本文在介子交换模型的框架下研究了Y（4260）和${\rm Z^{+}_2(4250)}$是否是${\rm D_1D}$或${\rm D_0D^{*}}$分子。由$π$交换引起的非对角相互作用起主导作用。$σ$交换已被考虑在内，这导致对角交互。$σ$交换的贡献不利于分子态${\rm with I^{G}(J^{PC})=0^{-}(1^{--})}$的形成，但有利于分子${\rm with I^{G}(J^{P})=1^{-}(1^{-})}$的结合。光矢量介子交换也导致对角相互作用。对于${\rm Z^{+}_2(4250)}$，$ρ$和$ω$交换的贡献几乎相互抵消。对于目前所允许的有效耦合常数和合理的截断值$Λ$（1-2 GeV），我们发现Y（4260）可以被容纳为${\rm D_1D}$和${\rm D_0D^{*}}$分子，而将${\rm Z^{+}_2(4250)}$解释为${\rm D_1D}$或${\rm D_0D^{*}}$分子是不利的. Y（4260）和${\rm Z^{+}_2(4250)}$的底部类似物可能存在，最有希望发现它们的途径分别是$π^{+}π^{-}Υ$和$π^{+}χ_{b1}$。
英文摘要：
In this work, we have investigated whether Y(4260) and ${\rm Z^{+}_2(4250)}$ could be ${\rm D_1D}$ or ${\rm D_0D^{*}}$ molecules in the framework of meson exchange model. The off-diagonal interaction induced by $π$ exchange plays a dominant role. The $σ$ exchange has been taken into account, which leads to diagonal interaction. The contribution of $σ$ exchange is not favorable to the formation of molecular state ${\rm with I^{G}(J^{PC})=0^{-}(1^{--})}$, however, it is beneficial to the binding of molecule ${\rm with I^{G}(J^{P})=1^{-}(1^{-})}$. Light vector meson exchange leads to diagonal interaction as well. For ${\rm Z^{+}_2(4250)}$, the contribution from $ρ$ and $ω$ exchange almost cancels each other. For the currently allowed values of the effective coupling constants and a reasonable cutoff $Λ$ in the range 1-2 GeV, We find that Y(4260) could be accommodated as a ${\rm D_1D}$ and ${\rm D_0D^{*}}$ molecule, whereas the interpretation of ${\rm Z^{+}_2(4250)}$ as a ${\rm D_1D}$ or ${\rm D_0D^{*}}$ molecule is disfavored. The bottom analog of Y(4260) and ${\rm Z^{+}_2(4250)}$ may exist, and the most promising channels to discovery them are $π^{+}π^{-}Υ$ and $π^{+}χ_{b1}$ respectively.
In the present work, we estimate the decays of the $X(5568)$ and $X(5616)$ in a $B \bar{K}$ and a $B^\ast \bar{K}$ $S$-wave hadronic molecule scenarios, respectively, which may corresponding to the structure observed by D0 Collaboration. Our estimation indicates both $B\bar{K}$ and $B^\ast \bar{K}$ hadronic molecule decay widths could explain the experimental data in a proper model parameter range.
We demonstrate that in calculation, where unitarity constraints are properly imposed, the deeply bound hadronic molecules recently proposed by Close and Downum do not exist.
We discuss the hadronic molecule issue in the light and heavy meson sector. Thereby we use the radiative decays of the scalars f0(980) and a0(980) to study its possible molecular K barK structure. Further on we extend our formalism to mesons with open charm and strangeness, Ds0*(2317) and Ds1(2460), whose hadronic molecule interpretation is analyzed in weak decays with f0(980) in the final state.
Properties of scalar mesons below 1.0 GeV have been studied by regarding them as hadronic molecular states. Using the effective Lagrangian approach, we have calculated their leptonic decays, strong decays and productions via the $ϕ$ meson radiative decays. Comparing our results with that given in the literature and the data, we conclude that it is difficult to arrange them in the same nonet if some of them are pure hadronic molecules.
