{*+}\Xi_c$-$D_s^{+}\Xi_c^{*}$-$D_s^{*+}\Xi_c^{'}$-$D_s^{*+}\Xi_c^{*}$ systems, these states, except those below the lowest channels in each $J^{P}$ sector, move into the complex energy plane and become resonances in the mass range of $4.43\sim4.76$ GeV. Their spin-parities and nearby thresholds are $1/2^-(D_s^{+}\Xi_c)$, $1/2^-(D_s^{+}\Xi_c^{'})$, $1/2^-(D_s^{*+}\Xi_c)$,$1/2^-(D_s^{*+}\Xi_c^{'})$, $1/2^-(D_s^{*+}\Xi_c^{*})$ , $3/2^-(D_s^{*+}\Xi_c)$, $3/2^-(D_s^{+}\Xi_c)$, $3/2^-(D_s^{*+}\Xi_c^{'})$, $3/2^-(D_s^{*+}\Xi_c^{*})$, and $5/2^-(D_s^{*+}\Xi_c^{*})$. The impacts of the $\delta(r)$-term in the one-boson-exchange model on these states are presented. Setting $\Lambda=1.5$ GeV as an illustrative value, it is found that $1/2^-(D_s^{+}\Xi_c)$ is a stable bound state (becoming unstable if turning on the coupling to lower channels), $1/2^-(D_s^{*+}\Xi_c)$ and $3/2^-(D_s^{*+}\Xi_c)$ are physical resonances in both cases of including or excluding the $\delta(r)$-term, while the other seven states are physical resonances or ``virtual-state-like" poles near thresholds, depending on including the $\delta(r)$-term or not. In addition, the partial decay widths of the physical resonances are provided. These double-charm hidden-strangeness pentaquark states, as the partners of experimentally observed $P_c$ and $P_{cs}$ states, can be searched for in the $D^{(*)}\Lambda_c$ final states in future., Comment: 15 pages, 6 figures, 9 tables

In the present work, we re-analyze the available data for $\gamma p\to K^{\ast +}\Sigma^0$ and $\gamma p \to K^{\ast 0}\Sigma^+$ by considering the contributions from the $N(2080){3/2}^-$ and $N(2270)3/2^-$ molecules instead of any nucleon resonances in the $s$ channel, where the $N(2080)3/2^-$ was proposed to be a $K^\ast \Sigma$ molecule as the strange partner of the $P_c^+(4457)$ hadronic molecular state, and the $N(2270)3/2^-$ was assumed to be a $K^*\Sigma^*$ molecule as the strange partner of the $\bar{D}^\ast \Sigma^\ast_c$ bound states that are predicated as members in the same heavy-quark spin symmetry multiplet as the $P_c$ states. It turns out that all the available cross-section data can be well reproduced, indicating that the molecular structures of the possible $N(2080){3/2}^-$ and $N(2270)3/2^-$ states are compatible with the available data for $K^\ast\Sigma$ photoproduction reactions. Further analysis shows that for both $\gamma p\to K^{\ast +}\Sigma^0$ and $\gamma p \to K^{\ast 0}\Sigma^+$ reactions, the $N(2080){3/2}^-$ exchange provides dominant contributions to the cross-sections in the near-threshold energy region, and significant contributions from the $N(2270)3/2^-$ exchange to the cross-sections in the higher energy region are also found. Predictions of the beam asymmetry $\Sigma$, target asymmetry $T$, and recoil baryon asymmetry $P$ are presented and compared with those from our previous work. Measurements of the data on these observables are called on to further constrain the reaction mechanisms of $K^\ast\Sigma$ photoproduction reactions and to verify the molecular scenario of the $N(2080){3/2}^-$ and $N(2270)3/2^-$ states., Comment: 10 pages, 8 figures

In this work, we interpret the newly observed $\eta_1(1855)$ resonance with exotic $J^{PC}=1^{-+}$ quantum numbers in the $I=0$ sector, reported by the BESIII Collaboration, as a dynamically generated state from the interaction between the lightest pseudoscalar mesons and axial-vector mesons. The interaction is derived from the lowest order chiral Lagrangian from which the Weinberg-Tomozawa term is obtained, describing the transition amplitudes among the relevant channels, which are then unitarized using the Bethe-Salpeter equation, according to the chiral unitary approach. We evaluate the $\eta_1(1855)$ decays into the $\eta\eta^{\prime}$ and $K\bar{K}^*\pi$ channels and find that the latter has a larger branching fraction. We also investigate its SU(3) partners, and according to our findings, the $\pi_1(1400)$ and $\pi_1(1600)$ structures may correspond to dynamically generated states, with the former one coupled mostly to the $b_1\pi$ component and the latter one coupled to the $K_1(1270)\bar{K}$ channel. In particular, our result for the ratio $\Gamma(\pi_1(1600)\to f_1(1285)\pi)/ \Gamma(\pi_1(1600)\to \eta^{\prime}\pi)$ is consistent with the measured value, which supports our interpretation for the higher $\pi_1$ state. We also report two poles with a mass about 1.7~GeV in the $I=1/2$ sector, which may be responsible for the $K^*(1680)$. We suggest searching for two additional $\eta_1$ exotic mesons with masses around 1.4 and 1.7~GeV. In particular, the predicted $\eta_1(1700)$ is expected to have a width around 0.1~GeV and can decay easily into $K\bar K\pi\pi$., Comment: Accepted for publication in Universe with a DOI link https://doi.org/10.3390/universe9020109

