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 Pc states, fit into the spectrum we obtain. We also highlight a ΛcΛc bound state that has
a pole consistent with the cross section of the e+e-→ ΛcΛc precisely measured by the BESIII
Collaboration.
