Heavy Hadronic Molecules Research Articles

Coupled-channel description of charmed heavy hadronic molecules within the meson-exchange model and its implication

Motivated by the first observation of the double-charm tetraquark Tcc+(3875) by the LHCb Collaboration, we investigate the nature of Tcc+ as an isoscalar DD* hadronic molecule in a meson-exchange potential model incorporated by the coupled-channel effects and three-body unitarity. The D0D0π+ invariant mass spectrum can be well-described and the Tcc+ pole structure can be precisely extracted. Under the hypothesis that the interactions between the heavy flavor hadrons can be saturated by the light meson-exchange potentials, the near-threshold dynamics of Tcc+ can shed light on the binding of its heavy-quark spin symmetry (HQSS) partner D*D* (I=0) and on the nature of other heavy hadronic molecule candidates such as X(3872) and Zc(3900) in the charmed-anticharmed systems. The latter states can be related to Tcc+ in the meson-exchange potential model with limited assumptions based on the SU(3) flavor symmetry relations. The combined analysis, on the one hand, indicates the HQSS breaking effects among those HQSS partners, and on the other hand, highlights the role played by the short and long-distance dynamics for the near threshold D(*)D(*) and D(*)D¯(*)+c.c. systems. Published by the American Physical Society 2024

Systematics of the heavy flavor hadronic molecules

With a quark level interaction, we give a unified description of the loosely bound molecular systems composed of the heavy flavor hadrons ({bar{D}},{bar{D}}^*), (Lambda _c, Sigma _c, Sigma _c^*), and (Xi _c, Xi _c^prime ,Xi _c^*). Using the P_c states as inputs to fix the interaction strength of light quark-quark pairs, we reproduce the observed P_{cs} and T_{cc}^+ states and predict another narrow T_{cc}^{prime +} state with quantum numbers [D^*D^*]_{J=1}^{I=0}. If we require a satisfactory description of the T_{cc}^+ and P_c states simultaneously, our framework prefers the assignments of the P_{c}(4440) and P_{c}(4457) as the [Sigma _c{bar{D}}^*]_{J=1/2}^{I=1/2} and [Sigma _c{bar{D}}^*]_{J=3/2}^{I=1/2} states, respectively. We propose the isospin criterion to explain naturally why the experimentally observed T_{cc}, P_c, and P_{cs} molecular candidates prefer the lowest isospin numbers. We also predict the loosely bound states for the bottom di-hadrons.

Axial meson exchange and the Zc(3900) and Zcs(3985) resonances as heavy hadron molecules

Early speculations about the existence of heavy hadron molecules were grounded on the idea that light-meson exchange forces could lead to binding. In analogy to the deuteron, the light mesons usually considered include the pion, sigma, rho and omega, but not the axial meson ${a}_{1}(1260)$. Though it has been argued in the past that the coupling of the axial meson to the nucleons is indeed strong, its mass is considerably heavier than that of the vector mesons and thus its exchange ends up being suppressed. Yet, this is not necessarily the case in heavy hadrons molecules; we find that even though the contribution to binding from the axial meson is modest, it cannot be neglected in the isovector sector where vector meson exchange cancels out. This might provide a natural binding mechanism for molecular candidates such as the ${Z}_{c}(3900)$, ${Z}_{c}(4020)$, or the more recently observed ${Z}_{cs}(3985)$. However, the ${Z}_{cs}(3985)$ is more dependent on a mixture of different factors, which (besides axial meson exchange) include $\ensuremath{\eta}$ exchange and the nature of scalar meson exchange. Together they point towards the existence of two ${Z}_{cs}(3985)$-like resonances instead of one, while the observations about the role of scalar meson exchange in the ${Z}_{cs}(3985)$ might be relevant for the ${P}_{cs}(4459)$. Finally, the combination of axial meson exchange and flavor-symmetry breaking effects indicates that the isovector ${J}^{PC}={0}^{++}$ ${D}^{*}{\overline{D}}^{*}$ and the strange ${J}^{P}={2}^{+}$ ${D}^{*}{\overline{D}}_{s}^{*}$ molecules are the most attractive configurations and thus the most likely molecular partners of the ${Z}_{c}(3900)$, ${Z}_{c}(4020)$, and ${Z}_{cs}(3985)$.