In hadron spectrum physics, the partial wave analysis is a primary method used to extract properties of hadronic resonances. The covariant orbital-spin coupling scheme holds unique advantages over other partial wave methods due to its Lorentz covariant form and determined orbital-spin quantum numbers. This paper presents a general form of the covariant orbital-spin coupling scheme based on the irreducible tensor of the homogeneous proper Lorentz group and its little groups. A systematic procedure for constructing partial wave amplitude in a Lorentz covariant way is provided, which can be applied to both massive and massless particles. Specific examples are also included., Comment: 37 pages and 2 figures

We have a look at the $P_{cs}$ states generated from the interaction of $\bar D^{(*)} \Xi^{(\prime*)}_c$ coupled channels. We consider the blocks of pseudoscalar-baryon $({\frac12}^+, {\frac32}^+)$ and vector-baryon $({\frac12}^+, {\frac32}^+)$, and find $10$ resonant states coupling mostly to $\bar D \Xi_c, \bar D^* \Xi_c,\bar D \Xi'_c, \bar D^* \Xi'_c,\bar D \Xi^*_c$ and $\bar D^* \Xi^*_c$. A novel aspect of the work is the realization that the $\bar D \Xi_c,\bar D_s\Lambda_c$ or $\bar D^* \Xi_c,\bar D^*_s\Lambda_c$ channels, with a strong transition potential, collaborate to produce a larger attraction than the corresponding states $\bar D \Sigma_c,\bar D\Lambda_c$ or $\bar D^* \Sigma_c,\bar D^*\Lambda_c$ appearing in the generation of the strangenessless $P_{c}$ states, since in the latter case the transition potential between those channels is zero. The extra attraction obtained in the $\bar D \Xi_c,\bar D^* \Xi_c$ pairs preclude the association of these channels to the $P_{cs}(4338)$ and $P_{cs}(4459)$ states respectively. Then we find a natural association of the $P_{cs}(4338)$ state coupling mostly to $\bar D^* \Xi_c$ while the $P_{cs}(4459)$ is associated to the state found that couples mostly to $\bar D \Xi'_c$. Four more states appear, like in other molecular pictures, and some of the states are degenerate in spin. Counting different spin states we find $10$ states, which we hope can be observed in the near future., Comment: 8 pages, 4 figures, accepted for publication in Physics Letters B

We propose that the $X(3915)$ observed in the $J/\psi\,\omega$ channel is the same state as the $\chi_{c2}(3930)$, and the $X(3960)$, observed in the $D_s^+D_s^-$ channel, is an $S$-wave $D_s^+ D_s^-$ hadronic molecule. In addition, the $J^{PC}=0^{++}$ {component in the $B^+\to D^+D^-K^+$} assigned to the $X(3915)$ in the current {\it Review of Particle Physics} has the same origin as the $X(3960)$, which has a mass around 3.94~GeV. To check the proposal, the available data in the $D\bar D$ and $D_s^+ D_s^-$ channels from both $ B$ decays and $\gamma\gamma$ fusion reaction are analyzed considering both the $D\bar D$-$D_s\bar D_s$-$D^*\bar D^*$-$D_s^*\bar D_s^*$ coupled channels with $0^{++}$ and a $2^{++}$ state introduced additionally. It is found that all the data in different processes can be simultaneously well reproduced, and the coupled-channel dynamics produce four hidden-charm scalar molecular states with masses around 3.73, 3.94, 3.99 and 4.23~GeV, respectively. The results may deepen our understanding of the spectrum of charmonia as well as of the interactions between charmed hadrons., Comment: 15 pages, 6 figures, 2 tables, to apear in Sci. Bull

We make a systematic calculation of the spectra and hadronic decays of the $D_s$ system in a coupled channel framework, where the unquenched effects are induced by the $^3P_0$ model. In the calculation, the wave functions are obtained by using a nonrelativistic potential model and are handled precisely with Gaussian Expansion Method. Even though the fitting mainly focuses on the spectrum, our model agrees well with the experiments on both the spectra and the hadronic decays, suggesting that the coupled channel effect could result in a reasonable and coherent description of the $D_s$ mesons. Based on the calculation, we give a detailed analysis on various aspects of the excited states, especially $D_s(2317), D_s(2460), D_s(2536), D_s(2860), D_s(3040)$. We also predict that $D_s(2{}^3P_0)$ should be a $D^*K^*$ dominant molecule with mass $2894$~MeV, which is only $5$~MeV below the $D^*K^*$ threshold., Comment: 10 pages, 1 figure

