Search

The total cross sections of the process $e^+ e^-\to \Lambda_c^+ \bar{\Lambda}_c^-$ close to the threshold are calculated within the vector meson dominance model. It is found that the theoretical results can describe the current experimental measurements. In particular, the results for the angular distribution parameters about the differential cross section are consistent with the experiments from BESIII Collaboration. In addition, the relative phase $\Delta \Phi$ of the electromagnetic form factors was given, and the spin polarization of $\Lambda_c^+$ is predicted at center-mass energy $4.7 \ \rm GeV$. It is hopeful to provide a new perspective on the characteristics of the charmed baryon $\Lambda_c^+$., Comment: 6 pages,6 figures

We propose a novel method to identify the two-pole structure of the $\Lambda(1405)$. The two poles owe their origin to different quark flavor irreducible representations in the meson-baryon coupled-channel interactions, thus they should be individually manifested in reactions that provide good flavor eigenstate sources. Hadronic decays of charmonia into $\bar{\Lambda}\Sigma\pi$ and $\bar{\Lambda}(1520)\Sigma\pi$ are such reactions, and the flavor octet and singlet poles can be approximately singled out in these two decay modes. This SU(3) flavor filter works even considering the flavor symmetry breaking. With the huge charmonium data sets collected, it is therefore promising to solve the long-standing $\Lambda(1405)$ puzzle employing the proposed flavor filter., Comment: 6 pages, 4 figures

The Belle collaboration recently reported a promising candidate for the spin-2 $D^*\bar{D}^*$ partner of the $X(3872)$, called the $X_2$ for short, having a mass of $(4014.3 \pm 4.0 \pm 1.5)~\mathrm{MeV}$ and a width of $(4 \pm 11 \pm 6)~\mathrm{MeV} $. In present work, we assume the $X_2$ as a pure molecule of the $D^*\bar{D}^*$ under three cases, i.e., pure neutral components ($\theta = 0$), isospin singlet ($\theta = \pi/4$) and neutral components dominant ($\theta = \pi/6$), where $\theta$ is a phase angle describing the proportion of neutral and charged constituents. Using an effective Lagrangian approach, we calculated the partial widths of $X_2\to VV$ and $X_2 \to PP$ ($V$ and $P$ stand for light vector and pseudoscalar mesons, respectively). The predicted decay widths of $X_2 \to VV$ can reach a few hundreds of $\mathrm{keV}$, while the decay widths of $X_2 \to PP$ are about several tens of $\mathrm{keV}$. In addition, the effects from the proportion of neutral and charged constituent on the decay widths of $X_2\to VV$ and $PP$ are also investigated. We hope that the present calculations will be checked experimentally in the future., Comment: 8 pages, 7figure, comments welcome

Recently, a new excited baryon state, $\Omega(2012)$, was observed in the invariant mass spectra of $K^-\Xi^0$ and $K^0_S \Xi^-$ by the Belle Collaboration. This state has a narrow width ($\sim 6$ MeV) compared to other baryon states with a similar mass. In this paper, we provide a mini-review on the $\Omega(2012)$ state from the molecular perspective, where it appears to be a dynamically generated state with spin-parity $3/2^-$ from the coupled-channels interactions of the $\bar{K} \Xi(1530)$ and $\eta \Omega$ in $s$-wave and $\bar{K} \Xi$ in $d$-wave. Additionally, alternative explanations for the $\Omega(2012)$ resonance are also discussed., Comment: Mini-review on the $\Omega(2012)$ state from the molecular perspective. Accepted by the Chinese Physics Letters

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: 8 pages, 2 figures

Motivated by the recent experimental measurements, we have investigated the Cabibbo-favored process $\Lambda_c^+ \to p \bar{K}^0\eta$, where the $N(1535)$ resonance is dynamically generated from the $S$-wave pseudoscalar meson-octet baryon interactions within the chiral unitary approach. The contributions from the intermediate $N(1650)$ and the predicted low-lying baryon $\Sigma^*(1/2^-)$ are also considered. In addition, a Breit-Wigner amplitude for the $N(1535)$ resonance is checked. By comparing with the measured $\eta p$, $\bar{K}^0 \eta$, and $p \bar{K}^0$ invariant mass squared distributions, our results support the interpretation of $N(1535)$ as a dynamically generated state. Furthermore, we demonstrate that, with the contribution from $\Sigma^*(1/2^-)$ taken into account, the calculated invariant mass spectrum agrees with the Belle measurements. Future precise measurements of the $\Lambda_c^+\to p \bar{K}^0\eta$ process can further elucidate the existence of the low-lying baryon $\Sigma^*(1/2^-)$., Comment: 9 pages, 5 figures, comments are welcome!

We investigated the pionic transitions between the $X_2$ [spin-2 partner of the $X(3872)$] and $\chi_{c1,2}$ using a nonrelativistic effective field theory. The $X_2$ is assumed to be a bound state of the $D^{*}$ and $\bar{D}^*$ mesons and to decay through several kinds of loops, including the bubble, triangle and box loops. Within the present model, the widths for the single-pion decays $X_2\to\pi^0\chi_{cJ}$ are predicted to be about $3$--$30$ keV. For the dipion decays, the widths are a few keVs. These widths yield a branching fraction of $10^{-3}$--$10^{-2}$. The ratio $R_{\mathrm{c}0}=\Gamma (X_2\to\pi^+\pi^-\chi_{cJ})/\Gamma (X_2\to\pi^0\pi^0\chi_{cJ}) \simeq 1.6$, which is a bit smaller than the expected value of $2$, and $R_{21}=\Gamma (X_2\to\pi\pi\chi_{c2})/\Gamma (X_2\to\pi\pi\chi_{c1}) \simeq 0.85$. These ratios are nearly independent of the $X_2$ mass and the coupling constants, which might be a good quantity for the experiments. Moreover, the invariant mass spectra of the $\pi^0\chi_{cJ}$ final state for the dipion processes are presented, showing a cusp structure at the $D {\bar D}^*$ threshold enhanced and narrowed by the nearby triangle singularity., Comment: 12 pages, 9 figure, Comments welcome

