Search

Weak radiative hyperon decays represent a rich interplay between weak interactions and the internal structure of baryons, offering profound insights into Quantum Chromodynamics and weak interactions. Recent experimental observations, particularly from BESIII, have revealed deviations from theoretical predictions. These deviations could signal new physics or the need for refined theoretical models incorporating intermediate resonance effects. This review discusses recent theoretical advancements and key experimental findings, focusing on recent measurements from BESIII and their implications for strong interactions and baryon structure., Comment: 9 pages, 5 figures, 9 tables

The hadronic molecular picture of the observed exotic states has inspired numerous investigations into few-body systems. Recently, the lattice effective field theory studied the effect of a three-body interaction on the binding energy of the $DD^{*}K$ system, revealing an intriguing phenomenon in the binding energy. This work uses the Gaussian expansion method to explore the underlying physics. Our results show that as the repulsive three-body interaction strengthens, the spatial size of the $DD^{(*)}K$ bound state gradually increases. Further enhancement of the three-body interaction causes the $DD^{(*)}K$ three-body bound state to break into a $D^{(*)}K$ two-body bound state, accompanied by a distant $D$ meson. The identical nature of the two $D$ mesons leads to the fact that the $DDK$ system consistently resembles an isosceles triangle-shaped spatial configuration., Comment: 8 pages, 6 figures

Understanding nuclear structure, reactions, and the properties of neutron stars from \textit{ab initio} calculations from the nucleon degrees of freedom has always been a primary goal of nuclear physics, in which the microscopic nuclear force serves as the fundamental input. So far, the Weinberg chiral nuclear force, first proposed by the Nobel laureate Weinberg, has become the \textit{de facto} standard input for nuclear \textit{ab initio} studies. However, compared to their non-relativistic counterparts, relativistic \textit{ab initio} calculations, which describe better nuclear observables, have only begun. The lack of modern relativistic nucleon-nucleon interactions is an important issue restricting their development. In this work, we briefly review the development and status of the Weinberg chiral nuclear force, as well as its limitations. We further present a concise introduction to the relativistic chiral nuclear force, show its description of the scattering phase shifts and observables such as differential cross sections, and demonstrate its unique features. Additionally, we show that the relativistic framework could be naturally extended to the antinucleon-nucleon interaction., Comment: 16 pages, to appear in the Memorial Issue dedicated to the late Professor Tom Kuo in the International Journal of Modern Physics E

The discovery of numerous new hadrons in the last two decades provides an unprecedented opportunity to explore the non-perturbative QCD and hadron structure. Many of these hadrons cannot be understood as conventional $q\bar{q}$ mesons and $qqq$ baryons but instead as hadronic molecules. The most essential ingredient in the hadronic molecule picture is the hadron-hadron interactions. Therefore, It is vital to calculate/verify the underlying hadron interactions both theoretically and experimentally. In this letter, utilizing the model-independent $DK$ potential extracted from the relevant experimental data, we predict an exotic $J^{PC}=0^{--}$ $\bar{D}_sDK$ three-body hadronic molecule with a mass of $4310^{+14}_{-24}$ MeV. This state is exotic in two ways. First, the quantum number of $J^{PC}=0^{--}$ cannot be formed by conventional $c\bar{c}$ mesons. Second, it cannot be a two-body state $\bar{D}_sD_{s0}^*$ because their interaction is weak rather robust. We further demonstrate that the $B^+ \to {D}^{*-}D^+ K^+$ decay could be a suitable channel for searching for the predicted exotic state.

