Explaining the Many Threshold Structures in the Heavy-Quark Hadron Spectrum

Tremendous progress has been made experimentally in the hadron spectrum containing heavy quarks in the last two decades. It is surprising that many resonant structures are around thresholds of a pair of heavy hadrons. There should be a threshold cusp at any $S$-wave threshold. By constructing a nonrelativistic effective field theory with open channels, we discuss the generalities of threshold behavior, and offer an explanation of the abundance of near-threshold peaks in the heavy quarkonium regime. We show that 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 threshold structures at any threshold of a 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. The structure becomes more pronounced if there is a near-threshold pole. Predictions of the possible pairs are also given for the ground state heavy hadrons. Precisely measuring the threshold structures will play an important role in revealing the heavy-hadron interactions, and thus understanding the puzzling hidden-charm and hidden-bottom structures.

Figure 1

Production of particles in channel 1 through intermediate states in both channels.

Figure 2

Illustration of threshold behaviors. Here we use the masses of the ${\pi }^{-}$ and $J/\psi$ for channel 1 and those of the $D^0$ and $D^{*-}$ for channel-2, and the values of used $a_{ij}$ parameters are given in the legend. (a) Line shapes of $|T_{21}{|}^2$, which are normalized at the threshold of channel 2, i.e., $E=0$; (b) line shapes of $|T_{11}{|}^2$, which are normalized at $E=-0.02\mathrm{GeV}$.