arXiv subjects

Lu Meng

Publications and source records attributed to Lu Meng.

At least 37 records · Page 2Linked to original sources

arXiv2025

Doubly charm tetraquark channel with isospin $1$ from lattice QCD

Experimentally, the doubly charm tetraquark channel $cc\bar q\bar q$ with $q\!=\!u,d$ features an exotic hadron, $T_{cc}$, with isospin $I\!=\!0$ near the $DD^*$ threshold, while no peak was observed for $I\!=\!1$. We present a lattice QCD study of this channel with $I\!=\!1$, $J^P\!=\!1^+$ and $m_π\simeq 280~$MeV. Finite-volume energies calculated across five charm quark masses consistently feature a positive energy shift with respect to non-interacting energies, indicating repulsive interaction at energies near threshold. These energies are used to compute the $DD^*$ scattering amplitude using both the standard Lüscher method and the recently proposed effective-field-theory-based approach in the plane-wave basis, which incorporates the long-range interactions and the left-hand cut. Both analyses render a small negative scattering length and the scattering amplitude that does not feature any poles in the energy region near the $DD^*$ threshold, in line with LHCb results. We identify that the Wick contraction resembling $t$-channel isovector-vector meson exchanges between $D$ and $D^*$ plays a key role in distinguishing between the $I=0$ and $I=1$ channels, leading to repulsion in the $I=1$ and attraction in the $I=0$ channel.

hep-lat↗

arXiv2025

Internal structure of the $T_{cc}(3875)^+$ from its light-quark mass dependence

We employ a chiral effective field theory-based approach to connect $DD^*$ scattering observables at the physical and variable pion masses accessible in lattice QCD simulations. We incorporate all relevant scales associated with three-body $DDπ$ dynamics and the left-hand cut induced by the one-pion exchange for pion masses higher than the physical one, as required by analyticity and unitarity. By adjusting the contact interactions to match experimental data at the physical pion mass and lattice finite-volume energy levels at $m_π = 280$ MeV, we predict the trajectory of the $T_{cc}$ pole as a function of the pion mass, finding it consistent with the hadronic-molecule scenario. In particular, we find that the explicit treatment of the one-pion exchange has a pronounced effect on the pole trajectory for $m_π\gtrsim 230$ MeV by pushing it into the complex energy plane.

hep-ph↗

arXiv2024

Fully heavy tetraquark resonant states with different flavors

We use the quark potential model to calculate the mass spectrum of the S-wave fully heavy tetraquark systems with different flavors, including the $ bc\bar b\bar c, bb\bar c\bar c, cc\bar c\bar b $ and $ bb\bar b\bar c $ systems. We employ the Gaussian expansion method to solve the four-body Schrödinger equation, and the complex scaling method to identify resonant states. The $ bc\bar b\bar c, bb\bar c\bar c, cc\bar c\bar b $ and $ bb\bar b\bar c $ resonant states are obtained in the mass regions of $ (13.2,13.5) $, $ (13.3,13.6) $, $ (10.0,10.3) $, $ (16.5,16.7) $ GeV, respectively. Among these states, the $ bc\bar b\bar c $ tetraquark states are the most promising ones to be discovered in the near future. We recommend the experimental exploration of the $ 1^{++} $ and $ 2^{++} $ $ bc\bar b\bar c $ states with masses near $ 13.3 $ GeV in the $ J/ψΥ$ channel. From the root-mean-square radii, we find that all the resonant states we have identified are compact tetraquark states.