Motivated by the Belle measurements of the process $\Lambda_c^+\to \eta\pi^+\Lambda$, we investigate this process by considering the contributions from the $\Lambda(1670)$, $a_0(980)$, and $\Sigma(1385)$. In addition, we also consider the predicted low-lying baryon $\Sigma^*(1/2^-)$. Our results involving the $\Sigma^*(1/2^-)$ are favored by fitting to the Belle data of the $\eta\Lambda$ and $\pi^+\Lambda$ invariant mass distributions. Furthermore, we predict the $\eta\pi^+$ invariant mass distribution and the angular distribution $d\Gamma/d{\rm cos}\theta$, which are significantly different depending on whether or not the contribution from the $\Sigma^*(1/2^-)$ is considered. Finally, we show that, with the contribution from the $\Sigma^*(1/2^-)$, the calculated Dalizt plot agrees with the Belle measurements. Future precise measurements of the process $\Lambda_c^+\to \eta\pi^+\Lambda$ could shed further light on the existence of the low-lying $\Sigma^*(1/2^-)$., Comment: 11 pages, 14 figures, comments are welcome

We have phenomenologically investigated the decays $B_s^0 \to X(3872) \pi^+\pi^- (K^+ K^-)$ and $B_s^0 \to \psi(2S) \pi^+ \pi^- (K^+K^-)$. In our analysis, the scalar meson $f_0(980)$ is formed through the final state interactions of coupled channels $\pi \pi$ and $K\bar{K}$. Our findings indicate that the $\pi^+\pi^-$ invariant mass distribution of the $B_s^0 \to \psi(2S)\pi^+\pi^-$ decay can be accurately reproduced. Furthermore, we have explored the $\pi^+\pi^- (K^+ K^-)$ invariant mass distribution of the $B_s^0 \to X(3872) \pi^+\pi^- (K^+ K^-)$ decay, accounting for the different production mechanisms between $X(3872)$ and $\psi(2S)$, up to a global factor. It is found that the production rates for $X(3872)$ and $\psi(2S)$ are much different, which indicates that the structure of $X(3872)$ is more complicated than the $\psi(2S)$, which is a conventional $c\bar{c}$ state. Additionally, we have considered the contributions from $f_0(1500)$ to $\pi^+\pi^-$ and the $\phi$ meson to $K^+ K^-$ in our analysis. Utilizing the model parameters, we have calculated the branching fraction of $B_s^0 \to X(3872) K^+ K^-$, and anticipate that the findings of our study can be experimentally tested in the future., Comment: 7 pages, 6 figures. Typos are corrected, and couplings are renormalized to be dimentionless

We studied the radiative transitions between the $\Upsilon(10753)$, the $S$-$D$ mixed state of the $\Upsilon(4S)$ and $\Upsilon_1(3\,{}^3D_1)$, and the $X_b$, the heavy quark flavor symmetry counterpart of the $X(3782)$ in the bottomonium sector. The radiative transition was assumed to occur through the intermediate bottom mesons, including $P$-wave $B_1^{(\prime)}$ mesons as well as the $S$-wave $B^{(*)}$ ones. The consideration of the $B_1^{(\prime)}$ mesons leads to the couplings to be in $S$-wave, and hence enhances the contributions of the intermediate meson loops. The radiative decay width for the $\Upsilon(10753)\to\gamma X_b$ is predicted to be order of $10~\mathrm{keV}$, corresponding to a branching fraction of $10^{-4}$. Based on the theoretical results, we strongly suggest to search for the $X_b$ in the $e^+e^-\to\gamma X_b$ with $X_b\to\pi\pi\chi_{b1}$ near $\sqrt{s}=10.754~\mathrm{GeV}$, and it is hoped that the calculations here could be tested by the future Belle II experiments., Comment: 7 pages, 4 figures, accepted by PRD(20240510)

We have investigated the process $J/\psi \to {\bar{K}}^0K^+\rho^-$ by taking into account the $S$-wave ${K^*\bar{K}^*}$, $\rho \omega$, and $\rho \phi$ final-state interactions, where the scalar meson $a_0(1710)$ is generated. In addition, we also take into account the contributions from the scalar $a_0(980)(\to \bar{K}^0K^+)$ and the intermediate resonances $K_1(1270)^{-}(\to {\bar{K}}^0\rho^-) $ and $K_1(1270)^{0}(\to K^+\rho^-)$. Our results show that, in the ${{\bar{K}}^0K^+}$ invariant mass distribution, a clear peak structure around 1.8~GeV appears, which could be associated with the scalar $a_0(1710)$, however, no significant structure of the $a_0(980)$ is observed. On the other hand, one can find clear peaks of the $K_1(1270)$ in the ${\bar{K}}^0\rho^-$ and $K^+\rho^-$ invariant mass distributions. The future precise measurement of this process by the BESIII and Belle II Collaborations and the planned Super Tau-Charm Facility (STCF) in the future could shed light on the nature of $a_0(1710)$., Comment: 12 pages, 13 figures, the version for PRD. arXiv admin note: substantial text overlap with arXiv:2306.15964

Within the extended vector meson dominance model, we investigate the $e^+ e^- \to \Lambda^+_c \bar{\Lambda}^-_c$ reaction and the electromagnetic form factors of the charmed baryon $\Lambda_c^+$. The model parameters are determined by fitting them to the cross sections of the process $e^+e^-\rightarrow \Lambda_c^+ \bar{\Lambda}_c^-$ and the magnetic form factor $|G_M|$ of $\Lambda^+_c$. By considering four charmoniumlike states, called $\psi(4500)$, $\psi(4660)$, $\psi(4790)$, and $\psi(4900)$, we can well describe the current data on the $e^+ e^- \to \Lambda^+_c \bar{\Lambda}^-_c$ reaction from the reaction threshold up to $4.96 \ \mathrm{GeV}$. In addition to the total cross sections and $|G_M|$, the ratio $|G_E/G_M|$ and effective form factor $|G_{\mathrm{eff}}|$ for $\Lambda^+_c$ are also calculated, and found that these calculations are consistent with the experimental data. Within the fitted model parameters, we have also estimated the charge radius of the charmed $\Lambda_c^+$ baryon., Comment: 7 pages, 6 figures. Published version

We investigate the nonmonotonic behavior observed in the time-like nucleon electromagnetic form factors. Using a phenomenological extending vector meson dominance model, where the ground states $\rho$ and $\omega$ and their excited states $\rho(2D)$, $\omega(3D)$, and $\omega(5S)$ are taken into account, we have successfully reproduced the cross sections of $e^+ e^- \to p \bar{p}$ and $e^+ e^- \to n \bar{n}$ reactions. Furthermore, we have derived the nucleon electromagnetic form factors in the time-like region, and it is found that the so-called periodic behaviour of the nucleon effective form factors is not confirmed. However, there are indeed nonmonotonic structures in the line shape of nucleon effective form factors, which can be naturally reproduced by considering the contributions from the low-lying excited vector states., Comment: Published version