The newly observed hidden-charm meson Zc(3900) with quantum numbers J(P) = 1(+) is considered as a hadronic molecule composed of DD*. We give detailed predictions for the decay modes Zc(+) -> J/psi + pi(+) + gamma and Zc(+) -> J/psi + pi(+) + l(+) + l(-) (l = e, mu) in a phenomenological Lagrangian approach.
I give a brief comment on the LHCb's discovery of $P_c$ and $P_{cs}$ pentaquark states. These pentaquark states not only reveal a new kind of hadronic molecules, but also shed new light on the possible structure of pentaquark components in baryons, hence may play very important role for understanding un-quenching dynamics and the whole baryon spectroscopy.
The two newly observed hidden-bottom mesons Zb(10610) and Zb'(10650) with quantum numbers J(P) = 1(+) are considered as hadronic molecules composed of BB(*) and B(*)B(*), respectively. We give predictions for the widths of the strong two-body decays Zb(+) to Upsilon(nS) + pi(+) and Zb'(+) to Upsilon(nS) + pi(+) in a phenomenological Lagrangian approach.
The isotriplet Sigmac(2800) baryon with possible quantum numbers J(P) = 1/2(+), 1/2(-) or 3/2(+), 3/2(-) is considered as a hadronic molecule composed of a nucleon and a D meson. We determine the strong two-body decay widths Sigmac to Lambdac + pi which are shown to be consistent with current data for the J(P) = 1/2(+) and J(P) = 3/2(-) assignments.
In order to understand the structure of the X(3872), the $c \bar c$ charmonium core state coupling to the $D^0 \bar D^{\ast 0}$ and $D^+ D^{\ast -}$ molecular states are studied. The strengths of the couplings between the charmonium state and the hadronic molecular states are determined so as to reproduce the observed mass of the the X(3872). The isospin symmetry breaking is introduced by the mass differences of the neutral and charged $D$ mesons. The obtained structure of the X(3872) is that about 7% is $\ccbar$ charmonium, 75% is the isoscalar $D \bar D^\ast$ molecule and 18% is the isovecto…
After examining the Feynman diagrams corresponding to the $\bar D^{(*)} Σ_c^{(*)}$, $\bar D^{(*)} Λ_c$, $D^{(*)} \bar K^{*}$, and $D^{(*)} \bar D^{(*)}$ 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 tot…
In this work we study the properties of hadronic molecules in the heavy-quark sector. These have become increasingly important since from the beginning of this century a large number of states have been measured that for different reasons do not fit the predictions of simple quark models. In particular we discuss two candidates in the open charm sector, $D_{s0}^*(2317)$ and $D_{s1}(2460)$, and two candidates in the bottomonium sector, $Z_b(10610)$ and $Z_b(10650)$. Theorists have proposed different explanations for these states including tetraquarks, hybrids, hadro-quarkonia and, subject of th…
In this proceeding, we present our recent work on decay behaviors of the $P_c$ hadronic molecules, which can help to disentangle the nature of the two $P_c$ pentaquark-like structures. The results turn out that the relative ratio of the decays of $P^+_c(4380)$ to $\bar{D}^* Λ_c$ and $J/ψp$ is very different for $P_c$ being a $\bar D^*Σ_c$ or $\bar DΣ_c^*$ bound state with $J^P=\frac{3}{2}^-$. And from the total decay width, we find that $P_c(4380)$ being a $\bar DΣ_c^*$ molecule state with $J^P=\frac{3}{2}^-$ and $P_c(4450)$ being a $\bar D^*Σ_c$ molecule state with $J^P=\frac{5}{2}^+$ is more…
We discuss the possible interpretation of X(3872) as a $DD^{\ast}$ hadronic molecule with $J^{PC} = 2^{-+}$. Using the phenomenological Lagrangian approach, we studied its radiative and strong decay properties. We find that our model with about 97.6% isospin zero component explains the existing data nicely. We predict the partial widths of the radiative and strong decays of X(3872) and show that the measurement of the ratio $\mathcal{B}(X(3872) \to χ_{c0}π^0)/\mathcal{B}(X(3872) \to χ_{c1}π^0)$ may signal the nature of X(3872).
