Search

In this work, we conduct a three-coupled-channel analysis of the $Z_c(3900)$ structure, focusing on the $D\bar{D}^*$, $J/\psi \pi$, and $\rho \eta_c$ channels, based on the one-boson exchange model. Drawing from previous study on the exotic state $T_{cc}$, we only utilize one more parameter to construct the interactions between the channels. Our model successfully reproduces the experimental line shapes of the invariant mass distribution at $\sqrt{s} = 4.23$ and $4.26$ GeV for the three channels. Additionally, the finite-volume energy levels in our model show agreement with current LQCD conclusion. Detailed analysis suggests that the $Z_c(3900)$ peaks in the $\pi J/\psi$ and $\rho \eta_c$ distributions primarily arise from the triangle loop involving the $D_1 \bar{D} D^*$ intermediate system. In the $D\bar{D}^*$ distribution, the threshold peak is generated by the cascade decay mechanism enhanced by a triangle diagram. Moreover, we find a virtual pole located far from the threshold, indicating that $Z_c(3900)$ peaks are not associated with physical pole. We conclude that the $Z_c(3900)$ peaks are predominantly caused by the threshold cusp.

We calculate the correlation functions for the $\bar K^0 p, \pi^+ \Sigma^0, \pi^0 \Sigma^+, \pi^+ \Lambda$, and $\eta \Sigma^+$ states, which in the chiral unitary approach predict an excited $\Sigma^*(1/2^-)$ state at the $\bar K N$ threshold, recently observed by the Belle collaboration. Once this is done, we tackle the inverse problem of seeing how much information one can obtain from these correlation functions. With the resampling method, one can determine the scattering parameters of all the channels with relative precision by means of the analysis in a general framework, and find a clear cusp-like structure corresponding to the $\Sigma^*(1/2^-)$ in the different amplitudes at the $\bar{K}N$ threshold., Comment: 10 pages, 4 figures, 7 tables

The $DDK$ system has gain increasing attention in recent research due to its potential to contain a three-hadron bound state. This article utilizes an extension of the Non-Relativistic Effective Field Theory (NREFT) and the finite volume particle-dimer framework to derive Lorentz-invariant quantization conditions for the $DDK$ three-body system. Using current model input conditions, the finite volume energy spectrum of the $DDK$ three-body system was calculated. This new calculation incorporates relativistic kinematics, allowing it to be applicable across a broader energy range starting from the threshold. In this work, we present a comprehensive \( O(p^{2}) \) calculation. The spurious pole is effectively subtracted within the framework of relativistic kinematics. The spectra in the moving frame are also obtained. These analyses provide a broader testing ground for future lattice simulations. They are expected to reveal more detailed properties of the $DDK$ system and other three-hadron systems., Comment: 20 pages, 7 figures

Convenient and consistent phase convention is important in the construction of the hadronic Lagrangian. However, the importance of phase convention has been overlooked for a long time and the sources of different conventions are never explicitly addressed. This obscure situation can cause mistakes and misinterpretations in hadron physics. In this paper, we systematically analyze and compare the flavor $SU_3$ phase conventions from the perspective of the quark model. All sources which could lead to different conventions are pointed out and carefully studied. With the tool of the quark model, we also clarify some misconceptions and demonstrate a consistent way to incorporate different conventions., Comment: 25 pages, 3 figures, submitted to Symmetry

$P_c(4457)$ has been discovered over five years, but the parity of this particle remains undetermined. In this letter we propose a new interpretation for $P_c(4457)$, which is the state generated from the coupled-channel $\bar{D}^0\Lambda_c^{+}(2595)$ and $\pi^0 P_c(4312)$ since they can exchange an almost on-shell $\Sigma_c^+$. In this scenario, the parity of $P_c(4457)$ will be positive, which is different from the candidate of the bound state of $\bar{D}^*\Sigma_c$. The main decay channel of $P_c(4457)$ in this model is $P_c(4312)\pi$. We propose three processes $\Lambda_b^0 \to J/\psi K_s p \pi^-$, $\Lambda_b^0 \to J/\psi K^- p \pi^0$, and $\Lambda_b^0 \to J/\psi p \pi^- \pi^+ K^-$ to verify $P_c(4457)\to P_c(4312)\pi$., Comment: 6 Pages, 2 figures