The three-body systems $\eta K^* \bar{K}^*$, $\pi K^* \bar{K}^*$, and $K K^* \bar{K}^*$ are further investigated within the framework of fixed-center approximation, where $K^* \bar{K}^*$ is treated as the fixed-center, corresponding to the possible scalar meson $a_0(1780)$ or the tensor meson $f_2'(1525)$. The interactions between $\eta$, $\pi$, $K$, and $K^*$ are taken from the chiral unitary approach. The resonance structures appear in the modulus squared of the three-body scattering amplitude and suggest that $\eta / \pi / K$-$(K^*\bar{K}^*)_{a_0(1780)/f'_2(1525)}$ hadron state can be formed. By scattering the $\eta$ meson on the fixed-center $(K^* \bar{K}^*)_{a_0(1780)}$, it is found that there is a distinct peak around 2100 MeV, as shown in the modulus squared of the three-body scattering amplitude, which can be associated with the meson $\pi(2070)$. For the scattering of the $\eta$ meson on the $(K^* \bar{K}^*)_{f_2'(1525)}$, a resonance structure around 1890 MeV is found and it can be associated with the $\eta_2(1870)$ meson. Other resonance structures are also found and can be associated with $\pi_2(1880)$ and $\eta(2010)$., Comment: Published version

We present a theoretical study of $\Xi^*(1690)$ resonance in the $\Lambda_c^+ \to \Lambda K^+ \bar{K}^0$ decay, where the weak interaction part proceeds through the Cabibbo-favored process $c \to s + u\bar{d}$. Next, the intermediate two mesons and one baryon state can be constructed with a pair of $q\bar{q}$ with the vacuum quantum numbers. Finally, the $\Xi^*(1690)$ is mainly produced from the final state interactions of $\bar{K}\Lambda$ in coupled channels, and it is shown in the $\bar{K}\Lambda$ invariant mass distribution. Besides, the scalar meson $a_0(980)$ and nucleon excited state $N^*(1535)$ are also taken into account in the decaying channels $K^+\bar{K}^0$ and $K^+\Lambda$, respectively. Within model parameters, the $K^+ \bar{K}^0$, $\bar{K}^0 \Lambda$ and $K^+ \Lambda$ invariant mass distributions are calculated, and it is found that our theoretical results can reproduce well the experimental measurements, especially for the clear peak around $1690$ MeV in the $\bar{K}\Lambda$ spectrum. The proposed weak decay process $\Lambda_c^+ \to \Lambda K^+ \bar{K}^0$ and the interaction mechanism can provide valuable information on the nature of the $\Xi^*(1690)$ resonance., Comment: 9 pages, 5 figures

We investigate the process $\eta_c \to {\bar{K}}^0K^+\pi^-$ by taking into account the $S$-wave ${K^*\bar{K}^*}$ and $\rho\omega$ interactions within the unitary coupled-channel approach, where the scalar meson $a_0(1710)$ is dynamically generated. In addition, the contributions from the intermediate resonances $K_0^*(1430)^{-}\to {\bar{K}}^0\pi^- $ and $K_0^*(1430)^{0}\to K^+\pi^-$ are also considered. We find a significant dip structure around 1.8~GeV, associated to the $a_0(1710)$, in the ${{\bar{K}}^0K^+}$ invariant mass distribution, and the clear peaks of the $K_0^*(1430)$ in the ${\bar{K}}^0\pi^-$ and $K^+\pi^-$ invariant mass distributions, consistent with the {\it BABAR} measurements. We further estimate the branching fractions $\mathcal{B}(\eta_c \to \bar{K}^{*0}K^{\ast+}\pi^-)= 5.5\times10^{-3}$ and $\mathcal{B}(\eta_c \to \omega\rho^+\pi^-)= 7.9\times10^{-3}$. Our predictions can be tested by the BESIII and BelleII experiments in the future., Comment: 9 pages, 9 figures

Since the lowest $\Sigma^{*}$ state, with quantum numbers spin-parity $J^{P} =1/2^{-}$, is far from established experimentally and theoretically, we have performed a theoretical study on the $\Sigma^*_{1/2^-}$ photo-production within the Regge-effective Lagrangian approach. Taking into account that the $\Sigma^*_{1/2^-}$ couples to the $\bar{K}N$ channel, we have considered the contributions from the $t$-channel $K$ exchange diagram. Moreover, these contributions from $t$-channel $K^*$ exchange, $s$-channel nucleon pole, $u$-channel $\Sigma$ exchange, and the contact term, are considered. The differential and total cross sections of the process $\gamma n \to K^{+}\Sigma^{*-}_{1/2^-}$ are predicted with our model parameters. The results should be helpful to search for the $\Sigma^*_{1/2^-}$ state experimentally in future., Comment: 7 pages, 4 figures

We investigate the production of $X_b$ in the process $\Upsilon(5S,6S)\to \gamma X_b$, where $X_b$ is assumed to be a $B {\bar B}^*$ molecular state. Two kinds of meson loops of $B^{(*)}{\bar B}^{(*)}$ and $B_1^{\prime}{\bar B}^{(*)}$ were considered. To explore the rescattering mechanism, we calculated the relevant branching ratios using the effective Lagrangian based on the heavy quark symmetry. The branching ratios for the $\Upsilon(5S\,,6S) \to \gamma X_b$ were found to be at the orders of $10^{-7} \sim 10^{-6}$. Such sizeable branching ratios might be accessible at BelleII, which would provide important clues to the inner structures of the exotic state $X_b$., Comment: 9 pages, 2 figures, comments are welcome

Here we study the quark orbital angular momentum of the ground octet baryons employing an extended chiral constituent quark model, within which the baryon wave functions are taken to be superposition of the traditional $qqq$ and the $qqqq\bar{q}$ higher Fock components. Coupling between the two configurations is estimated using the $^3P_{0}$ quark-antiquark creation mechanism, and the corresponding coupling strength is determined by fitting the sea flavor asymmetry of the nucleon. The obtained numerical results show that the quark angular momentum of the nucleon, $\Sigma$, $\Lambda$ and $\Xi$ hyperons are in the range $0.10$-$0.30$. In addition, the quark angular momentum of all the hyperons are a little bit smaller than that of the nucleon. And the octet baryons spin fractions taken by the intrinsic quark orbital angular momentum could be up to $60\%$ in present model., Comment: 9 pages, 3 figures, 3 tables