Production of Hyperons, Charmed Baryons, and Hadronic Molecule Candidates in Neutrino-Proton Reaction
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Tsinghua University（清华大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）
In recent years data have been accumulated at various experiments about states in the heavy quarkonium mass range that seem to be inconsistent with the most simple variants of the quark model. In this contribution it is demonstrated that most of those data are consistent with a dominant molecular nature of those states. It is also discussed which kind of observables are sensitive to the molecular component and which are not.
The Lambdac(2940)+ baryon with quantum numbers J(P) = 1/2(+) is considered as a molecular state composed of a nucleon and D* meson. We give predictions for the width of the radiative decay process Lambdac(2940)+ to Lambdac(2286)+ gamma in this interpretation. Based on our results we argue that an experimental determination of the radiative decay width of Lambdac(2940)+ is important for the understanding of its intrinsic properties.
The Lambdac(2940)+ baryon with possible quantum numbers J(P) = 1/2+ and 1/2- is studied as a molecular state composed of a nucleon and D* meson. We give predictions for the strong two-body decay channels Lambdac(2940)+ to p D0, Sigmac(++) pi(-) and Sigmac(0) pi(+) where the sum of partial widths is consistent with current data for the case of J(P) = 1/2(+). The case of J(P) = 1/2(-) is shown to be ruled out.
The $P_c(4380)$ and $P_c(4450)$ states observed recently by LHCb experiment were proposed to be either $\bar{D} Σ_c^*$ or $\bar{D}^* Σ_c$ S-wave bound states of spin parity $J^P={\frac32}^-$. We analyze the decay behaviors of such two types of hadronic molecules within the effective Lagrangian framework. With branching ratios of ten possible decay channels calculated, it is found that the two types of hadronic molecules have distinguishable decay patterns. While the $\bar{D} Σ_c^*$ molecule decays dominantly to $\bar{D}^* Λ_c$ channel with a branching ratio by 2 orders of magnitude larger than…
In this paper we confront both the hadronic molecule and the hadro-charmonium interpretations of the $\y$ with the experimental data currently available. We conclude that the data support the $\y$ being dominantly a $D_1\bar D+c.c.$ hadronic molecule while they challenge the hadro-charmonium interpretation. However, additional data is necessary to allow for stronger conclusions.
The X(3872) with quantum numbers J(PC) = 1(++) is considered as a composite hadronic state comprised of the dominant molecular D(0) D*(0) component and other hadronic pairs - D(+-) D*(-+), Jpsi omega and Jpsi rho. Applying the compositeness condition we constrain the couplings of the X(3872) to its constituents. We calculate two- and three-body hadronic decays of the X(3872) to charmonium states chi(cJ) and pions using a phenomenological Lagrangian approach. Next using the estimated X-Jpsi-omega and and X-Jpsi-rho couplings we calculate the widths of X(3872) to Jpsi + h, where h = pi(+) pi(-),…
Strong two- and three-body decays of the new excited hyperon $Ω^*(2012)$ are discussed in the hadronic molecular approach. The $Ω^*(2012)$ state is considered to contain the mixed $Ξ\bar K$ and $Ωη$ hadronic components. In our calculations we use a phenomenological hadronic Lagrangian describing the coupling of the bound states to its constituents and of the constituents to other hadrons occurring in the final state. Our results show that the decay widths of the two-body decay modes $Ω^*(2012) \to Ξ\bar K$ lie in the few MeV region and are compatible with or dominate over the rates of the thre…
We report on further evidence that the Y(3940) and the recently observed Y(4140) are heavy hadron molecule states with quantum numbers J(PC) = 0(++). The Y(3940) state is considered to be a superposition of D*(+)D*(-) and D*(0) barD*(0), while the Y(4140) is a bound state of Ds*(+) and Ds*(-) mesons. For the first time we give predictions for the strong Y(3940) to Jpsi omega, Y(4140) to Jpsi phi and radiative Y(3940)/Y(4140) to gamma gamma decay widths in a phenomenological Lagrangian approach. Results for the strong Jpsi V (V = omega, phi) decays clearly support the molecular interpretation o…
Motivated by the latest discovery of a new tetraquark $T_{cc}^+$ with two charm quarks and two light antiquarks by LHCb Collaboration, we investigated the $DD^*$ hadronic molecule interpretation of $T_{cc}^+$. By calculation, the mass and the decay width of this new structure $T_{cc}^+$ can be understood in one-meson exchange potential model. The binding energies for these $DD^*$ hadronic molecules with $J^P=1^+$ are around $1MeV$. Besides, we also studied the possible beauty-partners $T_{bb}(10598)$ of hadronic molecule $T^+_{cc}$, which may be feasible in future LHCb experiments.