Lots of charmonium-like structures have been observed in the last two decades. Most of them have quantum numbers that can be formed by a pair of charm and anticharm quarks, thus it is difficult to unambiguously identify the exotic ones among them. In this Letter, by exploiting heavy quark spin symmetry, we present a robust prediction of the hadronic molecular scenario, where the $\psi(4230),\psi(4360)$ and $\psi(4415)$ are identified as $D\bar D_1,D^*\bar D_1$ and $D^*\bar D^*_2$ bound states, respectively. We show that a flavor-neutral charmonium-like exotic state with quantum numbers $J^{PC}=0^{--}$, denoted as $\psi_0(4360)$, should exist as a $D^*\bar D_1$ bound state. The mass and width of the $\psi_0(4360)$} are predicted to be $(4366\pm18)$ MeV and less than 10 MeV, respectively. The $\psi_0(4360)$ is significant in two folds: no $0^{--}$ hadron has been observed so far, and a study of this state will enlighten the understanding of the mysterious vector mesons between 4.2 and 4.5 GeV, as well as the nature of previously observed exotic $Z_c$ and $P_c$ states. We propose that such an exotic state can be searched for in $e^+e^-\to \eta \psi_0(4360)$ and uniquely identified by measuring the angular distribution of the outgoing $\eta$ meson., Comment: 7+3 pages, 7 figures, 2 tables; version to be appeared in PRL

The interactions of $\bar{D}^{(*)} \Lambda_c - \bar{D}^{(*)}\Sigma_c^{(*)}$ are studied within the framework of a dynamical coupled-channel approach. A series of bound states and resonances with different spin and parity are dynamically generated in the hidden charm sector. Four $S$-wave bound states are found in the mass range of 4.3 to 4.5 GeV, close to the pentaquark states observed by LHCb. Two of the states have a spin parity of $J^P= 1/2^-$ and the other two have $J^P=3/2^-$. In addition, several resonances with different spin and parity in higher partial waves are predicted.

In recent years there has been a rapidly growing body of experimental evidence for existence of exotic, multiquark hadrons, i.e. mesons which contain additional quarks, beyond the usual quark-antiquark pair and baryons which consist of more than three quarks. In all cases with robust evidence they contain at least one heavy quark Q=c or b, the majority including two heavy quarks. Two key theoretical questions have been triggered by these discoveries: (a) how are quarks organized inside these multiquark states -- as compact objects with all quarks within one confinement volume, interacting via color forces, perhaps with an important role played by diquarks, or as deuteron-like hadronic molecules, bound by light-meson exchange? (b) what other multiquark states should we expect? The two questions are tightly intertwined. Each of the interpretations provides a natural explanation of parts of the data, but neither explains all of the data. It is quite possible that both kinds of structures appear in Nature. It may also be the case that certain states are superpositions of the compact and molecular configurations. This Whitepaper brings together contributions from many leading practitioners in the field, representing a wide spectrum of theoretical interpretations. We discuss the importance of future experimental and phenomenological work, which will lead to better understandingof multiquark phenomena in QCD., Comment: 47 pages, 10 figures. Corresponding authors: Marek Karliner, Elena Santopinto

We study dynamically generated $a_0$ resonances by interactions between vector mesons including their coupling to channels of pseudoscalar mesons within coupled-channel approach. Both vector and pseudoscalar mesons are considered as $t$-channel exchanged mesons for calculating interactions between vector mesons. Analogous to $a_0(980)$ as a $K\bar K-\pi\eta$ dynamically generated state, there is an $a_0(1710)$ as a coupled channel dynamically generated state near $K^*\bar{K}^*$ threshold. The channels involved are $\rho\phi,K^*\bar{K}^*,\rho\omega, K\bar{K},\pi\eta$. This $a_0$ mainly decays to $\rho\omega$, $\pi\eta$ and $K\bar{K}$. This pole is much tied to the coupled channel effect. If we turn off either $\rho\phi$ or $K^*\bar{K}^*$, the pole disappears. In addition, it is found that $a_0(1450)$ may also be dynamically generated by $\rho\omega$ interactions due to $\pi$ and $\eta$ exchange., Comment: arXiv admin note: substantial text overlap with arXiv:2107.14470

An exotic state with $J^{PC}=1^{-+}$, denoted by $\eta_1(1855)$, was observed by BESIII collaboration recently in $J/\psi \to \gamma \eta\eta'$. The fact that its mass is just below the threshold of $K\bar K_1(1400)$ stimulates us to investigate whether this exotic state can be interpreted as a $K\bar K_1(1400)+$ c.c { molecule or not}. Using the one boson exchange model, we show that it is possible for $K\bar K_1(1400)$ with $J^{PC}=1^{-+}$ to bind together by taking the momentum cutoff $\Lambda\gtrsim 2$ GeV and yield the same binding energy as the experimental value when $\Lambda\approx 2.5$ GeV. In this molecular picture, the predicted branch ratio $\mathrm{Br}(\eta_1(1855)\to\eta\eta') \approx 15\%$ is consistent with the experimental results, which again supports the molecular explanation of $\eta_1(1855)$. Relevant systems, namely $K\bar K_1(1400)$ with $J^{PC}=1^{--}$ and $K\bar K_1(1270)$ with $J^{PC}=1^{-\pm}$, are also investigated, some of which can be searched for in the future experiments., Comment: 7 pages, 5 figures

