A survey of heavy-heavy hadronic molecules

Abstract: 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 $D^{()}\Sigma_c^{()}$ 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 3pdate of the LHCb experiment as well as other experiments will provide more chances of observing the heavy-heavy hadronic molecules.

• The paper surveys the potential existence and properties of heavy-heavy hadronic molecules using quantum chromodynamics and heavy quark spin symmetry.
• It predicts a broad spectrum of heavy-heavy hadronic molecules, highlighting specific candidates like $DD^*$ and $D^{(*)}\Sigma_c^{(*)}$.
• Incorporating heavy quark symmetries is crucial for understanding forces, and experimental verification is possible in high-energy experiments.

Overview of Heavy-Heavy Hadronic Molecules

In the study titled "A survey of heavy-heavy hadronic molecules," the authors examine the potential existence and properties of hadronic molecules formed from heavy-heavy and heavy-antiheavy combinations of charmed hadrons. The research builds on the results obtained for heavy-antiheavy charmed hadrons, such as the well-known states like the $X(3872)$ and the $Y(4260)$, by using a theoretical framework that focuses on heavy-heavy systems, which have not received as much attention in the literature.

The study utilizes the principles of quantum chromodynamics (QCD) and heavy quark spin symmetry to explore the spectrum of such molecules. According to the authors, the spectrum of heavy-heavy molecules is naturally expected, particularly given the constant interaction model derived from resonance saturation, which has been successful in explaining several heavy-antiheavy states.

Methodology

The paper derives potentials for different heavy-heavy hadron combinations, using resonance saturation models for estimating leading-order interactions, where the interactions are approximated as constants. The interactions between hadrons containing heavy quarks, specifically charm ($c$) and beauty ($b$), are constrained by heavy quark symmetries and involve light vector meson exchange, such as $\rho$, $\omega$, and $\phi$ mesons. The study utilizes the Bethe-Salpeter equation to explore the formation of bound states or resonances in various channels of these systems.

Key Findings and Predictions

1. Existence of Heavy-Heavy Molecules: The study predicts the natural presence of numerous heavy-heavy hadronic molecules. These predictions are grounded on the observation that the dominant constant interaction from light vector meson exchanges, such as $\omega$ and $\phi$, leads to attractive potentials.
2. Highlighting Specific States: Notably, the authors discuss potential molecules such as the $DD^*$ and $D^{(*)}\Sigma_c^{(*)}$, which are viewed as counterparts to known heavy-antiheavy states. For instance, the $DD^*$ molecule is discussed in the context of the newly observed doubly charmed tetraquark state $T_{cc}$ by LHCb, aligning with their predictions.
3. Contributions from Symmetry Considerations: The study emphasizes that incorporating heavy quark spin and flavor symmetries is crucial for understanding the inter-hadron forces and the resulting spectrum of states.
4. Challenges and Considerations: While a broad spectrum of hadronic molecules is predicted, the authors acknowledge limitations due to omitted momentum-dependent interactions and possible coupled-channel effects that could alter the spectrum quantitatively. Additionally, the interactions are considered at the leading order, with higher-order effects ignored for simplicity.

Implications and Future Directions

The exploration of heavy-heavy hadronic molecules holds theoretical and experimental significance. From a theoretical standpoint, it enhances our understanding of the interplay between QCD forces and heavy quark symmetries, offering insights into the formation and stability of exotic states beyond the traditional quark model. Practically, the potential to observe such exotic states through high-energy experiments, like updates to the LHCb experiment, provides a pathway for experimental verification of the predictions.

The study sets the stage for further investigations into both the heavy-charm and the charm-bottom sectors, where similar methodologies could predict molecules in systems involving beauty quarks, and highlights the necessity of incorporating momentum-dependent interactions and incorporating coupled-channel dynamics to refine predictions.