Near Threshold Structures and Hadronic Molecules

Many candidates of the so-called exotic hadrons have been observed experimentally and most of them are located close to the threshold of a pair of hadrons. The general behavior of the near-threshold line shapes of invariant mass distributions is discussed. To be precise, the threshold cusp can show up as a peak only for channels with attractive interaction, and the width of the cusp is inversely proportional to the reduced mass relevant for the threshold. We argue that there should be (near-)threshold structures for any pair of heavy-quark and heavy-antiquark hadrons, which have attractive interaction at threshold, in the invariant mass distribution of a heavy quarkonium and light hadrons that couple to that open-flavor hadron pair. Predictions of the possible pairs that have near-threshold peaks are given for the ground state heavy hadrons based on the interaction saturated by vector mesons. We also give a survey of the possible hadronic molecules composed of a pair of charmed-anticharmed hadrons by solving the Bethe-Salpeter equation with constant interactions and the experimental candidates of hadronic molecules fit this spectrum well.