Hadronic Molecular States Research Articles

Compositeness of near-threshold exotic hadrons with decay and coupled-channel effects

Abstract. The near-threshold exotic hadrons such as Tcc and X(3872) are naively considered as the hadronic molecular state from the viewpoint of the low-energy universality. However, it is also known that the elementary dominant state is not completely excluded as the internal structure of the near-threshold states. Furthermore, the dominance of molecules is expected to be modified by the decay or coupled channels. We discuss these features of the near-threshold bound states by calculating the compositeness with the effective field theory.

New reaction approach to reflect exotic structure of hadronic molecular state

With the accumulation of experimental data, more and more exotic hadrons are observed. Among the interpretations of these exotic hadrons, molecular state and compact multiquark are two of the most popular pictures. However, it is still difficult to determine the structure of an exotic hadron. In this work, we propose a possible way to detect the internal structure of an exotic state. When a molecular state composed of two consistent hadrons is attacked by another particle, one of the constituents should be kicked out while another quasifree constituent stays almost unaffected. It is different from a compact multiquark which has no obvious subcluster. In this work, taking the $X(3872)$ as an example, we perform a Dalitz plot analysis of such reaction to find the effect of the different internal structures. Under the assumption of the $X(3872)$ as a molecular state or a compact tetraquark state, with the help of the effective Lagrangians, the Dalitz plot and the invariant mass spectrum are estimated with different total invariant mass of three final particles, and the effect of different binding energies is also discussed. Obvious event concentration can be observed as strips in the Dalitz plot and sharp peaks in the invariant mass spectrum for the $X(3872)$ with a small binding energy under the molecular state picture, while such concentration cannot be observed under the compact tetraquark picture. Such phenomenon can be applied to identify the internal structure of a new hadron state.

Production of in heavy ion collisions* *Supported by Guangdong Major Project of Basic and Applied Basic Research (2020B0301030008), the National Natural Science Foundation of China (12105107) and Science and Technology Program of Guangzhou (2019050001)

The yields of with its two possible configurations, i.e., the hadronic molecular state and tetraquark state, for Pb-Pb collisions at is studied. A volume effect is found from the centrality distribution of , which could help to distinguish the inner structure of . We also show the rapidity and the transverse momentum distributions of production as well as its elliptic flow coefficient as a function of the transverse momentum.

Identifying hadronic molecular states with a neural network

Neural networks are trained to judge whether or not an exotic state is a hadronic molecule of a given channel according its line-shapes. This method performs well in both trainings and validation tests. As applications, it is applied to study X(3872), X(4260) and Z_c(3900). The results show that Z_c(3900) should be regarded as a {bar{D}}^* D molecular state but X(3872) not. As for X(4260), it can not be a molecular state of chi _{c0}omega . Some discussions on X_1(2900) are also provided.

Covalent hadronic molecules induced by shared light quarks

After examining Feynman diagrams corresponding to the , , , and hadronic molecular states, we propose a possible binding mechanism induced by shared light quarks. This mechanism is similar to the covalent bond in chemical molecules induced by shared electrons. We use the method of QCD sum rules to calculate its corresponding light-quark-exchange diagrams, and the obtained results indicate a model-independent hypothesis: the light-quark-exchange interaction is attractive when the shared light quarks are totally antisymmetric so they obey the Pauli principle. We build a toy model with four parameters to formulize this picture and estimate binding energies of some possibly-existing covalent hadronic molecules. A unique feature of this picture is that the binding energies of the (I)J P = (0)1+ hadronic molecules are much larger than those of the (I)J P = (0)1+ ones, while the (I)J P = (1/2)1/2+ hadronic molecules have similar binding energies.

