Lattice QCD Investigation of the Doubly Charm Tetraquark Channel with Isospin 1

Core Concepts

Lattice QCD simulations indicate a repulsive interaction in the doubly charm tetraquark channel with isospin 1, supporting the experimental non-observation of a tetraquark peak in this channel and contrasting with the attractive interaction observed in the isospin 0 channel where the Tcc tetraquark exists.

Abstract

• Bibliographic Information: Meng, L., Ortiz-Pacheco, E., Baru, V., Epelbaum, E., Padmanath, M., & Prelovsek, S. (2024). Doubly charm tetraquark channel with isospin 1 from lattice QCD. arXiv preprint arXiv:2411.06266v1.
• Research Objective: This research paper investigates the interaction between D and D∗ mesons in the doubly charm tetraquark channel with isospin 1 (I=1) using lattice QCD simulations. The study aims to understand the nature of this interaction and its implications for the existence of tetraquark states in this channel.
• Methodology: The authors performed lattice QCD simulations at a pion mass of approximately 280 MeV and five different charm quark masses. They calculated the finite-volume energies of the DD∗ system with I=1 and used two methods to analyze the results: the standard Lüscher method and a recently proposed chiral effective field theory (EFT) approach. The EFT approach incorporates the one-pion exchange and the left-hand cut, which are important for this system.
• Key Findings: The finite-volume energy levels obtained from the simulations consistently indicate a repulsive interaction between D and D∗ mesons in the I=1 channel for all considered charm quark masses. The scattering amplitudes extracted using both the Lüscher method and the EFT approach confirm this repulsive interaction. No bound state or resonant behavior is observed near the DD∗ threshold.
• Main Conclusions: The authors conclude that the DD∗ interaction in the I=1 channel is repulsive, which explains the absence of an experimentally observed tetraquark peak in this channel. This result contrasts with the attractive interaction found in the I=0 channel, where the Tcc tetraquark has been observed. The study suggests that the different behavior in the two isospin channels might be attributed to the contribution of the Wick contraction resembling t-channel isovector-vector meson exchanges, which is present in the I=1 channel but absent in the I=0 channel.
• Significance: This research provides valuable insights into the nature of doubly charm tetraquark systems. It demonstrates the predictive power of lattice QCD for studying exotic hadrons and contributes to the understanding of the strong interaction in multi-quark systems.
• Limitations and Future Research: The study is limited to a single lattice spacing and a pion mass slightly heavier than the physical value. Future research could explore the dependence of the results on these parameters. Additionally, extending the analysis to higher energies and other quantum numbers would provide a more complete picture of the DD∗ interaction in the I=1 channel.

Stats

The simulations were performed at a pion mass of approximately 280 MeV.
Five different charm quark masses were used in the simulations.
Two different spatial volumes were used: N3L = 243 and N3L = 323.
The lattice spacing was a=0.08636(98)(40) fm.

Quotes

"Experimentally, the doubly charm tetraquark channel cc¯q¯q with q =u, d features an exotic hadron, Tcc, with isospin I =0 near the DD∗threshold, while no peak was observed for I =1."
"Finite-volume energies calculated across five charm quark masses consistently indicate a repulsive interaction in this channel."
"Both analyses reaffirm the repulsive interaction resulting in a 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."

Key Insights Distilled From

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

by Lu Meng, Emm... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2411.06266.pdf

Deeper Inquiries

How would the inclusion of dynamical charm quarks in the lattice simulations affect the results and conclusions regarding the DD∗ interaction in the isospin 1 channel?

Answer:
Including dynamical charm quarks in lattice QCD simulations, as opposed to using the current setup with heavier-than-physical charm quarks, could lead to several noticeable, albeit likely small, changes in the study of the DD∗ interaction in the isospin 1 channel.

Quantitative changes in energy levels: Dynamical charm quarks would directly impact the sea quark contributions, leading to shifts in the extracted finite-volume energy levels. These shifts would likely be small, especially given that the current simulations are already performed at multiple charm quark masses, with the lightest one being close to the physical charm quark mass. The observed mild dependence of the scattering parameters on the charm quark mass suggests that the impact of dynamical charm quarks might not drastically alter the qualitative conclusions.

Improved accuracy and reduced systematic uncertainties: Simulations with dynamical charm quarks would reduce a source of systematic uncertainty associated with the current extrapolation to the physical charm quark mass. This would lead to more precise determinations of the scattering parameters and potentially refine the understanding of the repulsive interaction.