Inspired by the LHCb's discovery of hidden-charm pentaquarks, the anticharmed strange pentaquarks $P_{\bar c s}$ in a favor of the hadronic molecule picture are investigated from the one-boson-exchange model. Similar to the hidden-charm pentaquarks, three molecular bound states, one with spin parity $J^P=1/2^-$ below the $\bar D\Sigma$ threshold and another two with $J^P=\{1/2^-,3/2^-\}$ below the $\bar D^*\Sigma$ threshold, are predicted at $3-3.2$ GeV mass region. The mass ordering of the later two states can be interchanged by different reductions of the $\delta(r)$ term. Furthermore, resonances associated with these three bound states are examined by considering $ D_s^-N-\bar D\Lambda-\bar D \Sigma-\bar D^*\Lambda-\bar D^*\Sigma$ coupled-channel dynamics, and decay widths of them are predicted. Our study indicates that the $ D_s^- p$ invariant mass spectrum in the $\bar B_s^0\to \bar n D_s^- p$ decay is an appropriate place to detect the $P_{\bar c s}$ pentaquarks., Comment: 15 pages, 3 figures and 6 tables

The effects of the $\Sigma_c\bar{D}^*$-$\Lambda_{c}(2595)\bar{D}$ coupled-channel dynamics and various one-boson-exchange (OBE) forces for the LHCb pentaquark states, $P_c(4440)$ and $P_c(4457)$, are reinvestigated. Both the pion and $\rho$-meson exchanges are considered for the $\Sigma_c\bar{D}^*$-$\Lambda_{c}(2595)\bar{D}$ coupled-channel dynamics. It is found that the role of the $\Lambda_{c}(2595)\bar{D}$ channel in the descriptions of the $P_c(4440)$ and $P_c(4457)$ states is not significant with the OBE parameters constrained by other experimental sources. The naive OBE models with the short-distance $\delta(\vec{r})$ term of the one-pion exchange (OPE) keep failing to reproduce the $P_c(4440)$ and $P_c(4457)$ states simultaneously. The OPE potential with the full $\delta(\vec{r})$ term results in a too large mass splitting for the $J^P=1/2^-$ and $3/2^-$ $\Sigma_c\bar{D}^*$ bound states with total isospin $I=1/2$. The OBE model with only the OPE $\delta(\vec{r})$ term dropped may fit the splitting much better but somewhat underestimates the splitting. Since the $\delta(\vec r)$ potential is from short-distance physics, which also contains contributions from the exchange of mesons heavier than those considered explicitly, we vary the strength of the $\delta(\vec r)$ potential and find that the masses of the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ can be reproduced simultaneously with the $\delta(\vec r)$ term in the OBE model reduced by about 80\%. While two different spin assignments are possible to produce their masses, in the preferred description, the spin parities of the $P_c(4440)$ and $P_c(4457)$ are $3/2^-$ and $1/2^-$, respectively., Comment: 34 pages, 6 figures, 8 tables

The spectrum of hadronic molecules composed of heavy-antiheavy charmed hadrons has been obtained in our previous work. The potentials are constants at the leading order, which are estimated from resonance saturation. The experimental candidates of hadronic molecules, say $X(3872)$, $Y(4260)$, three $P_c$ states and $P_{cs}(4459)$, fit the spectrum well. The success in describing the pattern of heavy-antiheavy hadronic molecules stimulates us to give more predictions for the heavy-heavy cases, which are less discussed in literature than the heavy-antiheavy ones. Given that the heavy-antiheavy hadronic molecules, several of which have strong experimental evidence, emerge from the dominant constant interaction from resonance saturation, we find that the existence of many heavy-heavy hadronic molecules is natural. Among these predicted heavy-heavy states we highlight the $DD^*$ molecule and the $D^{(*)}\Sigma_c^{(*)}$ molecules, which are the partners of the famous $X(3872)$ and $P_c$ states. Quite recently, LHCb collaboration reported a doubly charmed tetraquark state, $T_{cc}$, which is in line with our results for the $DD^*$ molecule. With the first experimental signal of this new kind of exotic states, the upcoming 3pdate of the LHCb experiment as well as other experiments will provide more chances of observing the heavy-heavy hadronic molecules., Comment: v3: the published version, mistakes about the quantum numbers of identical di-baryon system corrected and 122 double-charm hadronic molecules; v2: more discussion added and references updated; v1: 20 pages, 6 figures and 124 double-charm hadronic molecules including the recently discovered T_{cc} in LHCb measurement

The $f_0(1710)$ was previously proposed to be dynamically generated state by interactions between vector mesons. We extend the study of $f_0(1710)$ by including its coupling to channels of pseudoscalar mesons within coupled-channel approach. The channels involved are $K^*\bar{K}^*,\rho\rho,\omega\omega,\phi\phi, \omega\phi,\pi\pi,K\bar{K},\eta\eta$. We show that the pole assigned to $f_0(1710)$ does not change much. Then we calculate the partial decay widths of $f_0(1710) \to K^*\bar{K}^* \to \pi\pi,K\bar{K},\eta\eta$ as the coupled channel dynamically generated state as well as assuming it to be pure $K^*\bar{K}^*$ molecule. In both cases the ratios of partial decay widths agree fairly with that in PDG.