In-medium $\Lambda N$ interactions are crucial in hypernuclei and neutron star physics. In this work, we study the in-medium $\Lambda N$ interaction within the relativistic Brueckner-Hartree-Fock (RBHF) framework, employing the leading-order covariant chiral hyperon/nucleon-nucleon forces for the first time. We demonstrate that a consistent description of both the experimental cross-section data and the `empirical value' of the $\Lambda$ single-particle potential can be achieved. This contrasts with the majority of studies in the non-relativistic framework, where higher-order two-body chiral forces are typically required. This study offers a new perspective on the in-medium $\Lambda N$ interactions, urgently needed in relativistic \textit{ab initio} hypernuclear physics studies., Comment: 10 pages, 5 figures; Comments and suggestions are welcome

We discuss the landscape of flavor physics at the Circular Electron-Positron Collider (CEPC), based on the nominal luminosity outlined in its Technical Design Report. The CEPC is designed to operate in multiple modes to address a variety of tasks. At the $Z$ pole, the expected production of 4 Tera $Z$ bosons will provide unique and highly precise measurements of $Z$ boson couplings, while the substantial number of boosted heavy-flavored quarks and leptons produced in clean $Z$ decays will facilitate investigations into their flavor physics with unprecedented precision. We investigate the prospects of measuring various physics benchmarks and discuss their implications for particle theories and phenomenological models. Our studies indicate that, with its highlighted advantages and anticipated excellent detector performance, the CEPC can explore beauty and $\tau$ physics in ways that are superior to or complementary with the Belle II and Large-Hadron-Collider-beauty experiments, potentially enabling the detection of new physics at energy scales of 10 TeV and above. This potential also extends to the observation of yet-to-be-discovered rare and exotic processes, as well as testing fundamental principles such as lepton flavor universality, lepton and baryon number conservation, etc., making the CEPC a vibrant platform for flavor physics research. The $WW$ threshold scan, Higgs-factory operation and top-pair productions of the CEPC further enhance its merits in this regard, especially for measuring the Cabibbo-Kobayashi-Maskawa matrix elements, and Flavor-Changing-Neutral-Current physics of Higgs boson and top quarks. We outline the requirements for detector performance and considerations for future development to achieve the anticipated scientific goals.

Inspired by the newly reported $B\to D^*(\to D\pi)\ell\bar{\nu}_\ell$ differential decay rates by the Belle and Belle II Collaborations, we revisit the $V_{cb}$ puzzle in semi-leptonic $B\to D^*$ decays, considering the latest lattice QCD simulations and light-cone sum rule results. We examine the commonly used Caprini-Lellouch-Neubert (CLN), Boyd-Grinstein-Lebed (BGL), and heavy quark effective theory (HQET) parameterizations. We show that these three parameterizations lead to consistent results and reconfirm the $V_{cb}$ puzzle. Then, we use a state-of-the-art Bayesian method to estimate the impact of higher-order terms beyond the present HQET expansion on the uncertainty of $V_{cb}$. We show that higher-order effects cannot eliminate the deviation between the exclusive and inclusive determinations of $V_{cb}$. Finally, utilizing the best-fit results obtained in the HQET parameterization as inputs, we predict the relevant observables, i.e., $R_{D^*}$, $F_L^{D^*}$, and $P_\tau^{D^*}$, sensitive to new physics in the $B\to D^*\ell\bar{\nu}_\ell$ decays. We conclude that lepton-universality violations still exist in the $b\to c\tau\nu$ transitions., Comment: 21 pages, 1 figures, 9 tables

We have studied the $N D^* \bar{K}^*$ system in the framework of the Fixed Center Approximation to the Faddeev equations, taking the exotic $D^* \bar{K}^* $ system as the cluster and allowing the N to interact with the components of the cluster. Previous studies have determined the existence of three states of spin $0,1,2$ for the $D^* \bar{K}^* $ system, the one of spin $0$ associated to the $X_0(2900)$ state observed by the LHCb collaboration. From this perspective, we find five states with total spin $1/2,3/2,5/2$, with bindings from $10$ to $30$ MeV and widths below $60$ MeV, which could be well identified. We also discuss the decay channels of these states that should help in future experimental searches of these states., Comment: 5 pages, 2 figures

