The three pentaquark states, $P_{c}(4312)$, $P_{c}(4440)$, and $P_{c}(4457)$, discovered by the LHCb Collaboration in 2019, can be nicely arranged into a multiplet of $bar{D}^{(ast)}Sigma_{c}^{(ast)}$ of seven molecules dictated by heavy quark spin s
ymmetry. In this work we employ the effective Lagrangian approach to investigate the two decay modes of $P_{c}(4457)$, $P_{c}(4457) to P_{c}(4312) pi$ and $P_{c}(4457) to P_{c}(4312) gamma$, via the triangle mechanism, assuming that $P_{c}(4457)$ and $P_{c}(4312)$ are $bar{D}^{ast}Sigma_{c}$ and $bar{D}Sigma_{c}$ bound states but the spin of $P_{c}(4457)$ can be either 1/2 or 3/2. Our results show that the spin of $P_{c}(4457)$ can not be discriminated through these two decay modes. The decay widths of $P_{c}(4457) to P_{c}(4312) pi$ and $P_{c}(4457) to P_{c}(4312) gamma$ are estimated to be of order of 100 keV and 1 keV, respectively. The ratio of the partial decay widths of $P_{c}(4457) to P_{c}(4312) pi$ to $P_{c}(4457) to P_{c}(4312) gamma$ is similar to the ratio of $D^{ast}to Dpi$ to $D^{ast}to Dgamma$, which could be used to check the molecular nature of $P_{c}(4457)$ and $P_{c}(4312)$ if they can be observed in the future.
Recently, the LHCb Collaboration reported on the evidence for a hidden charm pentaquark state with strangeness, i.e., $P_{cs}(4459)$, in the $J/psiLambda$ invariant mass distribution of the $Xi_b^-to J/psi Lambda K^-$ decay. In this work, assuming th
at $P_{cs}(4459)$ is a $bar{D}^*Xi_c$ molecular state, we study this decay via triangle diagrams $Xi_brightarrow bar{D}_s^{(*)}Xi_cto (bar{D}^{(*)}bar{K})Xi_cto P_{cs} bar{K}to (J/psiLambda) bar{K}$. Our study shows that the production yield of a spin 3/2 $bar{D}^*Xi_c$ state is approximately one order of magnitude larger than that of a spin $1/2$ state due to the interference of $bar{D}_sXi_c$ and $bar{D}_s^*Xi_c$ intermediate states. We obtain a model independent constraint on the product of couplings $g_{P_{cs}bar{D}^*Xi_c}$ and $g_{P_{cs}J/psiLambda}$. With the predictions of two particular molecular models as inputs, we calculate the branching ratio of $Xi_b^-to (P_{cs}to)J/psiLambda K^- $ and compare it with the experimental measurement. We further predict the lineshape of this decay which could be useful to future experimental studies.
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 $D^+_s to a_0(980)^0pi^+$ decay modes, which are expected to occur through the pure $W$-annihilation proces
ses. 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 $D^+_s to pi^+pi^0eta$ 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 $K^*bar{K}/Kbar{K}^*$ 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.
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 $cbar{c}sbar{q}$ 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.
Lately, the LHCb Collaboration reported the discovery of two new states in the $B^+rightarrow D^+D^- K^+$ decay, i.e., $X_0(2866)$ and $X_1(2904)$. In the present work, we study whether these states can be understood as $D^*bar{K}^*$ molecules from t
he perspective of their two-body strong decays into $D^-K^+$ via triangle diagrams and three-body decays into $D^*bar{K}pi$. The coupling of the two states to $D^*bar{K}^*$ are determined from the Weinberg compositeness condition, while the other relevant couplings are well known. The obtained strong decay width for the $X_0(2866)$, in marginal agreement with the experimental value within the uncertainty of the model, hints at a large $D^*bar{K}^*$ component in its wave function. On the other hand, the strong decay width for the $X_1(2904)$, much smaller than its experimental counterpart, effectively rules out its assignment as a $D^*bar{K}^*$ molecule.
Employing the covariant baryon chiral perturbation theory, we calculate the leading and next-to-leading order two-pion exchange (TPE) contributions to $NN$ interaction up to order $O(p^3)$. We compare the so-obtained $NN$ phase shifts with $2leq Lleq
6$ and mixing angles with $2leq Jleq6$ with those obtained in the nonrelativistic baryon chiral perturbation theory, which allows us to check the relativistic corrections to the medium-range part of $NN$ interactions. We show that the contributions of relativistic TPE are more moderate than those of the nonrelativistic TPE. The relativistic corrections play an important role in F-waves especially the $^3text{F}_2$ partial wave. Moreover, the relativistic results seem to converge faster than the nonrelativistic results in almost all the partial waves studied in the present work, consistent with the studies performed in the one-baryon sector.