Probing the electromagnetic properties of the Σc(*)D(*) -type doubly charmed molecular pentaquarks

In this work, we discuss the electromagnetic properties of the $S$-wave ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{D}^{(*)}$-type doubly charmed molecular pentaquarks, which have close relation to their inner structures. Both the $S\ensuremath{-}D$ wave mixing effect and the coupled channel effect are taken into account. We analyze the magnetic moments for the $S$-wave ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{D}^{(*)}$ molecular states, and extend our theoretical framework to study the transition magnetic moments and the radiative decay widths between the $S$-wave ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{D}^{(*)}$ molecules. We discuss the relations between the magnetic moments and the transition magnetic moments for the $S$-wave ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{D}^{(*)}$-type doubly charmed molecular pentaquarks, which can be regarded as an indirect way to measure their magnetic moments experimentally. The present study may inspire the experimentalist's interest in measuring the electromagnetic properties of the hadronic molecular states.

Covalent hadronic molecules via QCD sum rules

After carefully examining Feynman diagrams corresponding to the $\bar D \Sigma_c$ hadronic molecular state, we propose a possible binding mechanism induced by shared light quarks. We systematically study its corresponding light-quark-exchange interaction using the method of QCD sum rules, and the obtained results suggest that there can be the $\bar D \Sigma_c$ covalent molecule of $I=1/2$. Our QCD sum rule analyses further indicate a model-independent hypothesis: the light-quark-exchange interaction is attractive when the shared light quarks are totally antisymmetric so that obey the Pauli principle.

Hidden-charm pentaquark states through current algebra: from their production to decay * *Supported by the National Natural Science Foundation of China (11722540, 12075019), the Jiangsu Provincial Double-Innovation Program (JSSCRC2021488), and the Fundamental Research Funds for the Central Universities

There may be seven hadronic molecular states. We construct their corresponding interpolating currents and calculate their masses and decay constants using QCD sum rules. Based on these results, we calculate their relative production rates in decays using current algebra, that is, , where and are two different states. We also study their decay properties via Fierz rearrangement and further calculate these ratios in the mass spectrum, that is, . Our results suggest that the molecular states of and may be observed in future experiments.

Induced Fission-Like Process of Hadronic Molecular States

We predict a new physical phenomenon, induced fission-like process and chain reaction of hadronic molecular states. As a molecular state, if induced by a D meson, the X(3872) can split into final state which is forbidden due to the spin-parity conservation. The breeding of the D meson of the reaction, such as , makes the chain reaction of X(3872) matter possible. We estimate the cross section of the D meson induced fission-like process of X(3872) into two D mesons. With very small D 0 beam momentum of 1 eV, the total cross section reaches an order of 1000 b, and decreases rapidly with the increasing beam momentum. With the transition of D* meson in molecular states to a D meson, the X(3872) can release large energy, which is acquired by the final mesons. The momentum distributions of the final D mesons are analyzed. In the laboratory frame, the spectator D meson in molecular state concentrates in the low momentum area. The energy from the transition from D* to D meson is mainly acquired by two scattered D mesons. The results suggest that the D meson environment will lead to the induced fission-like process and chain reaction of the X(3827). Such a phenomenon can be extended to other hadronic molecular states.

Hadronic molecules in B decays

There are eighteen possibly existing $D^{(*)} \bar D^{(*)}$, $D^{(*)} \bar K^{(*)}$, and $D^{(*)} D_s^{(*)-}$ hadronic molecular states. We construct their corresponding interpolating currents, and calculate their masses and decay constants using QCD sum rules. Based on these results, we calculate their relative production rates in $B$ and $B^*$ decays through the current algebra, and calculate their relative branching ratios through the Fierz rearrangement, as summarized in Table III. Our results support the interpretations of the $X(3872)$, $Z_c(3900)$, $Z_c(4020)$, and $X_0(2900)$ as the molecular states $D \bar D^*$ of $J^{PC} = 1^{++}$, $D \bar D^*$ of $J^{PC} = 1^{+-}$, $D^* \bar D^*$ of $J^{PC} = 1^{+-}$, and $D^* \bar K^*$ of $J^P = 0^{+}$, respectively. Our results also suggest that the $Z_{cs}(3985)$, $Z_{cs}(4000)$, and $Z_{cs}(4220)$ are strange partners of the $X(3872)$, $Z_c(3900)$, and $Z_c(4020)$, respectively. In the calculations we estimate the lifetime of a weakly-coupled composite particle $A = |BC\rangle$ to be $1/t_A \approx 1/t_B + 1/t_C + \Gamma_{A \to BC} + \cdots$, with $\cdots$ partial widths of other possible decay channels.