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

In this study, the impact of triangle singularity is investigated in the isospin-breaking process $J/\psi \to \Lambda \bar{\Lambda} \pi$. The triangle singularity is found to play a significant role in the process, resulting in the creation of a resonance-like structure around 1.4 GeV in the $\Lambda\pi(\bar{\Lambda}\pi)$ invariant mass spectrum. To amplify the impact of this triangle singularity, the presence of two $\Sigma^*(\frac{1}{2}^-)$ states around 1.4 GeV and 1.6 GeV is essential, yet these states have not been definitively identified in the current baryon spectrum. We recommend that experiments, particularly the Beijing Spectrometer (BESIII) and the future Super Tau-Charm Factory (STCF), to investigate the process $J/\psi \to \Lambda \bar{\Lambda} \pi$ to offer direct evidences for our predicted triangle singularity and additional evidence regarding the $\Sigma(\frac{1}{2}^-)$ states.

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

With the continuous accumulation of data from hadron collision experiments, efficient Partial Wave Analysis tools are indispensable for constructing a clear hadron spectrum. Currently, automated computations of scattering amplitudes primarily use the helicity scheme and covariant effective Lagrangian method. The automated calculations under the covariant $L$-$S$ scheme, which is one of the commonly used partial wave analysis schemes, have not been fully realized. In this work, we provide a general algorithm for computing partial wave amplitudes under the covariant $L$-$S$ scheme. This will lay the foundation for automated computation of partial wave amplitudes under the covariant $L$-$S$ scheme., Comment: 6 pages

The investigation of hadron interactions within lattice QCD has been facilitated by the well-known quantisation condition, linking scattering phase shifts to finite-volume energies. Additionally, the ability to utilise systems at finite total boosts has been pivotal in smoothly charting the energy-dependent behaviour of these phase shifts. The existing implementations of the quantization condition at finite boosts rely on momentum transformations between rest and moving frames, defined directly in terms of the energy eigenvalues. This energy dependence is unsuitable in the formulation of a Hamiltonian.In this work, we introduce a novel approach to generalise the three-momentum boost prescription, enabling the incorporation of energy-independent finite-volume Hamiltonians within moving frames. We demonstrate the application of our method through numerical comparisons, employing a phenomenological $\pi\pi$ scattering example., Comment: 30 pages, 5 figures

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

We derive the modified L\"uscher equation in the presence of the long-range force caused by the exchange of a light particle. It is shown that the use of this equation enables one to circumvent the problems related to the strong partial-wave mixing and the t-channel sub-threshold singularities. It is also demonstrated that the present method is intrinsically linked to the so-called modified effective-range expansion (MERE) in the infinite volume. A detailed comparison with the two recently proposed alternative approaches is provided., Comment: 28 pages, 4 figures

This presentation opens with a brief review of lattice QCD calculations showing the $2s$ radial excitation of the nucleon sits at approximately 2 GeV, well above the Roper resonance position. We then proceed to reconcile this observation with experimental scattering data. While the idea of dressing quark-model states in a coupled-channel analysis to describe scattering data has been around for decades, it's now possible to bring these descriptions to the finite-volume of lattice QCD for confrontation with lattice-QCD calculations. This combination of lattice QCD and experiment demands that we reconsider our preconceived notions about the quark-model and its excitation spectrum. We close with a discussion of an unanticipated resolution to the missing baryon resonances problem., Comment: 8 pages, 2 figures. To appear as a plenary contribution to the proceedings of HADRON 2023, the 20th International Conference on Hadron Spectroscopy and Structure, 5th-9th June 2023, Genova, Italy

In this work, an unquenched quark model is proposed for describing the heavy-light mesons by taking into account the coupled-channel effects induced by chiral dynamics. After including a relativistic correction term for the strong transition amplitudes, both the mass spectra and decay widths of the observed heavy-light mesons can be successfully described simultaneously in a unified framework, several long-standing puzzles related to the small masses and broad widths are overcome naturally. We also provide valuable guidance in searching new heavy-light mesons by the detailed predictions of their masses, widths, and branching ratios. The success of the unquenched quark model presented in this work indicates it may be an important step for understanding the hadron spectrum., Comment: 12 pages, 3 figures