hep-ph↗

arXiv2024

Doubly heavy tetraquark bound and resonant states

We calculate the energy spectrum of the S-wave doubly heavy tetraquark systems, including the $ QQ^{(\prime)}\bar q\bar q$, $QQ^{(\prime)}\bar s\bar q$, and $ QQ^{(\prime)}\bar s\bar s$ ($Q^{(\prime)}=b,c$ and $q=u,d$) systems within the constituent quark model. We use the complex scaling method to obtain bound states and resonant states simultaneously, and the Gaussian expansion method to solve the complex-scaled four-body Schrödinger equation. With a novel definition of the root-mean-square radii, we are able to distinguish between meson molecules and compact tetraquark states. The compact tetraquarks are further classified into three different types with distinct spatial configurations: compact even tetraquarks, compact diquark-antidiquark tetraquarks and compact diquark-centered tetraquarks. In the $ I(J^P)=0(1^+) $ $QQ\bar q\bar q$ system, there exists the $ D^*D $ molecular bound state with a binding energy of $ -14 $ MeV, which is the candidate for $ T_{cc}(3875)^+ $. The shallow $\bar B^*\bar B$ molecular bound state is the bottom analog of $T_{cc}(3875)^+$. Moreover, we identify two resonant states near the $D^*D^*$ and $\bar B^*\bar B^*$ thresholds. In the $ J^P=1^+ $ $bb\bar q\bar q\,(I=0)$ and $bb\bar s\bar q$ systems, we obtain deeply bound states with a compact diquark-centered tetraquark configuration and a dominant $χ_{\bar 3_c\otimes 3_c}$ component, along with resonant states with similar configurations as their radial excitations. These states are the QCD analog of the helium atom. We also obtain some other bound states and resonant states with ``QCD hydrogen molecule" configurations. Moreover, we investigate the heavy quark mass dependence of the $ I(J^P)=0(1^+) $ $ QQ\bar q\bar q $ bound states. We strongly urge the experimental search for the predicted states.

hep-ph↗

arXiv2024

Identification of the $G(3900)$ as the P-wave $D\bar{D}^/\bar{D}D^$ resonance

The BESIII Collaboration recently performed a precise measurement of the $e^+e^-\rightarrow D\bar{D}$ Born cross sections, and confirmed the $G(3900)$ structure reported by BaBar and Belle with high significance. We identify the $G(3900)$ as the first P-wave $\DDbar$ molecular resonance. The experimental and theoretical identification of the P-wave dimeson state holds paramount importance in enhancing our comprehension of the non-perturbative QCD and few-body physics. Its existence is firmly established in a unified meson-exchange model which simultaneously depicts the features of the $χ_{c1}(3872)$, $Z_c(3900)$ and $T_{cc}(3875)$. This scenario can be directly examined in the $e^+e^-\rightarrow D\bar{D}^*/\bar{D}D^*$ cross section by seeing whether a resonance exists at the threshold. The credibility of the investigations is also ensured by the fact that the P-wave interaction dominantly arises from the well-known long-range pion exchange. Additionally, thanks to the centrifugal barrier, it is easier to form resonances in P-wave than in S-wave. We extensively calculate all systems up to P-wave with various quantum numbers and predict a dense population of the $\DDbar$ and $\DD$ states, where the S-wave $\DDbar$ state with $I^G (J^{PC})=0^- (1^{+-})$, P-wave $\DDbar$ state with $I^G(J^{PC})=0^+(0^{-+})$, and P-wave $\DD$ state with $I(J^P)=0(0^-)$ are more likely to be observed in experiments.

hep-ph↗

arXiv2024

Double pole structures of $X_1(2900)$ as the $P$-wave $\bar{D}^K^$ resonances

We reveal the double pole structures of the manifestly exotic tetraquark state $X_1(2900)$ in the scenario of $P$-wave $\bar{D}^*K^*$ dimeson resonance. We find that the observed enhancement signal associated with $X_1(2900)$ in $B^+ \to D^+D^-K^+$ by LHCb contains two $P$-wave poles denoted as $T_{cs1-}(2900)$ and $T^{\prime}_{cs1-}(2900)$, respectively. After considering the channel couplings among the $\bar{D}K$, $\bar{D}^*K$, $\bar{D}K^*$ and $\bar{D}^*K^*$ and the width of the $K^*$ meson, the masses and widths of the $S$-wave pole $T_{cs0+}(2900)$ and two $P$-wave poles $T_{cs1-}(2900)$ and $T^{\prime}_{cs1-}(2900)$ coincide with those of the $X_0(2900)$ and $X_1(2900)$ remarkably, which provides strong support for identifying $X_0(2900)$ and $X_1(2900)$ as $\bar{D}^{(*)}K^{(*)}$ dimeson states. Furthermore, we extensively calculate all $S$-wave and $P$-wave $\bar{D}^{(*)}K^{(*)}$ systems up to $J=3$ and predict four new isoscalar charmed-strange dimeson-type tetraquark states: an $S$-wave state $T_{cs1+}(2900)$ with quantum number $J^P=1^+$, three $P$-wave states $T_{cs1-}(2760)$ with $J^P=1^-$, $T_{cs0-}(2760)$ with $J^P=0^-$ and $T_{cs2-}(2900)$ with $J^P=2^-$. These near-threshold poles can be searched for at LHCb, Belle II and BESIII.