In this paper, we investigate the helicity form factors (HFFs) of the $B_{(s)}$-meson decay into a scalar meson with a mass larger than 1~GeV, {\it i.e.,} $B \to a_0(1450)$, $B_{(s)} \to K_0^*(1430)$ and $B_{s} \to f_0(1500)$ by using light-cone sum rules approach. We take the standard currents for correlation functions. To enhance the precision of our calculations, we incorporate the next-to-leading order (NLO) corrections and retain the scalar meson twist-3 light-cone distribution amplitudes. Furthermore, we extend the HFFs to the entire physical $q^2$ region employing a simplified $z$-series expansion. At the point of $q^2=1\rm{~GeV^2}$, all NLO contributions to the HFFs are negative, with the maximum contribution around $25\%$. Then, as applications of these HFFs, we analyze the differential decay widths, branching ratios, and lepton polarization asymmetries for the semi-leptonic $B_{(s)} \to S \ell \bar{\nu}_\ell$, FCNC $B_{(s)} \to S \ell \bar{\ell}$ and rare $B_{(s)} \to S \nu \bar{\nu}$ decays. Our results are consistent with existing studies within uncertainties. The current data still suffer from large uncertainties and need to be measured more precisely, which can lead to a better understanding of the fundamental properties of light scalar mesons., Comment: 20 pages, 5 figures

The Weinberg compositeness criterion dictates that a pure shallow bound state is characterized by a large scattering length $a_0\gg\mathcal{O}(1/\beta)$ and a positive effective range $r_0$ that naturally scales to the size of $\mathcal{O}(1/\beta)$, where $1/\beta$ signifies the interaction range. In constructing the contact-range effective field theory (EFT) up to the next-to-leading order to describe the pentaquarks $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ observed by the LHCb collaboration in 2019, we match the effective range $r_0$ for these pentaquarks with the low-energy couplings within the EFT framework. Three different schemes are used to connect the couplings with the effective range. We find positive effective ranges $r_0$ of the natural size of $\mathcal{O}(1/\beta)$ for the spin configurations $J^P=\frac{3}{2}^-$ for $P_c(4440)$ and $J^P=\frac{1}{2}^-$ for $P_c(4457)$ within the molecular $\bar{D}^* \Sigma_c$ description. Additionally, predictions from the power counting for low-energy couplings or Wilsonian coefficients suggest that, under heavy quark spin symmetry, the broad $P_c(4380)$ resonance, discovered by the LHCb collaboration in 2015, when considered as part of the single-channel $\bar{D}^{(*)} \Sigma_c^{(*)}$ molecular system alongside $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$, has a mass of approximately $4376$ $\rm{MeV}$., Comment: 10 pages, 3 figures, 3 tables

We explore the potential of conducting an experiment on the Chinese Space Station (CSS) to constrain beyond-the-standard-model (BSM) long-range spin- and velocity-dependent interactions, which are mediated by the exchange of an ultralight $\left(m_{z^{\prime}}<10^{-10}\text{eV}\right)$ or massless intermediate vector boson. We demonstrate that the proposed experiment on the CSS offers several advantages compared to ground-based experiments. The high speed can enhance the sensitivity to velocity-dependent interactions. The periodicity allows efficient extraction of signals from background noises, thereby strengthening the experiment's accuracy. Combining these advantages, one can improve the existing bounds on such interactions by up to five orders of magnitude. With advancements in sensor technology, we anticipate a further enhancement of four orders of magnitude, resulting in a total potential improvement of up to nine orders of magnitude., Comment: 6 pages, 4 figures; comments welcome

A recent analysis of the LHCb data [Phys. Rev. D 105 (2022) L031503] obtained a sizable negative effective range for the $X(3872)$. This has attracted intensive discussions on whether $X(3872)$ can be deemed as a $D\bar{D}^*$ molecular state. This work explicitly demonstrates that the negative effective range of the $X(3872)$ does not contradict the molecular picture, adopting an effective field theory formulation of the $D\bar{D}^*$ interaction that can simultaneously reproduce the binding energy and effective range of the $X(3872)$. We elaborate on the implications of the large negative effective range of $X(3872)$ and the small binding energy on the underlying $D\bar{D}^*$ interaction. Such results are relevant for a better understanding of hadronic molecules and their binding mechanism., Comment: 6 pages, 4 figures; Comments and suggestions are welcome

