Could the near-threshold $XYZ$ states be simply kinematic effects?

We demonstrate that the spectacular structures discovered recently in various experiments and named as $X$, $Y$ and $Z$ states cannot be purely kinematic effects. Their existence necessarily calls for nearby poles in the $S$ matrix and they therefore qualify as states. We propose a way of distinguishing kinematic cusp effects from genuine $S$-matrix poles: the kinematic threshold cusp cannot produce a narrow peak in the invariant mass distribution in the elastic channel in contrast with a genuine $S$-matrix pole.

Figure 1

The tree-level (a), one-loop (b) and two-loop (c) Feynman diagrams for $Y(4260)\to \pi D{\overline{D}}^{*}$.

Figure 2

The tree-level (a), one-loop (b) and two-loop (c) Feynman diagrams for $Y(4260)\to \pi \pi J/\psi$.

Figure 3

Results for the $D{\overline{D}}^{*}$ invariant mass distribution in $Y(4260)\to \pi D{\overline{D}}^{*}$. The data are from Ref. [5] and the results from the tree-level, full one-loop and full two-loop calculations are shown by the dotted, solid and dashed curves, respectively. The dot-dashed line shows the one-loop result with the strength of the rescattering requested to be small to justify a perturbative treatment as described in the text.

Figure 4

Results for the $\pi J/\psi$ invariant mass distribution in $Y(4260)\to \pi \pi J/\psi$. The data are from Ref. [2] and the results from the tree-level, full one-loop and full two-loop calculations are shown by the dotted, solid and dashed curves, respectively, with the cutoff as well as $g_Y$ from the fit to the $D{\overline{D}}^{*}$ spectrum.