hep-ph↗

arXiv2024

Fully strange tetraquark resonant states as the cousins of $X(6900)$

We conduct systematic calculations of the S-wave fully strange systems with ``normal" $\left(J^{P C}=0^{++}, 1^{+-}, 2^{++}\right)$ and ``exotic" $\left(J^{P C}=0^{+-}, 1^{++}, 2^{+-}\right)$ C-parities, which are the strange analogue of the fully charmed tetraquark state $X(6900)$. Within a constituent quark potential model, we employ the Gaussian expansion method to solve the four-body Schrödinger equation and the complex scaling method to identify resonant states. We obtain a series of resonant states and zero-width states in the mass range of 2.7 to 3.3 GeV, with their widths ranging from less than 1 MeV to about 50 MeV. Their rms radii strongly indicate that they are compact tetraquark states. Among these states, the $T_{4s,2^{++}}(2714)$ may be the most likely one to be observed experimentally. We urge the experimental exploration of the $2^{++}$ $s s \bar{s} \bar{s}$ state around 2.7 GeV in the $ϕϕ$ channel. Since the lowest S-wave $s s \bar{s} \bar{s}$ state is around 2.7 GeV, the compact P-wave $s s \bar{s} \bar{s}$ states are expected to be heavier. Hence, $ϕ(2170)$ and $X(2370)$ are unlikely to be compact tetraquark states.

hep-ph↗

arXiv2024

Spectrum of the molecular hexaquarks

We investigate the mass spectra of molecular-type hexaquark states in the dibaryon systems. These systems are composed of the charmed baryons $[Σ_c^{(\ast)}$, $Ξ_c^{(\prime,\ast)}]$, doubly charmed baryons $[Ξ_{cc}^{(\ast)}]$, and hyperons $[Σ^{(\ast)}$, $Ξ^{(\ast)}]$. We consider all possible combinations of particle-particle and particle-antiparticle pairs, including the S-wave spin multiplets in each combination. We establish the underlying connections among the molecular tetraquarks, pentaquarks, and hexaquarks with the effective quark-level interactions. We find that the existence of molecular states in $DD^\ast$, $D\bar{D}^\ast$, and $Σ_c\bar{D}^{(\ast)}$ systems leads to the emergence of a large number of deuteron-like hexaquarks in the heavy flavor sectors. Currently, there have been several experimental candidates for molecular tetraquarks and pentaquarks. The experimental search for near-threshold hexaquarks will further advance the establishment of the underlying dynamical picture of hadronic molecules and deepen our understanding of the role of spin-flavor symmetry in near-threshold residual strong interactions.

hep-ph↗

arXiv2024

Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875)^+$ from finite volume energy levels

We discuss a novel effective-field-theory-based approach for extracting two-body scattering information from finite volume energies, serving as an alternative to Lüscher's method. By explicitly incorporating one-pion exchange, we overcome the challenging left-hand cut problem in Lüscher's method and can handle finite volume energy levels both below and above the left-hand cut. Applied to the lattice data for $DD^*$ scattering at a pion mass of 280 MeV, as an illustrative example, our results reveal the significant impact of the one-pion exchange on P-wave and S-wave phase shifts. The pole position of the $T_{cc}(3875)^+$ state, extracted from the finite-volume energy levels at this pion mass while taking into account left-hand cut effects, range corrections and partial-wave mixing, is consistent with a near-threshold resonance. This study demonstrates, for the first time, that two-body scattering information can be reliably extracted from lattice spectra including the left-hand cut.