In a recent measurement LHCb reported pronounced structures in the $J/\psi J/\psi$ spectrum. One of the various possible explanations of those is that they emerge from non-perturbative interactions of vector charmonia. It is thus important to understand whether it is possible to form a bound state of two charmonia interacting through the exchange of gluons, which hadronise into two pions at the longest distance. In this paper, we demonstrate that, given our current understanding of hadron-hadron interactions, the exchange of correlated light mesons (pions and kaons) is able to provide sizeable attraction to the di-$J/\psi$ system, and it is possible for two $J/\psi$ mesons to form a bound state. As a side result we find from an analysis of the data for the $\psi(2S)\to J/\psi \pi\pi$ transition including both $\pi\pi$ and $K\bar K$ final state interactions an improved value for the $\psi(2S)\to J/\psi$ transition chromo-electric polarisability: $|\alpha_{\psi(2S)J/\psi}|= (1.8\pm 0.1)~\mbox{GeV}^{-3}$, where the uncertainty also includes the one induced by the final state interactions., Comment: 11 pages, 7 figures, version to appear in Sci. Bull

By using the covariant L-S Scheme for the partial wave analysis, we deduce the ratios between the S-wave and D-wave contributions from the recent data of $\psi(1^-) \to B_8(1/2^+) \bar{B}_8(1/2^-)$ from the BESIII collaboration. For the $J/\psi\to \Lambda\bar{\Lambda}$ and $J/\psi(\psi(2S))\to \Sigma^{+}\bar{\Sigma}^{-}$, the ratios are fixed and the average angular momenta are computed to estimate the effective radii of these processes. The results show that the effective radii of these decays of $J/\psi(\psi(2S))$ are very small, which are around 0.04 fm. Thus, it is a nice place to search excited baryon resonances with lower spin in the decays of $J/\psi(\psi(2S))$. Furthermore, for the other $\psi(1^-) \to B_8(1/2^+) \bar{B}_8(1/2^-)$ reactions, we propose some methods to get such effective radius.

I give a brief comment on the LHCb's discovery of $P_c$ and $P_{cs}$ pentaquark states. These pentaquark states not only reveal a new kind of hadronic molecules, but also shed new light on the possible structure of pentaquark components in baryons, hence may play very important role for understanding un-quenching dynamics and the whole baryon spectroscopy., Comment: 2 pages

Many efforts have been made to reveal the nature of the overabundant resonant structures observed by the worldwide experiments in the last two decades. Hadronic molecules attract special attention because many of these seemingly unconventional resonances are located close to the threshold of a pair of hadrons. To give an overall feature of the spectrum of hadronic molecules composed of a pair of heavy-antiheavy hadrons, namely, which pairs are possible to form molecular states, we take charmed hadrons for example to investigate the interaction between them and search for poles by solving the Bethe-Salpeter equation. We consider all possible combinations of hadron pairs of the $S$-wave singly-charmed mesons and baryons as well as the narrow $P$-wave charmed mesons. The interactions, which are assumed to be meson-exchange saturated, are described by constant contact terms which are resummed to generate poles. It turns out that if a system is attractive near threshold by the light meson exchange, there is a pole close to threshold corresponding to a bound state or a virtual state, depending on the strength of interaction and the cutoff. In total, 229 molecular states are predicted. The observed near-threshold structures with hidden-charm, like the famous $X(3872)$ and $P_c$ states, fit into the spectrum we obtain. We also highlight a $\Lambda_c\bar \Lambda_c$ bound state that has a pole consistent with the cross section of the $e^+e^-\to\Lambda_c\bar \Lambda_c$ precisely measured by the BESIII Collaboration., Comment: Typos of the loop integral, Eq.53, corrected