We derive an explicit expression for the Lellouch-L\"uscher (LL) factor in the $K\to 3\pi$ decays at leading order (without derivative couplings). Several important technical details are addressed, like a proper decomposition into the isospin amplitudes, the choice of a minimal set of effective couplings and the renormalization, as well as the algorithm for the solution of the pertinent Faddeev equations in the infinite volume which is based on the contour deformation method. Most importantly, our numerical results demonstrate that the three-body force contributes very little to the LL factor. This result paves the way for the study of the $K\to 3\pi$ decays on the lattice., Comment: 41 pages, 14 figures

Recent LHCb data for $B^-\to J/\psi\Lambda\bar{p}$ show a clear peak structure at the $\Xi_c\bar{D}$ threshold in the $J/\psi\Lambda$ invariant mass ($M_{J/\psi\Lambda}$) distribution. The LHCb's amplitude analysis identified the peak with the first hidden-charm pentaquark with strangeness $P_{\psi s}^\Lambda(4338)$. We conduct a coupled-channel amplitude analysis of the LHCb data by simultaneously fitting the $M_{J/\psi\Lambda}$, $M_{J/\psi\bar{p}}$, $M_{\Lambda\bar{p}}$, and $\cos\theta_{K^*}$ distributions. Rather than the Breit-Wigner fit employed in the LHCb analysis, we consider relevant threshold effects and a unitary $\Xi_c\bar{D}$-$\Lambda_c\bar{D}_s$ coupled-channel scattering amplitude from which $P_{\psi s}^\Lambda$ poles are extracted for the first time. In our default fit, the $P_{\psi s}^\Lambda(4338)$ pole is almost a $\Xi_c \bar{D}$ bound state at $( 4338.2\pm 1.4)-( 1.9\pm 0.5 )\,i$ MeV. Our default model also fits a large fluctuation at the $\Lambda_c\bar{D}_s$ threshold, giving a $\Lambda_c\bar{D}_s$ virtual state, $P_{\psi s}^\Lambda(4255)$, at $4254.7\pm 0.4$ MeV. We also found that the $P_{\psi s}^\Lambda(4338)$ peak cannot solely be a kinematical effect, and a nearby pole is needed., Comment: 4 pages, 4 figures, Contribution to the Proceedings for 16th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2023), October 15-20, 2023, Mainz, Germany

We investigate the exclusive $J/\psi$ production at the future Electron-ion collider in China by utilizing the eSTARlight event generator. We model the cross-section and kinematics by fitting to the world data of $J/\psi$ photoproduction. Projected statistical uncertainties on $J/\psi$ production are based on the design of a central detector, which consists of a tracker and vertex subsystem. The precision of the pseudo-data allows us to probe the near-threshold mechanism, e.g. the re-scattering effect. The significance of the forward amplitudes is discussed as well. The design and optimization of the detector enhance the potential for exploring the near-threshold region and the realm of high four-momentum transfer squared, which is of particular interest on several physics topics.., Comment: 11 pages, 11 figures

We collect spectra extracted in the $I=\ell=1$ $\pi\pi$ sector provided by various lattice QCD collaborations and study the $m_\pi$ dependence of $\rho$-meson properties using Hamiltonian Effective Field Theory (HEFT). In this unified analysis, the coupling constant and cutoff mass, characterizing the $\rho - \pi \pi$ vertex, are both found to be weakly dependent on $m_\pi$, while the mass of the bare $\rho$, associated with a simple quark-model state, shows a linear dependence on $m_\pi^2$. Both the lattice results and experimental data can be described well. Drawing on HEFT's ability to describe the pion mass dependence of resonances in a single formalism, we map the dependence of the phase shift as a function of $m_\pi$, and expose interesting discrepancies in contemporary lattice QCD results., Comment: 24 pages, 16 figures

We investigate the doubly bottom state $T^-_{bb}$ composed of two bottom mesons with $J^P=1^+$. The potentials are obtained using the one-boson exchange model. With the heavy quark flavor symmetry, all the parameters in the model are determined by fitting the experimental data of doubly charmed state $T_{cc}^{+}$ from our previous work. Our analysis indicates that the isospin symmetry is well-preserved. We identify a deeply bound $T^-_{bb}$ state with quantum numbers $I(J^{P})=0(1^+)$, in contrast to the loosely bound $T_{cc}^{+}$. Additionally, we discover a resonant $T^-_{bb}$ state with $I(J^{P})=1(1^+)$. Furthermore, our investigation into the $\bar{B}\bar{B}^*$-$\bar{B}^*\bar{B}^*$ coupled channel effect reveals its important impact. The binding energy of the bound $I(J^{P})=0(1^+)$ states becomes deeper, while the resonant $T^-_{bb}$ state with $I(J^{P})=1(1^+)$ remains nearly unchanged., Comment: 24 pages, 7 figures, add discussions on the pole trajectory of the heavy meson pairs and a I=1 DD* resonance, accepted for publication in PRD