We propose a phenomenological extended vector meson dominance model for the baryon electromagnetic structure, and it is found that the current experimental data on the $\Sigma$ and $\Xi$ electromagnetic form factors in the time-like region can be well described. Meanwhile, we can also reproduce the ratios of the total cross sections of reactions $e^+e^- \to \Sigma^+\bar{\Sigma}^-$, $\Sigma^0\bar{\Sigma}^0$, and $\Sigma^-\bar{\Sigma}^+$, which are $9.7 \pm 1.3 : 3.3 \pm 0.7 :1$ at center-of-mass energies from $2.3864$ to $3.02$ GeV. We also analytically continue the expression of the form factors to space-like region and estimate the charge radii of the $\Sigma$ and $\Xi$ hyperons. The result for the $\Sigma^-$ is in agreement with the experimental date., Comment: 7 pages, 5 figures. Typos are fixed

We investigate the decays of $B^0 \to K^0 X(3872)$ and $B^+ \to K^+ X(3872)$ based on the picture where the $X(3872)$ resonance is strongly coupled to the $D\bar{D}^* + c.c.$ channel. In addition to the decay mechanism where the $X(3872)$ resonance is formed from the $c\bar{c}$ pair hadronization with the short-distance interaction, we have also considered the $D\bar{D}^*$ rescattering diagrams in the long-distance scale, where $D$ and $\bar{D}^*$ are formed from $c$ and $\bar{c}$ separately. Because of the difference of the mass thresholds of charged and neutral $D\bar{D}^*$ channels, and the rather narrow width of the $X(3872)$ resonance, at the $X(3872)$ mass, the loop functions of $D^0\bar{D}^{*0}$ and $D^+\bar{D}^{*-}$ are much different. Taking this difference into account, the ratio of $\mathcal{B}[B^0\to K^0X(3872)]/\mathcal{B}[B^+ \to K^+ X(3872)] \simeq 0.5$ can be naturally obtained. Based on this result, we also evaluate the decay widths of $B_s^0 \to \eta(\eta') X(3872)$. It is expected that future experimental measurements of these decays can be used to elucidate the nature of the $X(3872)$ resonance., Comment: 7 pages, 5 figures

The three-body $\eta K^*\bar{K}^*$, $\pi K^*\bar{K}^*$ and $KK^*\bar{K}^*$ systems are investigated within the framework of fixed-center approximation to the Faddeev equations, where $K^*\bar{K}^*$ is treated as the scalar meson $f_0(1710)$. The interactions between $\pi$, $\eta$, $K$ and $K^*$ are taking from the chiral unitary approach. By scattering the $\eta$ meson on the clusterized $(K^*\bar{K}^*)_{f_0(1710)}$ system, we find a peak in the modulus squared of the three-body scattering amplitude and it can be associated as a bound state with quantum numbers $I^G(J^{PC})=0^+(0^{-+})$. Its mass and width are around 2054 MeV and 60 MeV, respectively. This state could be associated to the $\eta(2100)$ meson. For the $\pi (K^*\bar{K}^*)_{f_0(1710)}$ scattering, we find a bump structure around 1900-2000 MeV with quantum numbers $1^-({0^{-+}})$. While for the $K K^* \bar{K}^*)_{f_0(1710)}$ system, there are three structures. One of them is much stable and its mass is about 2130 MeV. It is expected that these theoretical predictions here could be tested by future experimental measurements, such as by the BESIII, BelleII and LHCb collaborations., Comment: 10 pages, 15 figures

Based on our previous work about the role of $a_0(1710)$ in the $D_s^+\to\pi^+K_S^0K_S^0$ decay [Phy. Rev. D 105, 116010 (2022)], we perform a further theoretical study of $a_0(1710)^+$ in the process $D^+_s \to \pi^0 a_0(1710)^+ \to \pi^0 K^+ K^0_S$. In addition to $a_0(1710)$, the contributions of $K^*$ and $a_0(980)$ are also taken into account. Firstly, we consider the contributions from the tree diagrams of $K^{*+} \to K^+\pi^0$ and $\bar{K}^{*0} \to \pi^0 \bar{K}^0$. Secondly, we describe the final state interaction of $K\bar{K}$ in the chiral unitary approach to study the contribution of $a_0(980)$, while the $a_0(1710)$ state is dynamically generated from the $K^*\bar{K}^*$ interaction, and then decays into $K^+\bar{K}^0$. Since the final $K^+ K_S^0$ state is in pure isospin $I=1$, the $D_s^+\to\pi^0K^+K_s^0$ decay is an ideal process to study the $a_0(1710)^+$ and $a_0(980)^+$ resonances. Based on our theoretical calculations, it is found that the recent experimental measurements on the $K^+K^0_S$, $\pi^0K^+$, and $\pi^0 K_S^0$ invariant mass distributions can be well reproduced, which supports the molecular $K^*\bar{K}^*$ nature of the scalar $a_0(1710)$ resonance., Comment: 8 pages, 8 figures

We study the radiative decays $Z_c(3900)/Z_c(4020) \to \gamma \chi_{cJ}(\gamma\chi_{cJ}^\prime)$ ($J=0, 1, 2$), with the assumption that the $Z_c(3900)$ and $Z_c(4020)$ couple strongly to $D\bar D^* +c.c$ and $D^*{\bar D}^*$ channel, respectively. By considering the contributions of intermediate charmed mesons triangle loops within an effective Lagrangian approach, it is shown that the calculated partial widths of $Z_c(3900) \to \gamma \chi_{cJ}$ are about a few hundreds keVs, while the obtained partial widths $Z_c(4020) \to \gamma \chi_{cJ}$ are about tens of keVs. The predicted partial widths of $Z_c(3900)\to\gamma\chi_{c0,1}^\prime$ are less than 1 keV, which mainly due to the very small phase space. For $Z_c(4020)\to\gamma\chi_{c0,2}^\prime$, the calculated partial widths are usually smaller than 1 keV. For the $Z_c(4020)\to\gamma\chi_{c1}^\prime$ process, the obtained partial widths can reach up to the order of 10 keV. Furthermore, the dependence of these ratios between different decay modes on the masses of $Z_c(3900)$ or $Z_c(4020)$ are also investigated, which may be a good quantity for the experiments. It is hoped that these calculations here could be tested by future experiments., Comment: 9 pages, 6 figures. Accepted by Physical Review D