Potential for observing new bound states: While unlikely, the inclusion of dynamical charm quarks might, in principle, reveal new bound states or resonances in the I=1 channel that were not observed in the current setup. This is because dynamical charm quarks could introduce new interaction channels or modify the existing ones in a way that favors the formation of bound states. However, given the robust repulsive interaction observed across various charm quark masses, the emergence of such bound states seems improbable.
Overall, while the inclusion of dynamical charm quarks is expected to bring quantitative changes and improve the accuracy of the results, it is unlikely to overturn the primary conclusion of a repulsive DD∗ interaction in the isospin 1 channel.

Could there be other, yet unexplored, explanations for the observed repulsive interaction in the I=1 channel, such as contributions from higher-order interactions or multi-hadron states?

Answer:
Yes, besides the dominant role of the t-channel isovector-vector meson exchange (like the ρ meson) highlighted in the paper, other potential explanations for the repulsive interaction in the I=1 DD∗ channel could be at play:

Higher-order interactions: The current analysis focuses on leading-order interactions within the chiral EFT framework. Higher-order terms in the chiral expansion, while suppressed at low energies, could contribute to the interaction and potentially enhance the repulsion. Investigating these higher-order terms would require more computationally demanding simulations at finer lattice spacings and with a larger basis of interpolating operators.

Multi-hadron states: The presence of multi-hadron states, such as DDπ or D∗D∗π, could also influence the DD∗ interaction. These multi-hadron states can couple to the DD∗ channel and generate a repulsive interaction through virtual processes. Properly accounting for these multi-hadron contributions would require extending the current single-channel analysis to a coupled-channel framework, which is a challenging task.

Other meson exchanges: While the paper focuses on the ρ meson exchange as the primary source of isospin dependence, other meson exchanges, such as those involving heavier mesons, could also contribute. A more comprehensive study considering a wider range of meson exchanges would be needed to fully assess their impact.

Beyond the molecular picture: The current study primarily focuses on the molecular picture of the DD∗ interaction. However, other scenarios, such as those involving diquark dynamics or more complex color configurations, could also contribute to the observed repulsion. Exploring these alternative scenarios would require going beyond the current EFT framework and employing different theoretical tools.
Further investigations, both theoretical and computational, are necessary to explore these possibilities and gain a more complete understanding of the repulsive DD∗ interaction in the I=1 channel.

What are the implications of this research for understanding the formation and stability of other exotic hadrons, particularly those containing heavier quarks like bottom quarks?

Answer:
This research on the DD∗ interaction in the I=1 channel provides valuable insights that can be extrapolated to understand the formation and stability of other exotic hadrons, especially those containing heavier quarks like bottom quarks:

Predictive power for heavier systems: The observed repulsive interaction in the I=1 DD∗ channel, primarily driven by the ρ meson exchange mechanism, suggests that similar repulsive interactions might also be present in analogous systems containing heavier quarks, such as the B∗B system with I=1. This is because the underlying physics governing the interaction, particularly the isospin dependence arising from vector meson exchange, is expected to persist in heavier systems.

Impact on the stability of exotic hadrons: The repulsive nature of the I=1 interaction implies that the formation of bound states or resonances in this channel is unlikely. This finding has implications for the stability of exotic hadrons containing heavier quarks. For instance, it suggests that tetraquarks with configurations like bb¯u¯d with I=1 are less likely to be stable compared to their I=0 counterparts.

Guiding future experimental searches: The results of this study can guide future experimental searches for exotic hadrons. By understanding the dynamics of the interactions in different isospin channels, experimentalists can focus their efforts on channels that are more likely to host stable or resonant exotic states.

Extending the theoretical framework: The chiral EFT approach employed in this study can be extended to investigate the interactions in other exotic hadron systems, including those with heavier quarks. This framework allows for a systematic inclusion of the relevant physics, such as meson exchanges and coupled-channel effects, providing a powerful tool for studying the spectrum and properties of exotic hadrons.
In conclusion, this research not only sheds light on the specific case of the DD∗ interaction but also provides a broader understanding of the dynamics governing the formation and stability of exotic hadrons. The insights gained from this study will be crucial for interpreting future experimental results and advancing the theoretical description of the exotic hadron spectrum.