Tremendous progress has been made experimentally in the hadron spectrum containing heavy quarks in the last two decades. It is surprising that many resonant structures are around thresholds of a pair of heavy hadrons. There should be a threshold cusp at any $S$-wave threshold. By constructing a nonrelativistic effective field theory with open channels, we discuss the generalities of threshold behavior, and offer an explanation of the abundance of near-threshold peaks in the heavy quarkonium regime. We show that the threshold cusp can show up as a peak only for channels with attractive interaction, and the width of the cusp is inversely proportional to the reduced mass relevant for the threshold. We argue that there should be threshold structures at any threshold of a pair of heavy-quark and heavy-antiquark hadrons, which have attractive interaction at threshold, in the invariant mass distribution of a heavy quarkonium and light hadrons that couple to that open-flavor hadron pair. The structure becomes more pronounced if there is a near-threshold pole. Predictions of the possible pairs are also given for the ground state heavy hadrons. Precisely measuring the threshold structures will play an important role in revealing the heavy-hadron interactions, and thus understanding the puzzling hidden-charm and hidden-bottom structures., Comment: Title changed, version to appear in Phys. Rev. Lett.; 8 pages, 2 figures

Stimulated by recent experimental observation of $X_1(2900)$ just below the $\bar D_1K$ threshold, we extend our previous study of $\bar D_1D$ S-wave bound state by vector meson exchange to $\bar D_1K$ system as well as similar $\bar DK_1$, $D_1K$ and $DK_1$ systems to look for possible bound states. We find that the potential of $D K_1$ is attractive and strong enough to form bound states with mass around 3110 MeV for $DK_1(1270)$ and 3240 MeV for $DK_1(1400)$. $D_1 K$ is also attractive but weaker, hardly enough to form bound states. While $\bar DK_1$ becomes further less attractive, the potential between $\bar D_1 K$ is the weakest, definitely too weak to form any bound state, which excludes the recently observed $X_1(2900)$ to be a $\bar D_1 K$ bound state. We also give the decay properties of the predicted $D K_1$ bound states., Comment: 9 pages, 2 figures, version appears in EPJA

We propose to create a secondary beam of neutral kaons in Hall D at Jefferson Lab to be used with the GlueX experimental setup for strange hadron spectroscopy. The superior CEBAF electron beam will enable a flux on the order of $1\times 10^4~K_L/sec$, which exceeds the flux of that previously attained at SLAC by three orders of magnitude. The use of a deuteron target will provide first measurements ever with neutral kaons on neutrons. The experiment will measure both differential cross sections and self-analyzed polarizations of the produced $\Lambda$, $\Sigma$, $\Xi$, and $\Omega$ hyperons using the GlueX detector at the Jefferson Lab Hall D. The measurements will span CM $\cos\theta$ from $-0.95$ to 0.95 in the range W = 1490 MeV to 2500 MeV. The new data will significantly constrain the partial wave analyses and reduce model-dependent uncertainties in the extraction of the properties and pole positions of the strange hyperon resonances, and establish the orbitally excited multiplets in the spectra of the $\Xi$ and $\Omega$ hyperons. Comparison with the corresponding multiplets in the spectra of the charm and bottom hyperons will provide insight into he accuracy of QCD-based calculations over a large range of masses. The proposed facility will have a defining impact in the strange meson sector through measurements of the final state $K\pi$ system up to 2 GeV invariant mass. This will allow the determination of pole positions and widths of all relevant $K^\ast(K\pi)$ $S$-,$P$-,$D$-,$F$-, and $G$-wave resonances, settle the question of the existence or nonexistence of scalar meson $\kappa/K_0^\ast(700)$ and improve the constrains on their pole parameters. Subsequently improving our knowledge of the low-lying scalar nonet in general., Comment: Final version of the KLF Proposal [C12-19-001] approved by JLab PAC48. The intermediate version of the proposal was posted in arXiv:1707.05284 [hep-ex]. 103 pages, 52 figures, 8 tables, 324 references. Several typos were fixed

Due to the discovery of the hidden-charm pentaquark $P_c$ states by the LHCb collaboration, the interests on the candidates of hidden-bottom pentaquark $P_b$ states are increasing. They are anticipated to exist as the analogues of the $P_c$ states in the bottom sector and predicted by many models. We give an exploration of searching for a typical $P_b$ in the $\gamma p \to \Upsilon p$ reaction, which shows a promising potential to observe it at an electron-ion collider. The possibility of searching for $P_b$ in open-bottom channels are also briefly discussed. Meanwhile, the $t$-channel non-resonant contribution, which in fact covers several interesting topics at low energies, is systematically investigated., Comment: 18 pages,, publication version, references updated

The possibility of the Y(4260) being the molecular state of $D\bar D_1(2420)+\mathrm{c.c.}$ is investigated in the one boson exchange model. It turns out that the potential of $J^{PC}=1^{--}$ state formed by $D\bar D_1(2420)+\mathrm{c.c.}$ is attractive and strong enough to bind them together when the momentum cutoff $\Lambda \gtrsim 1.4$ GeV. To produce the Y(4260) with correct binding energy, we need $\Lambda\approx 2.1$ GeV. Besides, $D\bar D_1(2420)+\mathrm{c.c.}$ can also form a state with exotic quantum numbers, $J^{PC}=1^{-+}$, and its potential similar with that of the $J^{PC}=1^{--}$ state. Therefore, an exotic state with mass around 4240 MeV (called $\eta_{c1}(4240)$) is predicted to exist. Our estimation of the mass of the $J^{PC}=1^{-+}$ state in charmonium region is in agreement with those predicted by the chiral quark model and the lattice QCD. The possible decay modes and their relative widths are estimated and the results suggest that this exotic state can be searched for in $\eta\eta_c$ and $\eta\chi_{c1}$ channels., Comment: 11 pages, 5 figures, some errors corrected