In present work, spectrum of the $S$-wave fully-heavy tetraquark states $QQ\bar{Q}\bar{Q}$ ($Q=c,b$), i.e., $cc\bar{c}\bar{c}$, $bb\bar{b}\bar{b}$, $cc\bar{b}\bar{b}$/$bb\bar{c}\bar{c}$, $bc\bar{c}\bar{c}$/ $cc\bar{b}\bar{c}$, $bb\bar{c}\bar{b}$/$cb\bar{b}\bar{b}$, and $bc\bar{b}\bar{c}$ are systematically investigated within an nonrelativistic constituent quark model, in which the Instanton-induced and one-gluon-exchange interactions are taken into account as the residual spin-dependent hyperfine interaction. Our results show that the states with $cc\bar{c}\bar{c}$ and $bb\bar{b}\bar{b}$ components could be located around $ 6500$ MeV and $ 19200$ MeV, respectively. Based on our calculations, the new $X(6900)$ state observed by LHCb may be not a ground $cc\bar{c}\bar{c}$ tetraquark state, while it could be an orbitally or radially excited state of $cc\bar{c}\bar{c}$ system. On the other hand, the recently reported $X(6600)$ state by CMS and ATLAS can be explained as a ground $cc\bar{c}\bar{c}$ tetraquark state with spin-parity $J^{PC} =0^{++}$., Comment: Version to appear in Eur. Phys. J. C

The charmless decay processes of $X(3872)$ provide us a good platform to study the nature and the decay mechanism of $X(3872)$. Based on a molecular nature of $X(3872)$ as a $\bar{D}D^*$ bound state, we have investigated the charmless decays $X(3872) \to VV$ and $VP$ via intermediate $D^*{\bar D} +c.c.$ meson loops, where $V$ and $P$ stand for light vector and pseudoscalar mesons, respectively. We discuss three cases, i.e., pure neutral components ($\theta=0$), isospin singlet ($\theta=\pi/4$) and neutral components dominant ($\theta = \pi/6$), where $\theta$ is a phase angle describing the proportion of neutral and charged constituents. The proportion of neutral and charged constituent have an influence on the decay widths of $X(3872) \to VV$ and $VP$. With the coupling constant of $X(3872)$ to the $\bar{D}D^*$ channel obtained under the molecule ansatz of $X(3872)$ resonance, the predicted decay widths of $X(3872)\rightarrow VV$ are about tens of keVs, while the decay width can reach a few hundreds of keVs for $X(3872)\to VP$. The dependence of these ratios between different decay modes of $X(3872)\to VV$ and $X(3872)\to VP$ to the mixing angle $\theta$ is also investigated. It is expected that the theoretical calculations here can be tested by future experiments., Comment: 9 pages, 8 figures, submitted to Phys. Rev. D

In our previous works, we have analyzed the two-body strong decays of the low-lying $\Omega$ baryon states within a chiral quark model. The results show that the $\Omega(2012)$ resonance favors the three-quark state with $J^P=3/2^-$ classified in the quark model. With this assignment, in the present work we further study the three-body strong decay $\Omega(2012)\to \Xi^*(1530)\bar{K} \to \Xi\pi\bar{K}$ and coupled-channel effects on $\Omega(2012)$ from nearby channels $\Xi \bar{K}$, $\Omega\eta$ and $\Xi^*(1530)\bar{K}$ within the chiral quark model as well. It is found that the $\Omega(2012)$ resonance has a sizeable decay rate into the three-body final state $\Xi\pi\bar{K}$. The predicted ratio $R_{\Xi\bar{K}}^{\Xi\pi\bar{K}}=\mathcal{B}[\Omega(2012)\to \Xi^*(1530)\bar{K}\to \Xi\pi\bar{K}]/\mathcal{B}[\Omega(2012)\to \Xi\bar{K}]\simeq 12\%$ is close to the up limit $11\%$ measured by the Belle Collaboration in 2019, however, our predicted ratio is too small to be comparable with the recent data $0.97\pm 0.31$. Furthermore, our results show that the coupled-channel effects on the $\Omega(2012)$ is not large, its components should be dominated by the bare three-quark state, while the proportion of the molecular components is only $\sim 16\%$. To clarify the nature of $\Omega(2012)$, the ratio $R_{\Xi\bar{K}}^{\Xi\pi\bar{K}}$ is expected to be tested by other experiments., Comment: 7 pages, 3 figures

The molecular nature of $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ have been extensively studied from the perspective of their masses, decay properties, and production rates. In this work, we study the weak decays of $B \to \bar{D}^{(\ast)}D_{s0}^{*}(2317)$ and $B \to \bar{D}^{(\ast)}D_{s1}(2460)$ by invoking triangle diagrams where the $B$ meson first decays weakly into $\bar{D}^{(\ast)}D_{s}^{(\ast)}$ and $J/\psi K$($\eta_{c}K$), and then the $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ are dynamically generated by the final-state interactions of $D_{s}^{(\ast)}\eta$ and $D^{(\ast)}K$ via exchanges of $\eta$ and $D^{(\ast)}$ mesons. The obtained absolute branching fractions of Br$[B \to \bar{D}^{(\ast)}D_{s0}^{*}(2317)]$ are in reasonable agreement with the experimental data, while the branching fractions of Br$[B \to \bar{D}^{(\ast)}D_{s1}(2460)]$ are smaller than the experimental central values by almost a factor of two to three. We tentatively attribute such a discrepancy to either reaction mechanisms missing in the present work or the likely existence of a relatively larger $c\bar{s}$ component in the $D_{s1}(2460)$ wave function., Comment: 17 pages, 4 figures; to appear in Physical Review D

With the newly measurements of $X(3872) \to J/\psi\pi^+\pi^-$ from LHCb Collaboration, in addition to the dominant contribution from the $\rho^0$ meson, we perform a theoretical study on the contribution of $\omega$ meson in the $X(3872) \to J/\psi\pi^+\pi^-$ and $X(3872)\to J/\psi\pi^+\pi^-\pi^0$ processes. It is found that the recent experimental measurements on the $\pi^+ \pi^-$ invariant mass distributions can be well reproduced, and the ratio of the couplings between $X(3872) \to J/\psi\rho^0$ and $X(3872) \to J/\psi\omega$ is also evaluated. Within the parameters extracted from the $\pi^+ \pi^-$ invariant mass distributions of the $X(3872) \to J/\psi\pi^+\pi^-$ process, the branching fractions of the $X(3872) \to J/\psi \omega$ channel relative to that of the $X(3872) \to J/\psi \pi^+\pi^-\pi^0$ channel and the $\pi^+ \pi^- \pi^0$ invariant mass distributions of the $X(3872) \to J/\psi \pi^+\pi^-\pi^0$ decay are calculated, which gives a hint for the further high-statistic experiment., Comment: 8 pages, 3 figures