The two-body strong decays of the $f_0(1500)$, $f_0(1710)$, $a_0(1710)$, $f_2(1270)$, $f_2'(1525)$, and $K_2^*(1430)$ resonances are investigated, assuming them as dynamically generated states of two vector mesons via $s$-wave interactions. The partial decay widths of all the possible two-body pseudoscalar meson-pseudoscalar meson final states are calculated considering the triangular diagrams. It is found that the ratios of branching fractions are similar to the previous results for most channels, which were obtained by using the real-axis method and considering the box diagrams. However, there are also differences. In addition, our focus is on the partial decay widths. More precise experimental measurements are needed to test the model calculations and determine the nature of these scalar and tensor mesons. It is anticipated that the BES\uppercase\expandafter{\romannumeral3}, Belle\uppercase\expandafter{\romannumeral2} and LHCb collaborations will conduct these measurements in the future., Comment: 10 pages, 2 figures

The ground-breaking discovery of the first fully charmed tetraquark state $X(6900)$ in the $J/\psi J/\psi$ invariant mass distribution by the LHCb collaboration has inspired intensive theoretical studies. Various interpretations, such as molecular states, compact tetraquark states, and coupled-channel effects, have been proposed for these states. Of particular interest is the ongoing search for the triple-$J/\psi$ state--a fully-charmed hexaquark state. To deepen our understanding of the triple-$J/\psi$ state and to guide future experimental searches, we study the triple-$J/\psi$ system in this work employing the Gaussian expansion method and the $J/\psi J/\psi$ potential parameterized to yield a shallow bound state, as suggested in several theoretical works. Our results support a triple-$J/\psi$ bound state, even in cases where the attractive interaction between the two $J/\psi$ mesons is very weak. Moreover, our analysis implies the Efimov effect in the triple-$J/\psi$ system. In addition, we extend our investigation to the triple-$\Upsilon (1S)$ system and obtain results similar to those for the triple-$J/\psi$ system., Comment: 8 pages, 3 figures, 4 tables; comments welcome

The decay behavior of an exotic state can be used to probe its internal structure. We note that the hidden-charm pentaquark states, $P_{\psi}^{N}(4312)$, $P_{\psi}^{N}(4440)$, and $P_{\psi}^{N}(4457)$, have only been observed in the $J/\psi p$ channel. In this work, we employ the effective Lagrangian approach to systematically investigate the two-body and three-body decays of the heavy quark spin symmetry multiplet of hadronic molecules $\bar{D}^{(*)}\Sigma_c^{(*)}$. Our results show that the partial decay widths of the hidden-charm pentaquark molecules into $\bar{D}^{(*)}\Lambda_c \pi$ are sizable so that $\bar{D}^{(*)}\Lambda_c \pi$ are promising channels to search for them, which can help clarify their molecular nature., Comment: This version is to be published in Phys. Rev. D

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

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: 9 pages, 2 figures, the version of publication in Chinese Physics Letters

Motivated by the recent progress in developing high-precision relativistic chiral nucleon-nucleon interactions, we study the antinucleon-nucleon interaction in a hybrid approach where the real part of the potential is constructed in the leading-order covariant chiral effective field theory, and the imaginary part is described following the procedure adopted in the heavy baryon chiral effective field theory. The phase shifts and inelasticities with $J\leq 1$ are obtained and compared to those calculated in the next-to-leading order heavy baryon chiral effective field theory. For most partial waves, the descriptions of phase shifts and inelasticities in the hybrid approach are comparable to those in the next-to-leading order heavy baryon chiral effective field theory, confirming the relatively faster convergence of the relativistic approach observed in the nucleon-nucleon sector. In addition, we search for bound states/resonances near the $\bar{N}N$ threshold and find several structures that can be associated with those states recently observed by the BESIII Collaboration.