We investigate the observed pentaquark candidates $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ from the latest LHCb measurement, as well as four possible spin partners in the $\bar{D}^{(*)}\Sigma_c^*$ system predicted from the heavy quark spin symmetry with the hadronic molecule scenarios. Similar to the previous calculation on $P_c(4380)$ and $P_c(4450)$, the partial widths of all the allowed decay channels for these $P_c$ states are estimated with the effective Lagrangian method. The cutoff dependence of our numerical results are also presented. Comparing with the experimental widths, our results show that $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ can be described well with the spin-parity-$1/2^-$-$\bar{D}\Sigma_c$, $1/2^-$-$\bar{D}^*\Sigma_c$ and $3/2^-$-$\bar{D}^*\Sigma_c$ molecule pictures, respectively., Comment: 13 pages,8 figures

The BESIII Collaboration recently reported the observation of the $a_0(980)^0-f_0(980)$ mixing in the isospin breaking decay $J/\psi\to \eta\pi^0\phi$. In the Dalitz plot for that decay with the $\eta$ reconstructed from two photons, there is a band around $1.4$~GeV on the $\pi^0 \phi$ distribution. In general, this peak can be due to a resonance or a kinematic effect. In this paper, we study the effects of a set of $K^*K\bar K$ triangle diagrams, and show that due to triangle singularities such diagrams can lead to a peak around 1.4~GeV in the $\pi^0\phi$ invariant mass distribution. The Dalitz plot induced by such a mechanism has a feature consistent with the BESIII observation, namely events along the band accumulate at both ends close to the Dalitz plot boundary. The effect of the same mechanism on the $J/\psi\to \pi^0\pi^0\phi$ and $J/\psi \to \eta\pi^0 K^+K^-$ decays are also investigated. We suggest to take more data for the $J/\psi\to \eta\pi^0\phi\to \eta\pi^0 K^+ K^-$ and check whether the structure around $1.4$~GeV persists for the $K^+K^-$ invariant mass away from the $\phi$ mass region. This is crucial for understanding whether the band is due to triangle singularities or due to a resonance. Were it the latter, the band should remain while it would not if it is due to the former., Comment: 26 pages,9 figures

The excitations of nucleon resonances with hidden charm, $N^*_{c\bar{c}}$, in the $\gamma p$ reactions are investigated by using the predictions from the available meson-baryons (MB) coupled-channel models. For the $\gamma\,p\rightarrow J/\psi\, p$ process, we first calculate the Pomeron-exchange amplitudes with the parameters determined from fitting the available total cross section data up to invariant mass $W=300$ GeV. We then add the resonant amplitudes to examine the effects of $ N^*_{c\bar{c}}$ excitations on the cross sections of $\gamma\,p\rightarrow J/\psi\, p$ in the near threshold energy region. The $N^*_{c\bar{c}}\to MB$ transition matrix elements are determined from the partial decay widths predicted by the meson-baryons coupled-channel models. The $\gamma p \to N^*_{c\bar{c}}$ transition amplitudes are calculated from the Vector Meson Dominance (VMD) model. The total $\gamma p\rightarrow J/\psi\, p$ amplitudes then depend on an off-shell form factor, parameterized as $F_V(q^2)=\Lambda^4/(\Lambda^4 + (q^2 - m^2_V)^2)$ with $\Lambda=550$ MeV. We then demonstrate that the $N^*_{c\bar{c}}$ can be most easily identified in the differential cross sections at large angles of outgoing $J/\psi$ where the contribution from Pomeron-exchange becomes negligible. With the same VMD model and the same coupled-channel models of $N^*_{c\bar{c}}$, we also calculate the resonant amplitudes for the $\gamma\,p\rightarrow Vp\rightarrow N^*_{c\bar{c}} \rightarrow \bar{D}^0\Lambda_c^+ (\bar{D}^{*0}\Lambda_c^+)$ processes. By adding the non-resonant amplitudes due to the exchange of $\bar{D}^{*0}$ ($\bar{D}^{0})$, we then predict the cross sections of $\gamma\,p\rightarrow \bar{D}^0\Lambda_c^+(\bar{D}^{*0}\Lambda^+_c)$ for additional experimental tests of the available meson-baryon coupled-channel models of $N^*_{c\bar{c}}$., Comment: 23 pages, 10 figures