Recently, the Belle Collaboration has measured the $\Lambda_c^+ \to \eta \Lambda \pi^+$ decay and reported the $\eta\Lambda$ and $\Lambda\pi^+ $ invariant mass distributions, which show the clear signals of the resonances $\Lambda(1670)$ and $\Sigma(1385)$, respectively. Based on our previous works [Eur. Phys. J. C 76 (2016) 496 and Phys. Rev. D 95 (2017) 074024], we re-analyze this process by considering the $S$-wave $\eta\Lambda$ and $\eta\pi^+$ final state interactions within the chiral unitary approach, which dynamically generate the $\Lambda(1670)$ and $a_0(980)$, respectively. Our results are in good agreement with the Belle measurements, which supports the molecular nature of the $\Lambda(1670)$ and $a_0(980)$. In addition, the $\eta \pi^+$ invariant mass distributions are also computed and a cusp structure of $a_0(980)$ is cleary shown around the $K\bar{K}$ mass threshold., Comment: 8 pages, 9 figures

We have investigated the axial charges of the ground octet baryons within the extended chiral constituent quark model, where all the possible compact five-quark Fock components $qqq(q\bar{q}) (q=u, d, s)$ in the baryons are considered. The transition couplings between the three- and five-quark components in the baryons are assumed to be via the $^{3}P_{0}$ mechanism, which could reproduce the sea asymmetry in proton very well. The numerical results for the flavor-dependent axial charges of the octet baryons are comparable to those predicted by other theoretical approaches. It is shown that the singlet axial charges of the octet baryons, which should indicate total baryons spin arising from the spin of the quarks, fall in the range $0.45-0.75$ in present model. This is in consistent with the predictions by lattice QCD and chiral perturbation theory. It's also very interesting that the light quarks spin $\Delta u$ and $\Delta d$ in the $\Lambda$ baryon are of small but negative values, which exactly vanish in the traditional three-quark model., Comment: Submitted to Phys. Rev. C. arXiv admin note: text overlap with arXiv:2106.00866

We perform a theoretical study on the $D\bar{D}K$ three body system, using the fixed center approximation to the Faddeev equations, considering the interaction between $D$ and $K$, $D$ and $\bar{D}$ from the chiral unitary approach. We assume the scattering of $K$ meson on a clusterized system $D\bar{D}$, where a scalar meson $X(3720)$ could be formed. Thanks to the strong $DK$ interaction, where the scalar $D^*_{s0}(2317)$ meson is dynamically generated, a resonance structure shows up in the modulus squared of the three body $K$-$(D\bar{D})_{X(3720)}$ scattering amplitude and supports that a $D\bar{D}K$ bound state can be formed. The result is in agreement with previous theoretical studies, which claim a new excited hidden charm $K$ meson, $K_{c\bar{c}}(4180)$ with quantum numbers $I(J^P) = \frac{1}{2}(0^-)$ and mass about $4180$ MeV. It is expected that these theoretical results motivate its search in experimental measurements., Comment: 6 pages, 5 figures. Typos fixed, more discussions added

Spectrum of the low-lying hidden- and double-charm tetraquark states are investigated in a nonrelativistic quark potential model, where the Instanton-induced interaction is taken as the residual spin-dependent hyperfine interaction between quarks. The model parameters are fixed by fitting the spectrum of the ground hadron states. Our numerical results show that masses of several presently studied tetraquark states are close to those of the experimentally observed candidates of exotic meson, which indicates that the corresponding compact tetraquark components may take considerable probabilities in those observed exotic states., Comment: Version to appear in Eur. Phys. J. C

We present a theoretical study of $a_0(1710)$, the isovector partner of $f_0(1710)$, in the process $D^+_s \to \pi^+ K^0_SK^0_S$. The weak interaction part proceeds through the charm quark decay process: $c(\bar{s}) \to (s + \bar{d} + u)(\bar{s})$, while the hadronization part takes place in two mechanisms, differing in how the quarks from the weak decay combines into $\pi K^*$ with a quark-antiquark pair $q\bar{q}$ with the vacuum quantum numbers. In addition to the contribution from the tree diagram of the $K^{*+} \to \pi^+ K^0_S$, we have also considered the $K^*\bar{K}^*$ final-state interactions within the chiral unitary approach to generate the intermediate state $a_0(1710)$, then it decays into the final states $K^0_SK^0_S$. We find that the recent experimental measurements on the $K^0_SK^0_S$ and $\pi^+K^0_S$ invariant mass distributions can be well reproduced, and the proposed mechanism can provide valuable information on the nature of scalar $f_0(1710)$ and its isovector partner $a_0(1710)$., Comment: 9 pages, 9 figures, the version for PRD

Despite that quantum chromodynamics, the theory of strong interaction, has colorful quarks and gluons as its basic degrees of freedom, all fundamental particles participating the strong interaction that can be directly detected in experiments are colorless or color-singlet hadrons. This phenomenon is called color confinement. Because of that, the study of hadron spectroscopy is essential in improving our understanding of the nonperturbative regime of QCD and to reveal the mechanism of color confinement. The high-luminosity electron-positron collision machine under discussion, Super tau-Charm Facility (STCF), can play an essential role in hadron spectroscopy by discovering new hadron resonances and measuring properties of known hadrons with an unprecedented precision. In the following, we will discuss briefly the topics on hadron spectroscopy that will be investigated at STCF., Comment: Contribution to Snowmass 2021 RF07