Exotic states Pc(4312) , Pc(4440) , and Pc(4457) in pp collisions at s=7 , 13 TeV

The exotic resonant states ${P}_{c}^{\ifmmode\pm\else\textpm\fi{}}(4312)$, ${P}_{c}^{\ifmmode\pm\else\textpm\fi{}}(4440)$, and ${P}_{c}^{\ifmmode\pm\else\textpm\fi{}}(4457)$ are studied using the constrained phase-space coalescence model plus the parton and hadron cascade (paciae) model in $pp$ collisions at $\sqrt{s}=7$, 13 TeV, respectively. The pentaquark states, the nucleuslike states, and the hadronic molecular states are considered as their possible structures based on the ${P}_{c}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}J/\ensuremath{\psi}p(\overline{p})$ bound state. The predictions about the yield, the normalized ${p}_{\mathrm{T}}$-differential yield, and the normalized rapidity-differential yield are presented for the aforementioned scenarios. The results indicate a hierarchy of the yields for different possible structures; they are all on the order of ${10}^{\ensuremath{-}6}$. These predictions can be tested by future experimental measurements.

Predicting another doubly charmed molecular resonance Tcc′+ (3876)

The isospin breaking effect plays an essential role in generating hadronic molecular states with a very tiny binding energy. Very recently, the LHCb Collaboration observed a very narrow doubly charmed tetraquark $T_{cc}^+$ in the $D^0D^0\pi$ mass spectrum, which lies just below the $D^0D^{*+}$ threshold around 273 keV. In this work, we study the $D^0D^{*+}/D^+D^{*0}$ interactions with the one-boson-exchange effective potentials and consider the isospin breaking effect carefully. We not only reproduce the mass of the newly observed $T_{cc}^+$ very well in the doubly charmed molecular tetraquark scenario, but also predict the other doubly charmed partner resonance $T_{cc}^{\prime+}$ with $m=3876~\text{MeV}$, and $\Gamma= 412~\text{keV}$. The prime decay modes of the $T_{cc}^{\prime+}$ are $D^0D^+\gamma$ and $D^+D^0\pi^0$. The peculiar characteristic mass spectrum of the $D^0D^{*+}/D^+D^{*0}$ molecular systems can be applied to identify the doubly charmed molecular states.

Establishing the first hidden-charm pentaquark with strangeness

We study the P_{cs}(4459)^0 recently observed by LHCb using the method of QCD sum rules. Our results support its interpretation as the {{bar{D}}}^* varXi _c hadronic molecular state of either J^P=1/2^- or 3/2^-. Within the hadronic molecular picture, the three LHCb experiments observing P_c and P_{cs} states (Aaij et al., Phys Rev Lett 115:072001, 2015; Aaij et al., Phys Rev Lett 122:222001, 2019; Aaij et al., arXiv:2012.10380 [hep-ex], 2012) can be well understood as a whole. This strongly supports the existence of hadronic molecules, whose studies can significantly improve our understanding on the construction of the subatomic world. To verify this picture, we propose to further investigate the P_{cs}(4459)^0 to examine whether it can be separated into two states, and to search for the {{bar{D}}} varXi _c molecular state of J^P=1/2^{-}.