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: 10 pages, 5 figures, the version of publication in PRD

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

Chiral trajectories of dynamically generated resonances are intimately connected to the SU(3) breaking pattern and their nature. From an analysis of a recent LQCD simulation on the $\pi\Sigma-\bar{K}N$ scattering for $I=0$ and the study of the quark mass dependence of the octet baryon masses, we determine for the first time unambiguously the trajectories of the two poles associated to the $\Lambda(1405)$ towards the symmetric point over the $\mathrm{Tr}[M]=C$ trajectory accurately. At $m_\pi\simeq 200$ MeV, our results are consistent with the lattice simulations, and the extrapolations to the physical point, based on the NLO chiral Lagrangians, agree well with existing experimental analyses. We predict qualitatively similar trajectories at LO and up to NLO, consistent with the LO interaction's dominance. At the SU(3) symmetric point up to NLO in this trajectory, the lower pole is located at $E^{(1)}=1583(5)(1)$ MeV, being dominantly a SU(3) singlet, while the higher pole belongs to the octet representation with a mass of $E^{(8)}=1585(8)(2)$ MeV. We also make predictions on the evolution of the two poles over the $m_s=m_{s,\mathrm{phy}}$ trajectory. This can be tested in future LQCD simulations and experimental measurements., Comment: Updating in this version: prediction of the trajectories of the three poles with $m_s=m_{s,\mathrm{phy}}$. No results are changed. Comments are welcome

The decays of exotic states discovered experimentally always proceed via the strong and electromagnetic interactions. Recently, a tetraquark state with the quark content $bc\bar{q}\bar{q}$ was predicted by Lattice QCD simulations. It is below the mass threshold of $D\bar{B}$, which can only decay via the weak interaction. In this work, based on the decay mechanism of $T_{cc}$ as a $DD^*$ molecule, we propose that the decays of the $bc\bar{q}\bar{q}$ tertaquark state as a $D\bar{B}$ molecule proceed via the Cabibbo-favored weak decays of the $\bar{B}$ or $D$ meson, accompanied by the tree-level decay modes and the triangle decay modes. Our results indicate that the branching fraction of the $D\bar{B}$ molecule decaying into $\pi^+ K^{-} \bar{B}^0$ is sizable, which is a good channel to observe the $D\bar{B}$ molecule in future experiments., Comment: Version accepted for publication, Phys.Rev.D

There have been extended and heated discussions on the nature of the two exotic states, $Z_c(3900)$ and $Z_{cs}(3985)$, particularly whether they are resonances or virtual states. We demonstrate for the first time that the femtoscopic technique can be used to unambiguously distinguish between such two scenarios. More concretely, we show that the $D^0D^{*-}$/$D^0D_s^{*-}$ correlation functions are significantly different in the high-momentum region, especially in small collision systems of the order of 1 fm, as produced in pp collisions at the LHC, which can unambiguously tell whether $Z_c(3900)$/$Z_{cs}(3985)$ is a resonant or a virtual state. For the $Z_{cs}(3985)$, the $D^0D_s^{*-}$ results at zero momentum are significantly different in the two scenarios. We hope all these discoveries can stimulate further experimental studies and help clarify the nature of the many exotic states discovered., Comment: 4 pages, 2 figures. Comments are welcome

The two excited vector charmonium states $Y(4220)$ and $Y(4360)$ are difficult to be understood as pure $c\bar{c}$ charmonium states. Since they are located close to the mass thresholds of $\bar{D}D_{1}$ and $\bar{D}^*D_{1}$, they can be viewed as $\bar{D}D_{1}$ and $\bar{D}^*D_{1}$ molecules. Furthermore, recent studies indicated that the exotic states $X(3872)$/$Z_c(3900)$ and $X_2(4013)$/$Z_c(4020)$ are the isoscalar/isovector $\bar{D}D^{*}$ and isoscalar/isovector $\bar{D}^*D^{*}$ molecules, respectively. In this work, in the molecular picture, we employ the triangle diagram mechanism to study the productions of $ Z_{c}(3900) $ and $X(3872)$ in the pionic and radiative decays of $Y(4220)$, as well as their heavy-quark spin symmetry (HQSS) partners, i.e., the productions of $Z_{c}(4020)$ and $X_2(4013)$ in the pionic and radiative decays of $Y(4360)$. Using the effective Lagrangian approach, we obtain the ratios of the branching fractions $\mathcal{B}[Y(4360) \to Z_c(4020)\pi]/\mathcal{B}[Y(4220)\to Z_c(3900)\pi]=1.2$ and $\mathcal{B}[Y(4360)\to X_2(4013) \gamma]/\mathcal{B}[Y(4220)\to X(3872)\gamma]=0.5$, almost independent of model parameters, which indicate that the productions of $X_2(4013)$ and $Z_c(4020)$ in the radiative and pionic decays of $Y(4360)$ are likely to be measured in the future. The experimental studies of the predicted decay modes will help verify the molecular nature of $X(3872)$, $Z_c(3900)$, and $Y(4220)$. We hope the present work can stimulate experimental and further theoretical studies on these decay modes., Comment: This version is to be published in Phys. Rev. D