The nonleptonic weak decay processes $\Omega_c \to \Omega\pi^+/\Omega(1P)\pi^+/\Omega(1D)\pi^+/\Omega(2S)\pi^+$ are studied using the constituent quark model. The branching fraction of $\Omega_c \to \Omega\pi^+$ is predicted to be $1.1\%$. Considering the newly observed $\Omega(2012)$ resonance as a conventional $1P$-wave $\Omega$ excite state with spin-parity $J^P=3/2^-$, the newly measured ratio $\mathcal{B}[\Omega_c\to \Omega(2012)\pi^+ \to (\Xi\bar{K})^-\pi^+ ]/\mathcal{B}[\Omega_c\to \Omega \pi^+]$ at Belle can be well understood. Besides, the production rates for the missing $1P-$wave state $\Omega (1^2P_{1/2^-})$, two spin quartet $1D-$wave states $\Omega (1^4D_{1/2^+})$ and $\Omega (1^4D_{3/2^+})$, and two $2S$-wave states $\Omega(2^2S_{1/2^+})$ and $\Omega(2^4S_{3/2^+})$ are also investigated. It is expected that these missing excited $\Omega$ baryons should have large potentials to be discovered through the nonleptonic weak decays of $\Omega_c$ in forthcoming experiments by Belle II and/or LHCb., Comment: 9 pages,3 figures

Based on the recently precise measurements of the electron-positron annihilation reactions into a neutron and anti-neutron pair by BESIII collaboration, the effective form factor of neutron was determined in the time like region, and it was found that the effective form factor of neutron is smaller than the ones of proton. The effective form factors of neutron shows a periodic behaviour, similar to the case of proton. Here, a compared analysis for $\Lambda$, $\Sigma^0$ and $\Xi^0$ is performed. Fits of the available data on the effective form factors of $\Lambda$, $\Sigma^0$ and $\Xi^0$ with charge zero, allow to show a universal phenomenon of the oscillation behavior in their effective form factors. However, this needs to be confirmed by future precise experiments. Both theoretical and experimental investigations of this phenomenon can shed light on the reaction mechanisms of the electron-positron annihilation process., Comment: 4 figures, 5 pages. Experimental data on $\Xi^0$ are included, title is slightly modified

Spectrum of the low-lying $\Omega_{cc}$ resonances with negative parity, which are assumed to be dominated by $sccq\bar{q}$ pentaquark components, is investigated using the chiral constituent quark model. Energies of the $\Omega_{cc}$ resonances are obtained by considering the hyperfine interaction between quarks by exchanging Goldstone boson. Possible $sccq\bar{q}$ configurations with spin-parity $1/2^{-}$, $3/2^{-}$ and $5/2^{-}$ are taken into account. Numerical results show that the lowest $\Omega_{cc}$ resonances with negative parity may lie at $4050 \pm 100$ MeV. In addition, the transitions of the $\Omega_{cc}$ resonance to a pseudoscalar meson and a ground baryon state are also investigated within the chiral Lagrangian approach. We expect that these $\Omega_{cc}$ resonances could be observed in the $\bar{D}\Xi_{c}$ channel by future experiments., Comment: typos corrected

Inspired by the recent discovery of a doubly charmed tetraquark state $T_{cc}^+$ by the LHCb Collaboration, we employ the effective Lagrangian approach to investigate the decay width of $T_{cc}^{+}\to D^{+} D^{0}\pi^{0}/D^{0} D^{0}\pi^{+}$ and $T_{cc}^{+}\to D^{0}D^{+}\gamma$ with the assumption that $T_{cc}^{+}$ is an isoscalar $DD^{\ast}$ molecule. We show that both the $T_{cc}\to D D\pi$ and $T_{cc}\to DD\gamma$ modes contribute to the decay width of $T_{cc}$, with the former being dominant. The resulting total decay width of about $\Gamma=63$ keV is smaller than the experimental decay width obtained from the Breit-Wigner fit of the LHCb data, $\Gamma=410\pm 165\pm 43^{+18}_{-38}$ keV, while close to the number obtained from the alternative unitary analysis, $\Gamma=48\pm 2^{+0}_{-14}$ keV, which supports the molecular nature of $T_{cc}$.

The near-threshold $e^+e^- \to \Lambda\bar{\Lambda}$ reaction is studied with the assumption that the production mechanism is due to a near-$\Lambda \bar{\Lambda}$-threshold bound state. The cross section of $e^+e^- \to \Lambda\bar{\Lambda}$ reaction is parametrized in terms of the electromagnetic form factors of $\Lambda$ hyperon, which are obtained with the vector meson dominance model. It is shown that the contribution to the $e^+e^- \to \Lambda\bar{\Lambda}$ reaction from a new narrow state with quantum numbers $J^{PC}=1^{--}$ is dominant for energies very close to threshold. The mass of this new state is around 2231 MeV, which is very close to the mass threshold of $\Lambda \bar{\Lambda}$, while its width is just a few MeV. This gives a possible solution to the problem that all previous calculations seriously underestimate the near-threshold total cross section of the $e^+e^- \to \Lambda\bar{\Lambda}$ reaction. We also note that the near-threshold enhancement can be also reproduced by including these well established vector resonances $\omega(1420)$, $\omega(1650)$, $\phi(1680)$, or $\phi(2170)$ with a Flatt${\rm\acute{e}}$ form for their total decay width, and a strong coupling to the $\Lambda\bar{\Lambda}$ channel., Comment: Published version

A formalism is discussed that allows for a straightforward treatment of the relativistic three-body problem while keeping the correct analytic structure. In particular it is demonstrated that sacrificing covariance for analyticity can be justified by the hierarchy of different contributions in the spirit of an effective field theory. For definiteness the formalism is applied to the $KK\bar K$ system allowing for the emergence of the $a_0(980)$ and the $f_0(980)$ as hadronic molecules. For simplicity all inelastic channels are switched off.

We have performed a study of the isovector, octet and singlet axial charges of the proton in an extended chiral constituent quark model, where all the possible $uudq\bar{q}$~($q=u,d,s$) five-quark Fock components in the proton wave function are taken into account. The $^3P_0$ quark-antiquark creation mechanism is assumed to account for the transition coupling between three- and five-quark components in proton, and the corresponding transition coupling strength is fixed by fitting the intrinsic sea flavor asymmetry $\bar{d}-\bar{u}$ data for proton. Accordingly, with all the parameters fixed by empirical values, the probabilities of the intrinsic five-quark Fock components in proton wave function should be $\sim30 - 50\%$, which lead to the numerical results for quark spin $\Delta u$, $\Delta d$ and $\Delta s$, as well the axial charges of proton consistent with the experimental data and predictions by other theoretical approaches., Comment: 9 pages, 4 tables