The LHCb pentaquarks -- the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ -- have been theorized to be $Sigma_c bar{D}$ and $Sigma_c bar{D}^*$ S-wave molecules. Here we explore the possibility that two of these pentaquarks -- the $P_c(4440)$ and $P_c(4457
)$ -- contain in addition a $Lambda_c(2595) bar{D}$ component in P-wave. We will analyze the effects of this extra channel within two effective field theories: the first one will be a standard contact-range effective field theory and the second one will include the non-diagonal pion dynamics connecting the $Sigma_c bar{D}^*$ and $Lambda_c(2595) bar{D}$ channels, which happens to be unusually long-ranged. The impact of the coupled-channel dynamics between the $Sigma_c bar{D}^*$ and $Lambda_c(2595) bar{D}$ components is modest at best for the $P_c(4440)$ and $P_c(4457)$, which will remain to be predominantly $Sigma_c bar{D}^*$ molecules. However, if the quantum numbers of the $P_c(4457)$ are $J^P = frac{1}{2}^-$, the coupled-channel dynamics is likely to induce the binding of a $Lambda_c(2595) bar{D}$ S-wave molecule (coupled to $Sigma_c bar{D}^*$ in P-wave) with $J^P = frac{1}{2}^+$ and a mass similar to the $P_c(4457)$. If this is the case, the $P_c(4457)$ could actually be a double peak containing two different pentaquark states.
We report on a theoretical study of the newly observed $Omega(2012)$ resonance in the nonleptonic weak decays of $Omega_c^0 to pi^+ bar{K}Xi^*(1530) (eta Omega) to pi^+ (bar{K}Xi)^-$ and $pi^+ (bar{K}Xipi)^-$ via final-state interactions of the $bar{
K}Xi^*(1530)$ and $eta Omega$ pairs. The weak interaction part is assumed to be dominated by the charm quark decay process: $c(ss) to (s + u + bar{d})(ss)$, while the hadronization part takes place between the $sss$ cluster from the weak decay and a quark-antiquark pair with the quantum numbers $J^{PC} = 0^{++}$ of the vacuum, produces a pair of $bar{K}Xi^*(1530)$ and $eta Omega$. Accordingly, the final $bar{K}Xi^*(1530)$ and $eta Omega$ states are in pure isospin $I= 0$ combinations, and the $Omega_c^0 to pi^+ bar{K}Xi^*(1530)(eta Omega) to pi^+ (bar{K}Xi)^-$ decay is an ideal process to study the $Omega(2012)$ resonance. With the final-state interaction described in the chiral unitary approach, up to an arbitrary normalization, the invariant mass distributions of the final state are calculated, assuming that the $Omega(2012)$ resonance with spin-parity $J^P = 3/2^-$ is a dynamically generated state from the coupled channels interactions of the $bar{K}Xi^*(1530)$ and $eta Omega$ in $s$-wave and $bar{K}Xi$ in $d$-wave. We also calculate the ratio, $R^{bar{K}Xipi}_{bar{K}Xi} = {rm Br}[Omega_c^0 to pi^+ Omega(2012)^- to pi^+ (bar{K}Xi pi)^-] / {rm Br}[Omega_c^0 to pi^+ Omega(2012)^- to pi^+ (bar{K}Xi)^-$]. The proposed mechanism can provide valuable information on the nature of the $Omega(2012)$ and can in principle be tested by future experiments.
Recently, the Belle collaboration measured the ratios of the branching fractions of the newly observed $Omega(2012)$ excited state. They did not observe significant signals for the $Omega(2012) to bar{K} Xi^*(1530) to bar{K} pi Xi$ decay, and reporte
d an upper limit for the ratio of the three body decay to the two body decay mode of $Omega(2012) to bar{K} Xi$. In this work, we revisit the newly observed $Omega(2012)$ from the molecular perspective where this resonance 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. With the model parameters for the $d$-wave interaction, we show that the ratio of these decay fractions reported recently by the Belle collaboration can be easily accommodated.
We study the scattering of a pseudoscalar meson off one ground state octet baryon in covariant baryon chiral perturbation theory (BChPT) up to the next-to-next-to-leading order. The inherent power counting breaking terms are removed within extended-o
n-mass-shell scheme. We perform the first combined study of the pion-nucleon and kaon-nucleon scattering data in covariant BChPT and show that it can provide a reasonable description of the experimental data. In addition, we find that it is possible to fit the experimental baryon masses and the pion-nucleon and kaon-nucleon scattering data simultaneously at this order, thus providing a consistent check on covariant BChPT. We compare the scattering lengths of all the pertinent channels with available experimental data and those of other approaches. In addition, we have studied the leading order contributions of the virtual decuplet and found that they can improve the description of the $pi N$ phase shifts near the $Delta(1232)$ peak, while they have negligible effects on the description of the $K N$ phase shifts.