In the past two decades, a plethora of hadronic states beyond the conventional quark model of $q\bar{q}$ mesons and $qqq$ baryons have been observed experimentally, which motivated extensive studies to understand their nature and the non-perturbative strong interaction. Since most of these exotic states are near the mass thresholds of a pair of conventional hadrons, the prevailing picture is that they are primarily hadronic molecules. In principle, one can verify the molecular nature of these states by thoroughly comparing their masses, decay widths, and production rates in a particular picture with experimental data. However, this is difficult or impossible. First, quantum mechanics allows for the mixing of configurations allowed by symmetries and quantum numbers. Second, data are relatively scarce because of their small production rates and the many difficulties in the experimental measurements. As a result, other alternatives need to be explored. This review summarizes three such approaches that can help disentangle the nature of the many exotic hadrons discovered. In the first approach, based on the molecular interpretations for some exotic states, we study the likely existence of multiplets of hadronic molecules related by various symmetries, such as isospin symmetry, SU(3)-flavor symmetry, heavy quark spin/flavor symmetry, and heavy antiquark diquark symmetry. In the second approach, starting from some hadronic molecular candidates, one can derive the underlying hadron-hadron interactions. With these interactions, one can study related three-body systems and check whether three-body bound states/resonances exist. In the third approach, one can turn to the femtoscopy technique to derive the hadron-hadron interactions, hence inaccessible. This technique provided an unprecedented opportunity to understand the interactions between unstable hadrons., Comment: 171 pages, 43 figures; to appear in Physics Reports

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 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

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

Nuclear saturation is a crucial feature in nuclear physics that plays a fundamental role in understanding various nuclear phenomena, ranging from properties of finite nuclei to those of neutron stars. However, a proper description of nuclear saturation is highly nontrivial in modern nonrelativistic~\textit{ab initio}~studies because of the elusive three-body forces. In this letter, we calculate the equation of state for nuclear matter in the relativistic Brueckner-Hartree-Fock (RBHF) framework with the leading order covariant chiral nuclear force. We show that a simultaneous description of the nucleon-nucleon scattering data and the saturation of the symmetric nuclear matter can be achieved. In this regard, the relativistic effects nicely explain the saturation of nuclear matter. As a result, the present study based on the covariant chiral nuclear force shows that in the RBHF framework, one can achieve saturation with a leading order covariant chiral nuclear force with only two-body forces, in contrast to the vast majorities of studies in the non-relativistic framework, where the next-to-next-to-leading order two-body and three-body chiral forces are needed. This study sets the foundation for studying nuclear saturation with the covariant chiral force in the RBHF framework, which allows for a systematic understanding of one of the key features of nuclear physics more microscopically., Comment: 11 pages, 10 figures, version published in Physics Letters B

Assuming that $D_{s0}^{*}(2317)$ is a $DK$ molecular state with a binding energy of 45 MeV, we investigate the existence of four-hadron molecules, $DDKK$ and $D\Bar{D}K\Bar{K}$, with the Gaussian expansion method. Their binding energies are $138\sim155$ MeV and $123\sim163$ MeV below the mass thresholds of $DDKK$ and $D\Bar{D}K\Bar{K}$. The $D\Bar{D}K\Bar{K}$ state has a decay width of $36\sim54$ MeV due to the complex $K\Bar{K}$ interaction. Further theoretical studies of and experimental searches for such four-hadron molecules can help deepen the understanding of the nonperturbative strong interaction in a nontrivial way., Comment: 8 pages, 5 figures