We have investigated the internal structure of the open- and hidden-charmed ($DD^*$/$\bar DD^*$) molecules in the unified framework. We first fit the experimental lineshape of the $T^+_{cc}$ state and extract the $DD^*$ interaction, from which the $T^+_{cc}$ is assumed to arise solely. Then we obtain the $D\bar{D}^*$ interaction by charge conjugation. Our results show that the $D\bar{D}^*$ interaction is attractive but insufficient to form $X(3872)$ as a bound state. Instead, its formation requires the crucial involvement of the coupled channel effect between the $D\bar D^*$ and $c\bar c$ components, although the $c\bar c$ accounts for approximately $1\%$ only. Besides $X(3872)$, we have obtained a higher-energy state around $3957.9$ MeV with a width of $16.7$ MeV, which may be a potential candidate for the $X(3940)$. In $J^{PC}=1^{+-}$ sector, we have found two states related to the iso-scalar $\tilde X(3872)$ and $h_c(2P)$, respectively. Our combined study provides valuable insights into the nature of these $DD^*$/$D\bar D^*$ exotic states., Comment: 10 pages, 5 figures, version accepted for publication in Science Bulletin

Recent lattice QCD results for the low-lying odd-parity excitations of the nucleon near the $N^{*}(1535)$ and $N^{*}(1650)$ resonance positions have revealed that the lattice QCD states have magnetic moments consistent with predictions from a constituent-quark-model. Using Hamiltonian Effective Field Theory (HEFT) to describe pion-nucleon scattering in the $I(J^{P}) = \frac{1}{2}(\frac{1}{2}^{-})$ channel, we represent these two quark-model like states as two single-particle bare basis states, dressed and mixed by meson-baryon scattering channels. By constraining the free parameters of the Hamiltonian with $S_{11}$ pion-nucleon scattering data, we perform the first calculation of the finite-volume spectrum using two bare-baryon basis states. By comparing this spectrum to contemporary lattice QCD results at three lattice volumes, we analyse the eigenvectors of the Hamiltonian to gain insight into the structure and composition of these two low-lying resonances. We find that an interpretation of the two low-lying nucleon resonances as quark-model like states dressed by meson-baryon interactions is consistent with both the $S_{11}$ scattering data and lattice QCD. We introduce a novel HEFT formalism for estimating scattering-state contaminations in lattice QCD correlation functions constructed with standard three-quark operators. Not only are historical lattice QCD results described with excellent accuracy, but correlation functions with large scattering-state contaminations are identified., Comment: 17 pages, 12 figures

Low-lying baryon resonances have been explored using Hamiltonian Effective Field Theory (HEFT), in a formalism where resonances with a three-quark component are described by both two-particle meson-baryon states and a bare basis state. Here, we investigate the use of multiple bare states in the Hamiltonian, to extend the formalism to higher energy ranges, and represent a larger portion of the low-lying baryon spectrum. Introducing a second bare state into a toy model extension of the low-energy $\Delta(1232)$ system, we explore the influence of the second bare state on the position of poles in the infinite-volume $T$-matrix. Considering the same system in a finite-volume, we analyse the finite-volume energy spectrum in the presence of a second bare state, providing insight into the interplay between two bare basis states, representing quark-model states, and the relationship between infinite-volume poles and finite-volume eigenstates., Comment: 14 pages, 7 figures

We study the Borromean nuclei formed by a core nucleus and two neutrons in a nonrelativistic effective field theory formalism considering both neutron-neutron and neutron-core interactions. We provide formulae of the charge and matter radii, and successfully reproduce the universal relation proposed by Hongo and Son based on the approximation of an infinite neutron-neutron scattering length and neglecting the neutron-core scattering. Once the realistic finite neutron-neutron and neutron-core scattering lengths are used, the charge and matter radii are influenced by the neutron-core channel in a growingly relevant manner. We obtain a relation among the binding energy of the three-body Borromean system, the ratio between charge and matter radii, and the ratio between the neutron-neutron and core-neutron scattering lengths. We find that the two-neutron separation energy for $^{22}$C needs to be $\lesssim 2$ keV in order to be consistent with the experimental constraints of the matter radius of $^{22}$C and the $^{20}{\rm C}\,n$ $S$-wave scattering length., Comment: 26 pages, 14 figures

