A survey of heavy-antiheavy hadronic molecules

TL;DR

This survey reviews theoretical predictions of heavy-antiheavy hadronic molecules, using Bethe-Salpeter equations to identify potential bound states near thresholds, including known exotic states and new predicted ones.

Contribution

It provides a comprehensive prediction of 229 heavy-antiheavy molecular states using a unified meson-exchange model and Bethe-Salpeter equation analysis.

Findings

Predicted 229 molecular states near thresholds.

Identified poles corresponding to known states like X(3872).

Suggested a possible $\Lambda_car{\Lambda}_c$ bound state.

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 $\Lambda_c\bar \Lambda_c$ bound state that has a pole consistent with the cross section of the $e^+e^-\to\Lambda_c\bar \Lambda_c$ precisely measured by the BESIII Collaboration.