The three pentaquark states, $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, discovered by the LHCb Collaboration in 2019, can be arranged into a complete heavy quark spin symmetry multiplet of hadronic molecules of $\bar{D}^{(\ast)}Σ_{c}^{(\ast)}$. In the heavy quark mass limit, the $Σ_{c}^{(\ast)}$ baryons can be related to the doubly charmed tetraquark states of isospin 1, i.e., $T_{\bar{c}\bar{c}}^{(\ast)}$( $T_{\bar{c}\bar{c}}^{0}$, $T_{\bar{c}\bar{c}}^{1}$, $T_{\bar{c}\bar{c}}^{2}$), via heavy antiquark diquark symmetry, which dictates that the $\bar{D}^{(\ast)}Σ_{c}^{(\ast)}$ interactions are…
We examine the use of hadronic event generators, such as Pythia or Herwig, to estimate the production rate of loosely-bound hadronic molecules, such as the deuteron and the X(3872). In the case of the deuteron, we point out that there are large uncertainties in the normalization of the predictions using event generators, because baryon pair distributions are not among the inputs used to tune the event generators. Predictions using Pythia for anti-deuteron production in Upsilon decay are compared to measurements by the CLEO Collaboration. They suggest that Pythia overpredicts the probability of…
We study the interesting problem of interaction and identification of the hadronic molecules which seem to be deuteron-like structure. In particular, we propose a binding mechanism in which One Boson Exchange Potential plus Yukawa screen-like potential is applied in their relative s-wave state. We propose the dipole-like interaction between two color neutral states to form a hadronic molecule. For the identification of the hadronic molecules, the Weinberg's compositeness theorem is used to distinguish the molecule from confined (elementary) state. The present formalism predict some di-hadronic…
Among the newly observed structures in the heavy quarkonium mass region, some are proposed to be hadronic molecules. We investigate the consequences of heavy quark flavor symmetry on these heavy meson hadronic molecules. The symmetry allows us to predict new hadronic molecules on one hand, and test the hadronic molecular assumption of the observed structures on the other hand. We explore the consequences of the flavor symmetry assuming the X(3872) and $Z_b(10610)$ as a isoscalar $D\bar D^*$ and isovector $B\bar B^*$ hadronic molecule, respectively. A series of hadronic molecules composed of he…
We demonstrate that the relative ratio of the decays of hidden charm pentaquark-like structure $P^+_c(4380)$ to $\bar{D}^* Λ_c^+$ and $J/ψp$ are very different for $P^+_c$ being $\bar{D} Σ_c^*(2520)$ or $\bar{D}^* Σ_c(2455)$ molecule states. While the partial width of the $\bar{D} Σ_c^*(2520)$ molecule to the $\bar{D}^* Λ_c^+$ is much larger, by one order of magnitude, than that to the $J/ψp$, the $\bar{D}^* Σ_c(2455)$ molecule shows a different pattern. Our analysis shows that the $\bar{D} Σ_c^*$ bound state ansatz is more reasonable than the $\bar{D}^* Σ_c$ one to explain the broad $P_c(4380…
Using the general form of the generalized Bethe-Salpeter wave functions for four-quark states describing the meson-meson molecular structure given in our previous work, we obtain the general formulas for the decay widths of molecular states composed of two vector mesons with arbitrary spin and parity into two photons. Then this general formalism is applied to investigate the radiative two-photon decay of the obeserved \emph{X}(3915) state, where this exotic state \emph{X}(3915) is considered as a molecular state consisting of two heavy vector mesons $D^{*0}\bar{D}^{*0}$. The numerical result o…
Pion exchange in S-wave between hadrons that are themselves in a relative S-wave can shift energies by hundreds of MeV. In the case of charmed mesons $D,D^*,D_0,D_1$ a spectroscopy of quasi-molecular states may arise consistent with enigmatic charmonium states observed above 4 GeV in $e^+e^-$ annihilation. A possible explanation of $Y(4260)\to ψππ$ and $Y(4360) \to ψ'ππ$ is found. Searches in $D\bar{D}3π$ channels as well as B decays are recommended to test this hypothesis.