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

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

A manifestly relativistic-invariant Lellouch-L\"uscher formalism for the three-particle decays is proposed. Similarly to ref.[1], the formalism is based on the use of the non-relativistic effective Lagrangians. Manifest Lorentz invariance is guaranteed, as in ref.[2], by choosing the quantization axis along the total four-momentum of the three-particle system. A systematic inclusion of the higher-order derivative couplings, as well as higher partial waves is addressed., Comment: 36 pages, 4 figures

We present that by predicting the spectrum in discrete space from the phase shift in continuous space, the neural network can remarkably reproduce the numerical L\"uscher's formula to a high precision. The model-independent property of the L\"uscher's formula is naturally realized by the generalizability of the neural network. This exhibits the great potential of the neural network to extract model-independent relation between model-dependent quantities, and this data-driven approach could greatly facilitate the discovery of the physical principles underneath the intricate data., Comment: 7 figures, accepted by Chinese Physics C

A refined investigation on light flavor meson-baryon scatterings is performed using a dynamical coupled-channel approach, the J\"ulich-Bonn model, that respects unitartiy and analyticity constraints. The channel space of $\pi N$, $\pi \Delta$, $\sigma N$, $\rho N$, $\eta N$, $K \Lambda$ and $K \Sigma$ is extended by adding the $\omega N$ final state. The spectra of $N^*$ and $\Delta$ resonances are extracted in terms of complex poles of the scattering amplitudes, based on the result of a global fit to a worldwide collection of data, in the energy region from the $\pi N$ threshold to center-of-mass energy $z=2.3$ GeV. A negative value of the $\omega N$ elastic spin-averaged scattering length is extracted, questioning the existence of bound states of the $\omega$ meson in the nuclear matter., Comment: 23 pages, 16 figures, one supplemental material

Combining the quark model, the quark-pair-creation mechanism and $B^{(*)}\bar K$ interaction, we have investigated the near-threshold $P$-wave $B_s$ states in the framework of the Hamiltonian effective field theory. With the heavy quark flavor symmetry, all the parameters are determined in the $D_s$ sector by fitting the lattice data. The masses of the bottom-strange partners of the $D^{*}_{s0}(2317)$ and $D^{*}_{s1}(2460)$ are predicted to be $M_{B^{*}_{s0}}=5730.2_{-1.5}^{+2.4}$ MeV and $M_{B^{*}_{s1}}= 5769.6_{-1.6}^{+2.4}$ MeV, respectively, which are well consistent with the lattice QCD simulation. The two $P$-wave $B_s$ states are the mixtures of the bare $\bar b s$ core and $B^{(*)}\bar K$ component. Moreover, we find a crossing point between the energy levels with and without the interaction Hamiltonian in the finite volume spectrum in the $0^+$ case, which corresponds to a CDD (Castillejo-Dalitz-Dyson) zero in the $T$-matrix of the $B\bar K$ scattering. This CDD zero will help deepen the insights of the near-threshold states and can be examined by future lattice calculation., Comment: 20 pages, 4 figures. Version accepted by JHEP

In hadron physics, molecular-like multihadron states can interact with compact multiquark states. The latter are modeled as bare states in the Hilbert space of a potential model. In this work, we study several potential models relevant to the bare state, and solve their inverse scattering problems. The first model, called "cc", is a separable potential model. We show that it can approximate (single-channel short-range) $S$-wave near-threshold physics with an error of $\mathcal{O}(\beta^3/M_V^3)$, where $\beta$ sets the maximum momentum of the near-threshold region and $M_V$ is the typical scale of the potential. The second model, called "bc", serves as the bare-state-dominance approximation, where interaction between continuum states is ignored. Under this model, even though the bare state is always crucial for a bound state's generation, a shallow bound state naturally tends to have a small bare-state proportion. Therefore, we need other quantities to quantify the importance of the bare state. The last model, called "bcc", is a combination of the first two models. This model not only serves as a correction to the bare-state-dominance approximation, but can also be used to understand the interplay between quark and hadron degrees of freedom. This model naturally leads to the presence of a Castillejo-Dalitz-Dyson (CDD) zero. We consider the energy decomposition of a bound state. The potential ratio of the bare-continuum interaction to the continuum self-interaction is proposed to understand how the bound state is generated. Model independently, an inequality for the potential ratio is derived. Based on the model "bcc", the CDD zero can be used to estimate the potential ratio. Finally, we apply these studies to the deuteron, $\rho$ meson, and $D_{s0}^*(2317)$, and analyze their properties., Comment: 28 pages 2 figures