hep-lat↗

arXiv2024

Spectrum of the molecular pentaquarks

We investigate the mass spectrum of the molecular pentaquarks composed of a baryon and a meson. We establish the underlying relations among the near-threshold interactions of the molecular tetraquark and pentaquark systems. We find the existence of the molecule candidates in the $Σ_c\bar{D}^{(\ast)}$, $DD^\ast$, and $D\bar{D}^\ast$ systems indicates a substantial presence of the hadronic molecules in the {\it heavy} baryon plus {\it heavy} meson systems ({\it heavy} refers to the hadrons with the $c$ and/or $s$ quarks). We make an exhaustive prediction of the possible bound/virtual molecular states in the systems: $Σ_{c}^{(\ast)}\bar{D}^{(\ast)}$, $Σ_{c}^{(\ast)}D^{(\ast)}$, $Ξ_{c}^{(\prime,\ast)}\bar{D}^{(\ast)}$, $Ξ_{c}^{(\prime,\ast)}D^{(\ast)}$, $Σ_{c}^{(\ast)}K^{\ast}$, $Σ_{c}^{(\ast)}\bar{K}^{\ast}$, $Ξ_{c}^{(\prime,\ast)}K^{\ast}$, $Ξ_{c}^{(\prime,\ast)}\bar{K}^{\ast}$, $Ξ_{cc}^{(\ast)}\bar{D}^{(\ast)}$, $Ξ_{cc}^{(\ast)}D^{(\ast)}$, $Ξ_{cc}^{(\ast)}K^{\ast}$, $Ξ_{cc}^{(\ast)}\bar{K}^{\ast}$, $Σ^{(\ast)}\bar{D}^{(\ast)}$, $Σ^{(\ast)}D^{(\ast)}$, $Ξ^{(\ast)}\bar{D}^{(\ast)}$, $Ξ^{(\ast)}D^{(\ast)}$, $Σ^{(\ast)} K^\ast$, $Σ^{(\ast)} \bar{K}^\ast$, $Ξ^{(\ast)} K^\ast$, $Ξ^{(\ast)} \bar{K}^\ast$. Hunting for the predicted states in experiments will significantly deepen our understanding of the formation mechanism of the hadronic molecules, and shed light on the manifestation of flavor symmetry in the low-energy residual strong interactions.

hep-ph↗

arXiv2024

Doubly heavy tetraquark states in the constituent quark model using diffusion Monte Carlo method

We use the diffusion Monte Carlo method to calculate the doubly heavy tetraquark $T_{cc}$ system in two kinds of constituent quark models, the pure constituent quark model AL1/AP1 and the chiral constituent quark model. When the discrete configurations are complete and no spatial clustering is preseted, the AL1/AP1 model gives an energy of $T_{cc}$ close to the $DD^*$ threshold, and the chiral constituent quark model yields a deeply bound state. We further calculate all doubly heavy tetraquark systems with $J^P=0^+,1^+,2^+$, and provide the binding energies of systems with bound states. The $I(J^P)=0(0^+)$ $bc\bar{n}\bar{n}$, $0(1^+)$ $bb\bar{n}\bar{n}$, $0(1^+)$ $bc\bar{n}\bar{n}$, $\frac{1}{2}(1^+)$ $bb\bar{s}\bar{n}$ systems have bound states in all three models. Since the DMC method has almost no restriction on the spatial part, the resulting bound states have greater binding energies than those obtained in previous works.

hep-ph↗

arXiv2024

Benchmark calculations of fully heavy compact and molecular tetraquark states

We calculate the mass spectrum of the S-wave fully heavy tetraquark systems $ QQ\bar Q\bar Q~(Q=c,b) $ with both normal $ (J^{PC}=0^{++},1^{+-},2^{++}) $ and exotic $ (J^{PC}=0^{+-},1^{++},2^{+-}) $ C-parities using three different quark potential models (AL1, AP1, BGS). The exotic C-parity systems refer to the ones that cannot be composed of two S-wave ground heavy quarkonia. We incorporate the molecular dimeson and compact diquark-antidiquark spatial correlations simultaneously, thereby discerning the actual configurations of the states. We employ the Gaussian expansion method to solve the four-body Schrödinger equation, and the complex scaling method to identify the resonant states. The mass spectra in three different models qualitatively agree with each other. We obtain several resonant states with $ J^{PC} = 0^{++}, 1^{+-}, 2^{++}, 1^{++} $ in the mass region $(6.92,7.30)\, \mathrm{GeV}$, some of which are good candidates of the experimentally observed $X(6900)$ and $X(7200)$. We also obtain several exotic C-parity zero-width states with $ J^{PC}=0^{+-} $ and $ 2^{+-} $. These zero-width states have no corresponding S-wave diquarkonium threshold and can only decay strongly to final states with P-wave quarkonia. With the notation $T_{4Q,J(C)}(M)$, we deduce from the root mean square radii that the $ X(7200) $ candidates $ T_{4c,0(+)}(7173), T_{4c,2(+)}(7214) $ and the state $ T_{4c,1(-)}(7191) $ look like molecular states although most of the resonant and zero-width states are compact states.

hep-ph↗

arXiv2024

Dynamic Perturbation-Adaptive Adversarial Training on Medical Image Classification