In the present article we report on evidence for hadronic molecule structures in the charmonium sector. In particular we discuss the Y(3940) and the recently observed Y(4140) as heavy hadron molecule states with quantum numbers $J^{PC} = 0^{++}$ or $2^{++}$. The Y(3940) state is considered to be a superposition of $D^{\ast +}D^{\ast -}$ and $D^{\ast 0} \overline{D^{\ast 0}}$, while the Y(4140) is a bound state of $D_s^{\ast +}$ and $D_s^{\ast -}$ mesons. We give predictions for both the strong Y(3940) to J/psi omega, Y(4140) to J/psi phi and radiative Y(3940)/Y(4140) to gamma gamma decay width…
We discuss selected and important features of hadronic molecules as one of promising forms of exotic hadrons near thresholds. Using examples of $D \bar D^*$ systems such as $X(3872)$ and $Z_c$, emphasis is put on the roles of the one pion exchange interaction between them and their coupling to intrinsic quark states. Thus hadronic molecules emerge as admixtures of the dominant long-range hadron structure and short-range quark structure. For the pion exchange interaction, properties of the tensor force are analyzed in detail. More coupled channels supply more attractions, and heavier constituen…
Very recently the LHCb Collaboration reported their observation of the first two fully open-flavor tetraquark states, the $X_0(2900)$ of $J^P = 0^+$ and the $X_1(2900)$ of $J^P = 1^-$. We study their possible interpretations using the method of QCD sum rules, paying special attention to an interesting feature of this experiment that the higher resonance $X_1(2900)$ has a width significantly larger than the lower one $X_0(2900)$. Our results suggest that the $X_0(2900)$ can be interpreted as the $S$-wave $D^{*-}K^{*+}$ molecule state of $J^P = 0^+$, and the $X_1(2900)$ can be interpreted as the…
Pion exchange in S-wave between hadrons that are themselves in a relative S-wave is shown to shift energies by hundreds of MeV, leading to deeply bound quasi-molecular states. In the case of charmed mesons $D^*,D_1$ a spectroscopy arises consistent with enigmatic charmonium states observed above 4 GeV in $e^+e^-$ annihilation. A possible explanation of $Y(4260)\to ψππ$ and $Y(4360) \to ψ'ππ$ is found. We give results for all isospin and charge-conjugation combinations, and comment on flavor exotic doubly charmed states and bottomonium analogs. A search in $D\bar{D}3π$ is recommended to test th…
In 2010, $Λ^*_{c\bar{c}}$ states were predicted as the strange number $S=-1$ partners of $N^*_{c\bar{c}}$, which are well known now as the $P_c$ states and observed experimentally by LHCb Collaboration. We analyze the decay behaviors of $Λ_{c\bar{c}}$ as S-wave hadronic molecules within the effective Lagrangian framework by a similar method, which has been applied on $P_c$ states successfully. With partial widths of possible decay channels calculated, we find that $Λ_{c\bar{c}}(4213)$ and $Λ_{c\bar{c}}(4403)$, which are formed as pseudoscalar meson baryon molecules, mainly decay to the $η_c Λ$…
Radiative decays of hadronic molecules: From confusion to inspiration
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Hadronic Molecules and Low-Energy Hadron-Hadron Scattering Amplitudes