XJ(2900) states in a hot hadronic medium

In this work we investigate the hadronic effects on the $X_{J=0,1} (2900)$ states in heavy-ion collisions. We make use of Effective Lagrangians to estimate the cross sections and their thermal averages of the processes $X_J \pi \to \bar{D}^{*} K , K^{*} \bar{D} $, as well as those of the corresponding inverse processes, considering also the possibility of different isospin assignments ($I=0,1$). We complete the analysis by solving the rate equation to follow the time evolution of the $X_J (2900)$ multiplicities and determine how they are affected by the considered reactions during the expansion of the hadronic matter. We also perform a comparison of the $X_J (2900)$ abundances considering them as hadronic molecular states ($J=0$ as a $S$-wave and $J=1$ as a $P$-wave) and tetraquark states at kinetic freeze-out.

Exotic double-charm molecular states with hidden or open strangeness and around 4.5∼4.7 GeV

In this work, we investigate the interactions between the charmed-strange meson ($D_s, D_s^{*}$) in $H$-doublet and the (anti-)charmed-strange meson ($D_{s1}, D_{s2}^{*}$) in $T$-doublet, where the one boson exchange model is adopted by considering the $S$-$D$ wave mixing and the coupled-channel effects. By extracting the effective potentials for the discussed $H_s\bar{T}_s$ and $H_s{T}_s$ systems, we try to find the bound state solutions for the corresponding systems. We predict the possible hidden-charm hadronic molecular states with hidden strangeness, i.e., the $D_s^{*}\bar D_{s1}+c.c.$ states with $J^{PC}$=$0^{--}, 0^{-+}$ and the $D_s^{*}\bar D_{s2}^{*}+c.c.$ states with $J^{PC}$=$1^{--}, 1^{-+}$. Applying the same theoretical framework, we also discuss the $H_s T_s$ systems. Unfortunately, the existence of the open-charm and open-strange molecular states corresponding to the $H_s T_s$ systems can be excluded.

Decay properties of the Zc(3900) through the Fierz rearrangement * * Supported by the National Natural Science Foundation of China (11722540)

We systematically construct all the tetraquark currents/operators of JPC = 1+- with the quark configurations , , and ( ), and derive their relations through the Fierz rearrangement of the Dirac and color indices. Using the transformations of and , we study decay properties of the as a compact tetraquark state; while using the transformation of , we study its decay properties as a hadronic molecular state.

Hadronic Molecular States Characterized by Compositeness of Resonances

Hadronic Molecular States Characterized by Compositeness of Resonances

Heavy quark spin multiplet structure of Pc-like pentaquarks as a P-wave hadronic molecular state

Abstract We study the heavy quark spin (HQS) multiplet structure of P-wave $Q\bar{Q}qqq$-type pentaquarks treated as molecules of a heavy meson and a heavy baryon. We define the light-cloud spin (LCS) basis decomposing the meson–baryon spin wave function into LCS and HQS parts. Introducing the LCS basis, we find HQS multiplets classified by the LCS: five HQS singlets, two HQS doublets, and three HQS triplets. We construct the one-pion exchange potential respecting the heavy quark spin and chiral symmetries to demonstrate which HQS multiplets are realized as a bound state. By solving the coupled channel Schrödinger equations, we study the heavy meson–baryon systems with $I=1/2$ and $J^P=(1/2^+, 3/2^+, 5/2^+, 7/2^+)$. The bound states which have the same LCS structure are degenerate at the heavy quark limit, and the degeneracy is resolved for finite mass. This HQS multiplet structure will be measured in future experiments.

カイラル動力学と K ^^- 中間子を含むハドロン分子的状態 （解説）

カイラル動力学と K ^^- 中間子を含むハドロン分子的状態 （解説）

Hadronic molecular states composed of spin-$\frac{3}{2}$32 singly charmed baryons

We investigate the possible deuteron-like molecules composed of a pair of charmed spin-$\frac{3}{2}$ baryons, or one charmed baryon and one charmed antibaryon within the one-boson-exchange (OBE) model. For the spin singlet and triplet systems, we consider the couple channel effect between systems with different orbital angular momentum. Most of the systems have binding solutions. The couple channel effect plays a significant role in the formation of some loosely bound states. The possible molecular states of $\Omega_c^*\Omega_c^*$ and $\Omega_c^*\bar{\Omega}_c^*$ might be stable once produced.