Remarkable successes were made in Medical Image Classification (MIC) recently, mainly due to wide applications of convolutional neural networks (CNNs). However, adversarial examples (AEs) exhibited imperceptible similarity with raw data, raising serious concerns on network robustness. Although adversarial training (AT), in responding to malevolent AEs, was recognized as an effective approach to improve robustness, it was challenging to overcome generalization decline of networks caused by the AT. In this paper, in order to reserve high generalization while improving robustness, we proposed a dynamic perturbation-adaptive adversarial training (DPAAT) method, which placed AT in a dynamic learning environment to generate adaptive data-level perturbations and provided a dynamically updated criterion by loss information collections to handle the disadvantage of fixed perturbation sizes in conventional AT methods and the dependence on external transference. Comprehensive testing on dermatology HAM10000 dataset showed that the DPAAT not only achieved better robustness improvement and generalization preservation but also significantly enhanced mean average precision and interpretability on various CNNs, indicating its great potential as a generic adversarial training method on the MIC.

eess.IV↗

arXiv2024

Virtual states in the coupled-channel problems with an improved complex scaling method

We improve the complex scaling method (CSM) to obtain virtual states, which were previously challenging in the conventional CSM. Our approach solves the Schrödinger equation in the momentum space as an eigenvalue problem by choosing the flexible contours. It proves to be highly effective in identifying the poles across the different Riemann sheets in the multichannel scatterings. It is more straightforward and efficient than searching for the zeros of the Fredholm determinant of the Lippmann-Schwinger equation using the root-finding algorithms. This advancement significantly extends the capabilities of the CSM in accurately characterizing the resonances and virtual states in quantum systems.

hep-ph↗

arXiv2024

Unified description of the $Qs \bar q \bar q$ molecular bound states, molecular resonances and compact tetraquark states in the quark potential model

We calculate the mass spectrum of the $Qs\bar q \bar q$ $(Q=c, b)$ tetraquark states with $J^P=(0,1,2)^+$ using the AL1 quark potential model, which successfully describes the conventional hadron spectrum. We employ the Gaussian expansion method to solve the four-body Schrödinger equation, and use the complex scaling method to identify the resonances. With the notation $T_{Q s, I(J)}^{\text {Theo. }}(M)$, we find several near-threshold bound states and resonances, including $T_{cs,0(0)}^{\mathrm{Theo.}}(2350)$, $T_{cs,0(0)}^{\mathrm{Theo.}}(2906)$, $T_{bs,0(0)}^{\mathrm{Theo.}}(5781)$, $T_{bs,0(1)}^{\mathrm{Theo.}}(5840)$, and $T_{bs,0(0)}^{\mathrm{Theo.}}(6240)$ which are close to the $D\bar{K}$, $D^*\bar{K}^*$, $\bar{B}\bar{K}$, $\bar{B}^*\bar{K}$ and $\bar{B}^*\bar{K}^*$ thresholds, respectively. Furthermore, their spatial structures clearly support their molecular natures. The resonance $T_{cs,0(0)}^{\mathrm{Theo.}}(2906)$ has a mass of $2906$ MeV, a width of $20$ MeV, and quantum numbers $I(J^P)=0(0^+)$, which may serve as a good candidate for the experimental $T_{cs0}(2900)$ state. We strongly urge the experimental search of the predicted states.

hep-ph↗

arXiv2023

Spectrum of the molecular tetraquarks: Unraveling the $T_{cs0}(2900)$ and $T_{c\bar{s}0}^a(2900)$

We relate the interactions of the $\bar{D}^{(\ast)} K^\ast$ and $D^{(\ast)} K^\ast$ systems to those of $D^{(\ast)}D^{(\ast)}$ and $D^{(\ast)}\bar{D}^{(\ast)}$ respectively, considering the residual strong interactions at the near-threshold energy is too weak to excite the strange quarks inside the hadrons. We propose an effective model to describe the low-energy S-wave interactions that are undertaken by the light $u$, $d$ quarks between two separated heavy hadrons. We find that the existence of molecules in the heavy-(anti)heavy sectors will naturally lead to the emergence of molecular states in $\bar{D}^{(\ast)} K^\ast$ and $D^{(\ast)} K^\ast$ systems. The recently observed $T_{cs0}(2900)$ and $T_{c\bar{s}0}^a(2900)$ can be well identified as the $0(0^+)$ and $1(0^+)$ partners of $T_{cc}(3875)$ and $Z_c(3900)$ in the charmed strange sector, respectively. We also predict their members under the {\it heavy} ($c$ and $s$) quark symmetry and SU(2) flavor symmetry. Most of them are very good molecule candidates, for example, (i) the $0(1^+)$ states in $D^\ast D^\ast$, $\bar{D}K^\ast$, $\bar{D}^\ast K^\ast$; (ii) the $0^{(+)}(2^{+(+)})$ states in $D^\ast \bar{D}^\ast$, $\bar{D}^\ast K^\ast$, $D^\ast K^\ast$; (iii) the $1^-(0^{++})$ state in $D^\ast\bar{D}^\ast$ and $1(1^+)$ state in $D^\ast K^\ast$. The $0^+(0^{++})$ state in $D\bar{D}$ and the $0(1^+)$ state in $DK^\ast$ might also exist as virtual states, and the $0(1^+)$ $DK^\ast$ can serve as a key to infer the existence of $0^+(0^{++})$ $D\bar{D}$. The $D_sπ$ invariant mass spectrum of $T_{c\bar{s}0}^a(2900)$ is also studied within the coupled-channel approach, and the molecular interpretation of $T_{c\bar{s}0}^a(2900)$ is consistent with the experimental data. Searching for the predicted states in experiments is crucial to discriminate the different pictures for interpreting these near-threshold exotica.