分子是强子对的弱束缚态，近年来引起了人们极大的兴趣。分子存在的问题与确定低能强子-强子散射振幅的更一般的问题密切相关，人们普遍认为这需要非微扰方法。在这篇文章中，我们报告夸克模型计算使用一个简单的微扰散射机制，一个胶子交换后，组分交换。我们把相关的图称为“夸克玻恩图”。对于选择隔离这种机制的情况下，I=2 $ππ$，I=3/2 K $π$和KN的结果通常是在良好的协议与实验S波散射振幅给定的标准势模型参数，和NN我们发现微扰的结果非常相似的非微扰硬核的奥卡和矢崎。我们还讨论了我们的研究结果为其他不太熟悉的渠道，这些包括预测的矢量矢量束缚态，其中之一可能是$θ(1710)$。
The spectrum of hadronic molecules composed of heavy-antiheavy charmed hadrons has been obtained in our previous work. The potentials are constants at the leading order, which are estimated from resonance saturation. The experimental candidates of hadronic molecules, say $X(3872)$, $Y(4260)$, three $P_c$ states and $P_{cs}(4459)$, fit the spectrum well. The success in describing the pattern of heavy-antiheavy hadronic molecules stimulates us to give more predictions for the heavy-heavy cases, which are less discussed in literature than the heavy-antiheavy ones. Given that the heavy-antiheavy h…
We extend our previous study on the decay behavior of $P_c$ hadronic molecules to their strange and beauty partners. While $P_c(4380)$ and $P_c(4450)$ locate just below the $\bar DΣ_c^*$ and $\bar D^*Σ_c$ thresholds, respectively, their proposed strange partners $N(1875)$ and $N(2080)$ sit just below the $KΣ^*$ and $K^*Σ$ thresholds, respectively. Using the effective Lagrangian approach as the same as for the study of $P_c$ hadronic molecular states and with the couplings determined by the $\mathrm{SU}(3)$ flavor symmetry, the decay patterns of $N(1875)$ and $N(2080)$ are obtained assuming the…
The possibility for a common effective field theory for hadronic molecules with different heavy-quark flavours is examined critically. It is argued that such a theory does not allow one to draw definite conclusions for doubly heavy molecules. In particular, it does not allow one to relate binding energies for the molecules in the c-quark and b-quark sectors with controlled uncertainties. Therefore, while this kind of reasoning does not preclude from employing heavy-quark spin symmetry for charmonium- and bottomonium-like states separately within a well established effective field theory framew…
In recent years, many heavy mesons and charmonia were observed which do not fit in the conventional quark model expectations. Some of them are proposed to be hadronic molecules. Here we investigate the consequences of heavy quark spin symmetry on these heavy meson hadronic molecules. Heavy quark spin symmetry enables us to predict new heavy meson molecules and provides us with a method to test heavy meson molecule assumptions of some newly observed states. In particular, we predict an η_c'f_0(980) bound state as the spin-doublet partner of the Y(4660) proposed as a ψ'f_0(980) bound state with …
In this work, we investigated the decays of the fully open-flavor tetraquark state $X_0(2900)$ which was observed by the LHCb Collaboration very recently. Here, the $X_0(2900)$ was assigned as a $S-$wave $\bar D^\ast K^\ast$ hadronic molecule with $I=0$, and the effective lagrangian approach was applied to estimate the partial decay widths. Moreover, we also predicted the decay behaviors of the other unobserved $X_{J(J=1,2)}$, which were the spin partners of the $X_0(2900)$ in the $S-$wave $\bar D^\ast K^\ast$ picture. It was pointed out that the $X_1$ state with $I=0$ was a broad state with t…