Using effective-range expansion for the two-body amplitudes may generate spurious sub-threshold poles outside of the convergence range of the expansion. In the infinite volume, the emergence of such poles leads to the inconsistencies in the three-body equations, e.g., to the breakdown of unitarity. We investigate the effect of the spurious poles on the three-body quantization condition in a finite volume and show that it leads to a peculiar dependence of the energy levels on the box size $L$. Furthermore, within a simple model, it is demonstrated that the procedure for the removal of these poles, which was recently proposed in Ref.[1] in the infinite volume, can be adapted to the finite-volume calculations. The structure of the exact energy levels is reproduced with an accuracy that systematically improves order by order in the EFT expansion., Comment: 26 pages, 9 figures

The analytical formulae for the phase space factors and the three-momenta of three- and four-body final states are derived for all sets of independent kinematic variables containing invariant mass variables. These formulae will help experimental physicist to perform the data analysis. As an example, we show how to use these formulae to distinguish the different mechanisms of $e+p\to e+J/\psi+ p$ process for searching the signals of $P_c$ states at the energy region of Electron-Ion collider at China (EicC)., Comment: 27 pages, 6 figures

The process of renormalisation in nonperturbative Hamiltonian Effective Field Theory (HEFT) is examined in the $\Delta$-resonance scattering channel. As an extension of effective field theory incorporating the L\"uscher formalism, HEFT provides a bridge between the infinite-volume scattering data of experiment and the finite-volume spectrum of energy eigenstates in lattice QCD. HEFT also provides phenomenological insight into the basis-state composition of the finite-volume eigenstates via the state eigenvectors. The Hamiltonian matrix is made finite through the introduction of finite-range regularisation. The extent to which the established features of this regularisation scheme survive in HEFT is examined. In a single-channel $\pi N$ analysis, fits to experimental phase shifts withstand large variations in the regularisation parameter, $\Lambda$, providing an opportunity to explore the sensitivity of the finite-volume spectrum and state composition on the regulator. While the L\"uscher formalism ensures the eigenvalues are insensitive to $\Lambda$ variation in the single-channel case, the eigenstate composition varies with $\Lambda$; the admission of short distance interactions diminishes single-particle contributions to the states. In the two-channel $\pi N$, $\pi \Delta$ analysis, $\Lambda$ is restricted to a small range by the experimental data. Here the inelasticity is particularly sensitive to variations in $\Lambda$ and its associated parameter set. This sensitivity is also manifest in the finite-volume spectrum for states near the opening of the $\pi \Delta$ scattering channel. Finally, HEFT has the unique ability to describe the quark-mass dependence of the finite-volume eigenstates. The robust nature of this capability is presented and used to confront current state-of-the-art lattice QCD calculations., Comment: 21 pages, 22 figures

A three-particle quantization condition on the lattice is written down in a manifestly relativistic-invariant form by using a generalization of the non-relativistic effective field theory (NREFT) approach. Inclusion of the higher partial waves is explicitly addressed. A partial diagonalization of the quantization condition into the various irreducible representations of the (little groups of the) octahedral group has been carried out both in the center-of-mass frame and in moving frames. Furthermore, producing synthetic data in a toy model, the relativistic invariance is explicitly demonstrated for the three-body bound state spectrum., Comment: 38 pages, 7 figures

We generalize the time-honored Weinberg's compositeness relations by including the range corrections through considering a general form factor. In Weinberg's derivation, he considered the effective range expansion up to $\mathcal{O}(p^2)$ and made two additional approximations: neglecting the non-pole term in the Low equation; approximating the form factor by a constant. We lift the second approximation, and work out an analytic expression for the form factor. For a positive effective range, the form factor is of a single-pole form. An integral representation of the compositeness is obtained and is expected to have a smaller uncertainty than that derived from Weinberg's relations. We also establish an exact relation between the wave function of a bound state and the phase of the scattering amplitude neglecting the non-pole term. The deuteron is analyzed as an example, and the formalism can be applied to other cases where range corrections are important., Comment: 9 pages, 2 figures