hep-ph↗

arXiv2023

Tetraquark bound states in constituent quark models: benchmark test calculations

We investigate the tetraquark bound states that are manifestly exotic using three distinct few-body methods: Gaussian Expansion Method (GEM), Resonating Group Method (RGM), and Diffusion Monte Carlo (DMC). We refer to manifestly exotic states that do not involve a mixture with the conventional mesons through the creation and annihilation of $n\bar{n}$, where $n=u, d$. Our calculations are conducted with two types of quark models: the pure constituent quark model featuring one-gluon-exchange interactions and confinement interactions, and the chiral constituent quark model, supplemented by extra one-boson-exchange interactions. This study represents a comprehensive benchmark test of various few-body methods and quark models. Our findings reveal the superiority of GEM over RGM and DMC methods based on present implements for the tetraquark bound states. Additionally, we observe a tendency for the chiral quark model to overestimate the binding energies. We systematically explore the fully, triply, doubly, and singly heavy tetraquark states with $J^P=0^+,1^+,2^+$, encompassing over 150 states in total. We successfully identify several bound states, including $[cc\bar{n}\bar{n}]_{J^{P}=1^{+}}^{I=0}$, $[bb\bar{n}\bar{n}]_{J^{P}=1^{+}}^{I=0}$, $[bc\bar{n}\bar{n}]_{J^{P}=0^{+},1^{+},2^{+}}^{I=0}$, $[bs\bar{n}\bar{n}]_{J^{P}=0^{+},1^{+}}^{I=0}$, $[cs\bar{n}\bar{n}]_{J^{P}=0^{+}}^{I=0}$, and $[bb\bar{n}\bar{s}]_{J^{P}=1^{+}}$, all found to be bound states below the dimeson thresholds.

hep-ph↗

arXiv2023

Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules

Chiral symmetry and its spontaneous breaking play an important role both in the light hadron and heavy hadron systems. The chiral perturbation theory ($χ$PT) is the low energy effective field theory of the QCD. In this work, we shall review the investigations on the chiral corrections to the properties of the heavy mesons and baryons within the framework of $χ$PT. We will also review the scatterings of the light pseudoscalar mesons and heavy hadrons, through which many new resonances such as the $D_{s0}^\ast(2317)$ could be understood. Moreover, many new hadron states were observed experimentally in the past decades. A large group of these states is near-threshold resonances, such as the charged charmoniumlike $Z_c$ and $Z_{cs}$ states, bottomoniumlike $Z_b$ states, hidden-charm pentaquark $P_c$ and $P_{cs}$ states and the doubly charmed $T_{cc}$ state, etc. They are very good candidates of the loosely bound molecular states composed of a pair of charmed (bottom) hadrons, which are very similar to the loosely bound deuteron. The modern nuclear force was built upon the chiral effective field theory ($χ$EFT), which is the extension of the $χ$PT to the systems with two matter fields. The long-range and medium-long-range interactions between two nucleons arise from the single- and double-pion exchange respectively, which are well constrained by the chiral symmetry and its spontaneous breaking. The short-distance interactions can be described by the low energy constants. Such a framework works very well for the nucleon-nucleon scattering and nuclei. In this work, we will perform an extensive review of the progress on the heavy hadronic molecular states within the framework of $χ$EFT. We shall emphasize that the same chiral dynamics not only govern the nuclei and forms the deuteron, but also dictates the shallow bound states or resonances composed of two heavy hadrons.

hep-ph↗