[Paper Review] A survey of heavy-antiheavy hadronic molecules

Xiang-Kun Dong, Feng-Kun Guo+1 more|arXiv (Cornell University)|Jan 4, 2021

Quantum Chromodynamics and Particle Interactions4 references129 citations

TL;DR

The paper systematically predicts a spectrum of heavy-antiheavy hadronic molecular states by solving the on-shell Bethe-Salpeter equation with vector-meson exchange–saturated contact interactions, focusing on S- and P-wave heavy mesons and baryons, and finds 229 predicted states with several known near-threshold structures fitting into the spectrum.

ABSTRACT

Many efforts have been made to reveal the nature of the overabundant resonant structures observed by the worldwide experiments in the last two decades. Hadronic molecules attract special attention because many of these seemingly unconventional resonances are located close to the threshold of a pair of hadrons. To give an overall feature of the spectrum of hadronic molecules composed of a pair of heavy-antiheavy hadrons, namely, which pairs are possible to form molecular states, we take charmed hadrons for example to investigate the interaction between them and search for poles by solving the Bethe-Salpeter equation. We consider all possible combinations of hadron pairs of the $S$-wave singly-charmed mesons and baryons as well as the narrow $P$-wave charmed mesons. The interactions, which are assumed to be meson-exchange saturated, are described by constant contact terms which are resummed to generate poles. It turns out that if a system is attractive near threshold by the light meson exchange, there is a pole close to threshold corresponding to a bound state or a virtual state, depending on the strength of interaction and the cutoff. In total, 229 molecular states are predicted. The observed near-threshold structures with hidden-charm, like the famous $X(3872)$ and $P_c$ states, fit into the spectrum we obtain. We also highlight a $Λ_c\bar Λ_c$ bound state that has a pole consistent with the cross section of the $e^+e^- oΛ_c\bar Λ_c$ precisely measured by the BESIII Collaboration.

Motivation & Objective

• Motivate understanding of exotic near-threshold resonances as hadronic molecules built from heavy-antiheavy pairs.
• Provide a unified spectrum of possible molecular states across S- and P-wave heavy meson and baryon combinations.
• Use a resonance-saturated, contact-interaction potential and solve the Bethe-Salpeter equation to locate near-threshold poles.

Proposed method

• Construct heavy-meson and heavy-baryon Lagrangians invariant under heavy quark spin symmetry and chiral SU(3).
• Estimate interaction potentials from light-vector exchange saturated by resonances; keep leading-order constant contact terms.
• Solve the on-shell Bethe-Salpeter equation T = V + VGT to locate poles.
• Consider HQFS to relate charm and bottom sectors by using charmed-hadron interactions as a proxy for bottomed systems.
• Focus on near-threshold dynamics and neglect coupled channels for a unified first-pass spectrum.

Experimental results

Research questions

• RQ1 What heavy-antiheavy hadron pair combinations can form near-threshold molecular states under HQSS and chiral constraints?
• RQ2 How do vector-meson exchange–saturated contact interactions generate poles in the Bethe-Salpeter equation for these systems?
• RQ3 How many molecular states are predicted across the explored heavy-meson and heavy-baryon sectors, and how do they align with observed near-threshold structures?
• RQ4 Can the model accommodate known states like X(3872) and P_c within the predicted spectrum?
• RQ5 Is there a pole corresponding to a Λ_c Λ_c̄ bound state compatible with BESIII cross-section data?

Key findings

• A total of 229 molecular states are predicted near various heavy-antiheavy thresholds.
• Observed near-threshold structures with hidden charm, such as X(3872) and P_c states, fit into the predicted spectrum.
• The analysis highlights a Λ_c Λ̄_c bound-state pole consistent with BESIII measurements of e+e− → Λ_c Λ̄_c cross sections.
• The approach shows how threshold dynamics and pole structures relate to line shapes in invariant mass distributions.
• The leading-order constant interaction, saturated by vector-meson exchange and resummed, suffices to generate near-threshold poles and meaningful line shapes.
• The study provides a unified framework linking several famous near-threshold states to a larger molecular-spectrum prediction.