A survey of heavy–heavy hadronic molecules

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 hadronic molecules, several of which have strong experimental evidence, emerge from the dominant constant interaction from resonance saturation, we find that the existence of many heavy–heavy hadronic molecules is natural. Among these predicted heavy–heavy states we highlight the DD * molecule and the molecules, which are the partners of the famous X(3872) and P c states. Quite recently, LHCb collaboration reported a doubly charmed tetraquark state, T cc , which is in line with our results for the DD * molecule. With the first experimental signal of this new kind of exotic states, the upcoming update of the LHCb experiment as well as other experiments will provide more chances of observing the heavy–heavy hadronic molecules.

Heavy Hadronic Molecules Coupled with Multiquark States

We investigate the hidden-charm pentaquarks as a \(\varLambda _c{\bar{D}}^{(*)}-\varSigma _c^{(*)}{\bar{D}}^{(*)}\) hadronic molecule coupling to a compact five-quark state. The coupling to the compact state leads to an hadron short-range interaction generating an attraction. In addition, the one pion exchange potential (OPEP) as a long-range interaction is introduced by the Lagrangians satisfying the chiral and heavy quark spin symmetries. The OPEP has been known as a driving force to bind atomic nuclei, where the tensor term leading the coupled-channel effect generates a strong attraction. The mass degeneracy of heavy hadrons due to the heavy quark spin symmetry enhances the OPEP derived by the \(\pi D^{(*)}{\bar{D}}^{(*)}\) and \(\pi \varSigma _c^{(*)}\varSigma _c^{(*)}\) couplings. Introducing those interactions, we consistently explain the masses and widths of the \(P_c\) states reported by LHCb in 2019. The short range interaction has a dominant role to determine the energy-level structures, while the OPEP tensor term does the decay width.

Heavy hadron molecules in effective field theory: the emergence of exotic nuclear landscapes

Heavy hadron molecules were first theorized from a crude analogy with the deuteron and the nuclear forces binding it, a conjecture which was proven to be on the right track after the discovery of the $X(3872)$. However, this analogy with nuclear physics has not been seriously exploited beyond a few calculations in the two- and three-body sectors, leaving a great number of possible theoretical consequences unexplored. Here we show that nuclear and heavy hadron effective field theories are formally identical: using a suitable notation, there is no formal difference between these two effective field theories. For this, instead of using the standard heavy superfield notation, we have written the heavy hadron interactions directly in terms of the light quark degrees of freedom. We give a few examples of how to exploit this analogy, e.g. the calculation of the two-pion exchange diagrams. Yet the most relevant application of the present idea is the conjecture of exotic nuclear landscapes, i.e. the possibility of few heavy hadron bound states with characteristics similar to those of the standard nuclei.

Remarks on the heavy-quark flavour symmetry for doubly heavy hadronic molecules

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 framework, relations between different heavy-quark sectors can only be obtained using phenomenological approaches with uncontrolled uncertainties.

Scale invariance in heavy hadron molecules

We discuss a scenario in which the $P_c(4450)^{+}$ heavy pentaquark is a $\Sigma_c \bar{D}^*$-$\Lambda_{c}(2595) \bar{D}$ molecule. The $\Lambda_{c1} \bar{D} \to \Sigma_c \bar{D}^*$ transition is mediated by the exchange of a pion almost on the mass shell that generates a long-range $1/r^2$ potential. This is analogous to the effective force that is responsible for the Efimov spectrum in three-boson systems interacting through short-range forces. The equations describing this molecule exhibit approximate scale invariance, which is anomalous and broken by the solutions. If the $1/r^2$ potential is strong enough this symmetry survives in the form of discrete scale invariance, opening the prospect of an Efimov-like geometrical spectrum in two-hadron systems. For a molecular pentaquark with quantum numbers $\frac{3}{2}^{-}$ the attraction is not enough to exhibit discrete scale invariance, but this prospect might very well be realized in a $\frac{1}{2}^{+}$ pentaquark or in other hadron molecules involving transitions between particle channels with opposite intrinsic parity and a pion near the mass shell. A very good candidate is the $\Lambda_{c}(2595) \bar{\Xi}_b - \Sigma_c \bar{\Xi}_b'$ molecule. Independently of this, the $1/r^2$ force is expected to play a very important role in the formation of this type of hadron molecule, which points to the existence of $\frac{1}{2}^{+}$ $\Sigma_c D^*$-$\Lambda_{c}(2595) D$ and $1^+$ $\Lambda_{c}(2595) {\Xi}_b - \Sigma_c {\Xi}_b'$ molecules and $0^{+}$/$1^{-}$ $\Lambda_{c}(2595) \bar{\Xi}_b - \Sigma_c \bar{\Xi}_b'$ baryonia.