We address a general problem in the evaluation of triangle loops stemming from the consideration of the range of the interaction involved in some of the vertices, as well as the energy dependence of the width of some unstable particles in the loop. We find sizeable corrections from both effects. We apply that to a loop relevant to the $D_s^+ \to \pi^+ \pi^0 \eta $ decay, and find reductions of about a factor of $4$ in the mass distribution of invariant mass of the $\pi \eta$ in the region of the $a_0(980)$. The method used is based on the explicit analytical evaluation of the $q^0$ integration in the $d^4q$ loop integration, using Cauchy's residues method, which at the same time offers an insight on the convergence of the integrals and the effect of form factors and cutoffs., Comment: 6 pages, 4 figures

We have conducted a model independent analysis of the $K^+ \bar{K}^0$ pair correlation function obtained from ultra high energy $pp$ collisions, with the aim of extracting the information encoded in it related to the $K\bar{K}$ interaction and the coupled channel $\pi^+ \eta$. With the present large errors at small relative $K^+\bar{K}^0$ momenta, we find that the information obtained about the scattering matrix suffers from large uncertainties. Even then, we are able to show that the data imply the existence of the $a_0$ resonance, $a_0(980)$, showing as a strong cusp close to the $K\bar{K}$ threshold. We also mention that the measurement of the $\pi^+ \eta$ correlation function will be essential in order to constrain more the information on $K\bar{K}$ dynamics that can be obtained from correlation functions., Comment: 7 pages, 9 figures

Recent studies show that $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ contain large molecular components. In this work, we employ the naive factorization approach to calculate the production rates of $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ as hadronic molecules in $B_{(s)}$ and $\Lambda_b(\Xi_b)$ decays, where their decay constants are estimated in the effective Lagrangian approach. With the so-obtained decay constants $f_{D_{s0}^{\ast}(2317)}$ and $f_{D_{s1}(2460)}$, we calculate the branching fractions of the $b$-meson decays $B_{(s)}\to \bar{D}_{(s)}^{(*)}D_{s0}^*$ and $B_{(s)}\to \bar{D}_{(s)}^{(*)}D_{s1}$ and the $b$-baryon decays $\Lambda_b(\Xi_{b}) \to \Lambda_c(\Xi_{c}) D_{s0}^*$ and $\Lambda_b(\Xi_{b}) \to \Lambda_c(\Xi_c) D_{s1}$. Our results show that the production rates of $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ in the $B_s$, $\Lambda_b$ and $\Xi_b$ decays are rather large that future experiments could observe them. In particular, we demonstrate that one can extract the decay constants of hadronic molecules via the triangle mechanism because of the equivalence of the triangle mechanism to the tree diagram established in calculating the decays $B \to \bar{D}^{(*)}D_{s0}^{\ast}(2317)$ and $B \to \bar{D}^{(*)}D_{s1}(2460)$.

Motivated by the recent lattice QCD study of the $DD^*$ interaction at unphysical quark masses, we perform a theoretical study of the $DD^*$ interaction in covariant chiral effective field theory (ChEFT). In particular, we calculate the relevant leading-order two-pion exchange contributions. The results compare favorably with the lattice QCD results, supporting the conclusion that the intermediate-range $DD^*$ interaction is dominated by two-pion exchanges and the one-pion exchange contribution is absent. At a quantitative level, the covariant ChPT results agree better with the lattice QCD results than their non-relativistic counterparts, showing the relevance of relativistic corrections in the charm sector., Comment: 12 pages, 7 figures

The $\Xi N$ interaction plays an important role in our understanding on the long-anticipated $H$-dibaryon. Recent lattice QCD calculations verified the attractive nature of the $\Xi N$ interaction. On the other hand, whether it is strong enough to generate a bound state remains inconclusive.In this work, assuming that it can generate a weakly bound state, we study the yields of the $\Xi N$ dibaryon for different binding energies in $pp$ collisions at 7 TeV using the coalescence model and the transport model PACIAE. The yields are estimated first numerically and then analytically adopting a Yukawa-type wave function. In particular, we find that in the weak binding limit, there exists a universal relation between the yield and the binding energy, valid for $pp$ collisions., Comment: 7 pages, 6 figures; comments welcome