In 2010, $\Lambda^*_{c\bar{c}}$ states were predicted as the strange number $S=-1$ partners of $N^*_{c\bar{c}}$, which are well known now as the $P_c$ states and observed experimentally by LHCb Collaboration. We analyze the decay behaviors of $\Lambda_{c\bar{c}}$ as S-wave hadronic molecules within the effective Lagrangian framework by a similar method, which has been applied on $P_c$ states successfully. With partial widths of possible decay channels calculated, we find that $\Lambda_{c\bar{c}}(4213)$ and $\Lambda_{c\bar{c}}(4403)$, which are formed as pseudoscalar meson baryon molecules, mainly decay to the $\eta_c \Lambda$ channel. For the two vector meson baryon molecule states, our results show that the total decay width with $J^P=\frac12^-$ is by one order of magnitude larger than that with $J^P=\frac32^-$. The decay patterns and relative decay ratios are very different for $\Lambda_{c\bar{c}}(4370)$ being a $D_s^{* -} \Lambda_c^+$ or $\bar{D}^{*} \Xi_c$ molecule state. The main decay channels of $\Lambda_{c\bar{c}}(4550)$ are $\bar{D}^{(*)} \Xi^{(*,\prime)}_c$ because of the pseudoscalar meson exchange mechanism. In addition, $\bar{D}^{*} \Xi_c$ is the dominant decay channel of $\Lambda_{c\bar{c}}(4490)$ which is assumed as a $\bar{D} \Xi_c^{*}$ bound state. These decay patterns of the $\Lambda^*_{c\bar{c}}$ states would provide a guidance for their future experimental searches and help us to understand their internal structures.

The $\rho\rho$ scattering has been studied by two groups which both claimed a dynamical generated scalar meson, most likely to be $f_0(1370)$. Here we investigate the influence of coupled-channels of pseudoscalar mesons, i.e., $\pi\pi$ and $\bar KK$, on this dynamical generated scalar state. With the coupled channel effect included, the pole and partial decay widths are found to be more close to PDG values for $f_0(1500)$., Comment: 11 pages with 4 figures

Very recently, a new $\Omega^{*}$ state was reported by the Belle Collaboration, with its mass of $2012.4 \pm 0.7\ \text{(stat)}\pm 0.6\ \text{(syst)}\ \mathrm{MeV}$, which locates just below the $K\Xi^*$ threshold and hence hints to be a possible $K\Xi^*$ hadronic molecule. Using the effective Lagrangian approach as the same as our previous works for other possible hadronic molecular states, we investigate the decay behavior of this new $\Omega^*$ state within the hadronic molecular picture. The results show that the measured decay width can be reproduced well and its dominant decay channel is predicted to be the $K\pi\Xi$ three-body decay. This suggests that the newly observed $\Omega^*$ may be ascribed as the $J^P={3/2}^-$ $K\Xi^*$ hadronic molecular state and can be further checked through its $K\pi\Xi$ decay channel., Comment: 7pages, 6 figures

Invoked by the recent CMS observation regarding candidates of the $\chi_b(3P)$ multiplet, we analyze the ultrafine and mass splittings among $3P$ multiplet in our unquenched quark model (UQM) studies. The mass difference of $\chi_{b2}$ and $\chi_{b1}$ in $3P$ multiplet measured by CMS collaboration ($10.6 \pm 0.64 \pm 0.17$ MeV) is very close to our theoretical prediction ($12$ MeV). Our corresponding mass splitting of $\chi_{b1}$ and $\chi_{b0}$ enables us to predict more precisely the mass of $\chi_{b0}(3P)$ to be ($10490\pm 3$) MeV. Moreover, we predict ratios of the radiative decays of $\chi_{bJ}(nP)$ candidates, both in UQM and quark potential model. Our predicted relative branching fraction of $\chi_{b0}(3P)\to\Upsilon(3S)\gamma$ is one order of magnitude smaller than $\chi_{b2}(3P)$, this naturally explains the non-observation of $\chi_{b0}(3P)$ in recent CMS search. We hope these results might provide useful references for forthcoming experimental searches.

The discovery of $\Xi_{cc}^{++}$ by the LHCb Collaboration triggers predictions of more doubly charmed baryons. By taking into account both the $P$-wave excitations between the two charm quarks and the scattering of light pseudoscalar mesons off the ground state doubly charmed baryons, a set of negative-parity spin-1/2 doubly charmed baryons are predicted already from a unitarized version of leading order chiral perturbation theory. Moreover, employing heavy antiquark-diquark symmetry the relevant low-energy constants in the next-to-leading order are connected with those describing light pseudoscalar mesons scattering off charmed mesons, which have been well determined from lattice calculations and experimental data. Our calculations result in a spectrum richer than that of heavy mesons. We find two very narrow $J^P=1/2^-$ $\Omega_{cc}^P$, which very likely decay into $\Omega_{cc}\pi^0$ breaking isospin symmetry. In the isospin-1/2 $\Xi_{cc}^P$ sector, three states are predicted to exist below 4.2~GeV with the lowest one being narrow and the other two rather broad. We suggest to search for the $\Xi_{cc}^{P}$ states in the $\Xi_{cc}^{++}\pi^-$ mode. Searching for them and their analogues are helpful to establish the hadron spectrum., Comment: 6 pages, 3 figures; accepted for publication as a Rapid Communication in Physical Review D