In this work, we propose that there exists a moving triangle singularity in the $\psi(2S) \to \pi^+ \pi^- K^+ K^-$ process, whose position can vary from 1.158 to 1.181 GeV in the invariant mass spectrum of $K^+K^-$. After a precise analysis on this process, it turns out that after doing some cuts on $m_{\pi^+\pi^-}$, experiments do have the opportunity to observe this triangle singularity. In addition, when changing the cuts on $m_{\pi^+\pi^-}$, the movement of the predicted triangle singularity can also be observed. Thus, we suggest future experiments, especially Super Tau-Charm Facility (STCF), to do an anlysis on the $\psi(2S) \to \pi^+ \pi^- K^+ K^-$ process to verify our prediction.

An extended two-hadron operator is developed to extract the spectra of irreducible representations (irreps) in the finite volume. The irreps of the group for the finite volume system are projected using a coordinate-space operator. The correlation function of this operator is computationally efficient to extract lattice spectra of the specific irrep. In particular, this new formulation only requires propagators to be computed from two distinct source locations, at fixed spatial separation. We perform a proof-of-principle study on a $24^3 \times 48$ lattice volume with $m_\pi\approx 900$ MeV by isolating various spectra of the $\pi\pi$ system with isospin-2 including a range of total momenta and irreps. By applying the L\"uscher formalism, the phase shifts of $S$-, $D$- and $G$-wave $\pi\pi$ scattering with isospin-2 are extracted from the spectra., Comment: 29 Pages, 5 figures

A novel framework is proposed to extract near-threshold resonant states from finite-volume energy levels of lattice QCD and is applied to elucidate structures of the positive parity $D_s$. The quark model, the quark-pair-creation mechanism and $D^{(*)}K$ interaction are incorporated into the Hamiltonian effective field theory. The bare $1^+$ $c\bar s$ states are almost purely given by the states with heavy-quark spin bases. The physical $D^*_{s0}(2317)$ and $D^*_{s1}(2460)$ are the mixtures of bare $c\bar s$ core and $D^{(*)}K$ component, while the $D^*_{s1}(2536)$ and $D^*_{s2}(2573)$ are almost dominated by bare $c\bar{s}$. Furthermore, our model reproduces the clear level crossing of the $D^*_{s1}(2536)$ with the scattering state at a finite volume., Comment: 7 pages, 3 figures; accepted for publication in Physical Review Letters

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

We extend previous work concerning rest-frame partial-wave mixing in Hamiltonian effective field theory to both elongated and moving systems, where two particles are in a periodic elongated cube or have nonzero total momentum, respectively. We also consider the combination of the two systems when directions of the elongation and the moving momentum are aligned. This extension should also be applicable in any Hamiltonian formalism. As a demonstration, we analyze lattice QCD results for the spectrum of an isospin-2 $\pi\pi$ scattering system and determine the $s$, $d$, and $g$ partial-wave scattering information. The inclusion of lattice simulation results from moving frames significantly improves the uncertainty in the scattering information., Comment: 31 pages, 5 figures

In this work, the triangle singularity mechanism is investigated in the $\psi(2S) \to p \bar{p} \eta / p \bar{p} \pi^0$ process. The triangle loop composed by $J/\psi$, $\eta$ and $p$ has a singularity in the physical kinematic range for the $\psi(2S) \to p \bar{p} \eta / p \bar{p} \pi^0$ process, and it would generate a very narrow peak in the invariant mass spectrum of $p\eta (\pi)$ around $1.56387$ GeV, which is far away from both the threshold and relative resonances. In these processes, all the involved vertices are constrained by the experimental data. Thus, we can make a precise model independent prediction here. It turns out that the peak in the $p\eta$ invariant mass spectrum is visible, while it is very small in the $p\pi^0$ invariant mass spectrum. We expect this effect shown in $p \bar{p} \eta$ final state can be observed by the Beijing Spectrometer (BESIII) and Super Tau-Charm Facility (STCF) in the future.