New Exotic Meson and Baryon Resonances from Doubly Heavy Hadronic Molecules.

We predict several new exotic doubly heavy hadronic resonances, inferring from the observed exotic bottomoniumlike and charmoniumlike narrow states X(3872), Z_{b}(10610), Z_{b}(10650), Z_{c}(3900), and Z_{c}(4020/4025). We interpret the binding mechanism as mostly molecularlike isospin-exchange attraction between two heavy-light mesons in a relative S-wave state. We then generalize it to other systems containing two heavy hadrons which can couple through isospin exchange. The new predicted states include resonances in meson-meson, meson-baryon, baryon-baryon, and baryon-antibaryon channels. These include those giving rise to final states involving a heavy quark Q=c,b and antiquark Q[over ¯]^{'}=c[over ¯],b[over ¯], namely, DD[over ¯]^{*}, D^{*}D[over ¯]^{*}, D^{*}B^{*}, B[over ¯]B^{*}, B[over ¯]^{*}B^{*}, Σ_{c}D[over ¯]^{*}, Σ_{c}B^{*}, Σ_{b}D[over ¯]^{*}, Σ_{b}B^{*}, Σ_{c}Σ[over ¯]_{c}, Σ_{c}Λ[over ¯]_{c}, Σ_{c}Λ[over ¯]_{b}, Σ_{b}Σ[over ¯]_{b}, Σ_{b}Λ[over ¯]_{b}, and Σ_{b}Λ[over ¯]_{c}, as well as corresponding S-wave states giving rise to QQ^{'} or Q[over ¯]Q[over ¯]^{'}.

Long-distance structure of the X(3872)

We investigate heavy quark symmetries for heavy meson hadronic molecules, and explore the consequences of assuming the X(3872) and Zb(10610) as an isoscalar DD̄* and an isovector BB̄* hadronic molecules, respectively. The symmetry allows to predict new hadronic molecules, in particular we find an isoscalar 1++ BB̄* bound state with a mass about 10580 MeV and the isovector charmonium partners of the Zb(10610) and the Zb(10650) states. Next, we study the X(3872) → D0D̄0π0 three body decay. This decay mode is more sensitive to the long-distance structure of the X(3872) resonance than its J/ψππ and J/ψ3π decays, which are mainly controlled by the short distance part of the X (3872) molecular wave function. We discuss the D0D̄0 final state interactions, which in some situations become quite important. Indeed in these cases, a precise measurement of this partial decay width could provide precise information on the interaction strength between the D(*)D̄(*) charm mesons.

Consequences of heavy-quark symmetries for hadronic molecules

Among the newly observed structures in the heavy-quarkonium mass region, some have been 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 ${Z}_{b}(10\text{ }610)$ as an isoscalar $D{\overline{D}}^{*}$ and isovector $B{\overline{B}}^{*}$ hadronic molecule, respectively. A series of hadronic molecules composed of heavy mesons are predicted. In particular, there is an isoscalar ${1}^{++}$ $B{\overline{B}}^{*}$ bound state with a mass about 10 580 MeV which may be searched for in the $\ensuremath{\Upsilon}(1S,2S){\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$ mass distribution; the isovector charmonium partners of the ${Z}_{b}(10\text{ }610)$ and the ${Z}_{b}(10\text{ }650)$ are also predicted, which probably corresponds to the very recently observed ${Z}_{c}(3900)$ and ${Z}_{c}(4025)$ resonances by the BESIII Collaboration.

The Beauty of Spin

I review recent developments in theoretical spin physics. Topics include pion production in nucleon-nucleon collisions, the implications of heavy quark spin symmetry for heavy hadron molecules, the nucleon electric dipole form factors and ab initio calculations of the width of hadron resonances. A few spin physics high-lights from experiments at the COSY accelerator are also discussed.

Two-photon decay of heavy hadron molecules

We discuss the two-photon decay width of heavy hadron molecules and study the dependence on the constituent meson masses and on the binding energy. In addition finite-size effects due to the extended structure of the bound state are shown to have a strong influence on the predictions for this decay width.

Heavy quark spin symmetry and heavy flavor hadronic molecules

We argue that the heavy quark spin symmetry can lead to important consequences for heavy flavor hadronic molecules. It can be used to predict new heavy flavor hadronic molecules and hence provides a method to identify the nature of some newly observed exotic hadrons. For example, if the Y(4660) were an S-wave Ψ'f0(980) shallow bound state, then the mass, width and line shape of its spin partner are predicted.