Lepton scattering is an established ideal tool for studying inner structure of small particles such as nucleons as well as nuclei. As a future high energy nuclear physics project, an Electron-ion collider in China (EicC) has been proposed. It will be constructed based on an upgraded heavy-ion accelerator, High Intensity heavy-ion Accelerator Facility (HIAF) which is currently under construction, together with a new electron ring. The proposed collider will provide highly polarized electrons (with a polarization of $\sim$80%) and protons (with a polarization of $\sim$70%) with variable center of mass energies from 15 to 20 GeV and the luminosity of (2-3) $\times$ 10$^{33}$ cm$^{-2}$ s$^{-1}$. Polarized deuterons and Helium-3, as well as unpolarized ion beams from Carbon to Uranium, will be also available at the EicC. The main foci of the EicC will be precision measurements of the structure of the nucleon in the sea quark region, including 3D tomography of nucleon; the partonic structure of nuclei and the parton interaction with the nuclear environment; the exotic states, especially those with heavy flavor quark contents. In addition, issues fundamental to understanding the origin of mass could be addressed by measurements of heavy quarkonia near-threshold production at the EicC. In order to achieve the above-mentioned physics goals, a hermetical detector system will be constructed with cutting-edge technologies. This document is the result of collective contributions and valuable inputs from experts across the globe. The EicC physics program complements the ongoing scientific programs at the Jefferson Laboratory and the future EIC project in the United States. The success of this project will also advance both nuclear and particle physics as well as accelerator and detector technology in China., Comment: EicC white paper, written by the whole EicC working group

From the amplitude analysis of the $D^+_s \to \pi^+ \pi^0 \eta$ decay, the BESIII Collaboration firstly observed the $D^+_s \to a_0(980)^+\pi^0$ and $D^+_s \to a_0(980)^0\pi^+$ decay modes, which are expected to occur through the pure $W$-annihilation processes. The measured branching fraction $\mathcal{B}[D_{s}^{+}\to a_{0}(980)^{+(0)}\pi^{0(+)},a_{0}(980)^{+(0)}\to \pi^{+(0)}\eta]$ is, however, found to be larger than those of known $W$-annihilation decays by one order of magnitude. This apparent contradiction can be reconciled if the two decays are induced by internal $W$-conversion or external $W$-emission mechanisms instead of $W$-annihilation mechanism. In this work, we propose that the $D^+_s$ decay proceeds via both the external and internal $W$-emission instead of $W$-annihilation mechanisms. In such a scenario, we perform a study of the $D^+_s \to \pi^+\pi^0\eta$ decay by taking into account the contributions from the tree diagram $D^+_s \to \rho^+ \eta \to \pi^+ \pi^0 \eta$ and the intermediate $\rho^+ \eta$ and $K^*\bar{K}/K\bar{K}^*$ triangle diagrams. The intermediate $a_0(980)$ state can be dynamically generated from the final state interactions of coupled $K \bar{K}$ and $\pi \eta$ channels, and it is shown that the experimental data can be described fairly well, which supports the interpretation of $a_0(980)$ as a molecular state., Comment: 14 pages, 8 figures

We have investigated the process of $\Lambda_b\to \Lambda D\bar{D}$, by taking into account the contributions from the $s$-wave $D\bar{D}$ interaction within the coupled-channel unitary approach, and the intermediate $\psi(3770)$ resonance. In addition to the peak of the $\psi(3770)$, an enhancement near the $D\bar{D}$ mass threshold is found in the $D\bar{D}$ invariant mass distributions, which should be the reflection of the $D\bar{D}$ bound state. We would like to encourage our experimental colleagues to measure the $D\bar{D}$ invariant mass distribution of the $\Lambda_b\to \Lambda D\bar{D}$ process, which is crucial to search for the $D\bar{D}$ bound state and to understand the heavy-hadron heavy-hadron interactions., Comment: 7 pages, 9 figures, comments are welcome

Based on the recently measurements of the $e^{+} e^{-} \to \Sigma^{+} \bar{\Sigma}^{-}$ and $e^{+} e^{-} \to \Sigma^{-} \bar{\Sigma}^{+}$ processes, the electromagnetic form factors of the hyperon $\Sigma^+$ and $\Sigma^-$ in the timelike region are investigate by using the vector meson dominance model. We have included the contributions from the $\rho$, $\omega$ and $\phi$ mesons. The model parameters are determined with the BESIII experimental data on the timelike effective form factors $|G_{\rm eff}|$ of $\Sigma^{+}$ and ${\Sigma}^{-}$ for center-of-mass energy from 2.3864 to 3.02 GeV. Then, we analytically continue the electromagnetic form factors to spacelike region and evaluate the spacelike form factors of $\Sigma^+$ and $\Sigma^-$. The obtained electromagnetic form factors of the $\Sigma^+$ and $\Sigma^-$ baryons are comparable with other model calculations., Comment: 5 pages, 5 figures.Accepted for publication in communications in theoretical physics

We study the $Z_{cs}(3985)$ state recently observed by the BESIII Collaboration in the one-boson-exchange model, assuming that it is a $\bar{D}_s^{(*)}D^{(*)}$ molecule, which has the quark content $c\bar{c}s\bar{q}$ with $q = u$, $d$. It is shown that the one-boson-exchange potential is too weak to generate dynamcally $\bar{D}_s D$, $\bar{D}^*_s D$, and $\bar{D}_sD^*$ states, while for the case of $\bar{D}^*_s D^*$, very loosely bound states are likely, with binding energies of the order of several MeV. We conclude that, the observed $Z_{cs}(3985)$ state, if confirmed by further experiments, cannot be a pure hadronic molecular state of $\bar{D}_s D^*$ and $\bar{D}_s^*D$ and could consist of large components of compact nature., Comment: During the numerical calculation, an unfortunate coding error occurred which mis-identified the exchange of $K$ and $K^*$ mesons, which could not happen. As a result, the OBE potential could not provide a relevant binding mechanism for the $\bar{D}_s^{(*)}D^{(*)}$ systems studied in the present work

We have studied the $J/\psi\phi$ mass distribution of the process $B^+\to J/\psi\phi K^+$ from the threshold to about 4250 MeV, by considering the contribution of the $X(4140)$ with a narrow width, together with the $X(4160)$ state. Our results show that the cusp structure at the $D^*_s\bar{D}^*_s$ threshold is tied to the molecular nature of the $X(4160)$ state., Comment: 5 pages, 3 figures, contribution to the 18th International Conference on Hadron Spectroscopy and Structure (HADRON 2019)