The partial decay widths and production mechanism of the three pentaquark states, $P_{\psi}^{N}(4312)$, $P_{\psi}^{N}(4440)$, and $P_{\psi}^{N}(4457)$, discovered by the LHCb Collaboration in 2019, are still under debate. In this work, we employ the contact-range effective field theory approach to construct the $\bar{D}^{(*)}\Sigma_{c}^{(*)}$, $\bar{D}^{*}\Lambda_c$, $\bar{D}\Lambda_c$, $J/\psi p$, and $\eta_c p$ coupled-channel interactions to dynamically generate the multiplet of hidde-charm pentaquark molecules by reproducing the masses and widths of $P_{\psi}^{N}(4312)$, $P_{\psi}^{N}(4440)$, and $P_{\psi}^{N}(4457)$. Assuming that the pentaquark molecules are produced in the $\Lambda_b$ decay via the triangle diagrams, where $\Lambda_{b}$ firstly decays into $D_{s}^{(\ast)}\Lambda_{c}$, then $D_{s}^{(\ast)}$ scatters into $\bar{D}^{(\ast)}K$, and finally the molecules are dynamically generated by the $\bar{D}^{(\ast)}\Lambda_{c}$ interactions, we calculate the branching fractions of the decays $\Lambda_b \to {P_{\psi}^{N}}K$ using the effective Lagrangian approach. With the partial decay widths of these pentaquark molecules, we further estimate the branching fraction of the decays $ \Lambda_b \to ( P_{\psi}^{N} \to J/\psi p )K $ and $ \Lambda_b \to ( P_{\psi}^{N}\to \bar{D}^* \Lambda_c )K $. Our results show that the pentaquark states $P_{\psi}^{N}(4312)$, $P_{\psi}^{N}(4440)$, and $P_{\psi}^{N}(4457)$ as hadronic molecules can be produced in the $\Lambda_b$ decay, and on the other hand their heavy quark spin symmetry partners are invisible in the $J/\psi p$ invariant mass distribution because of the small production rates. Our studies show that is possible to observe some of the pentaquark states in the $\Lambda_b\to \bar{D}^*\Lambda_c K$ decays.

Magicity, or shell closure, plays an important role in our understanding of complex nuclear phenomena. In this work, we employ one of the state-of-the-art density functional theories, the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with the density functional PC-PK1, to investigate the evolution of the $N=20,28,50$ shell closures in the $ 20 \leqslant Z \leqslant 30$ region. We show how these three conventional shell closures evolve from the proton drip line to the neutron drip line by studying the charge radii, two-neutron separation energies, two-neutron gaps, quadrupole deformations, and single-particle levels. In particular, we find that in the $ 21 \leqslant Z \leqslant 27$ region, the $N=50$ shell closure disappears or becomes quenched, mainly due to the deformation effects. Similarly, both experimental data and theoretical predictions indicate that the $N=28$ shell closure disappears in the Mn isotopic chain, also predominantly due to the deformation effects. The DRHBc theory predicts the existence of the $N=20$ shell closure in the Ca, Sc, and Ti isotopic chains, but the existing data for the Ti isotopes suggests the contrary, and therefore more investigations are needed., Comment: 9 pages, 9 figures

One-proton radioactivity in 149Lu, the latest identified proton emitter, is studied in the Wentzel-Kramers-Brillouin (WKB) approach with the proton-nucleus potential extracted from the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) for the first time. The predicted half-life turns out to be consistent with the experimental measurement within uncertainties and (almost) independent of the density functionals in the DRHBc theory. Such a microscopic self-consistent calculation reveals that 149Lu is oblately deformed with a quadrupole deformation -0.18, and rules out the possibility of a prolate quadrupole deformation suggested in the nonadiabatic quasiparticle model. We also check the validity of this approach in the description of 150,151Lu and their isomeric states. The deviations of the predicted half-lives from their experimental counterparts are mostly smaller than those of the theoretical studies without considering deformation effects. Furthermore, we predict 148Lu to be a more oblately deformed proton-emitter with a longer half-life than that of 149Lu, which can be checked in the future. Our studies show that the DRHBc plus WKB approach provides a new alternative method to evaluate the half-lives of well-deformed proton emitters.