Two-pole structures in QCD: Facts, not fantasy!

The two-pole structure refers to the fact that particular single states in the spectrum as listed in the PDG tables are often two states. The story began with the $\Lambda(1405)$, when in 2001, using unitarized chiral perturbation theory, it was observed that there are two poles in the complex plane, one close to the $\bar{K}p$ and the other close to the $\pi\Sigma$ threshold. This was later understood combining the SU(3) limit and group-theoretical arguments. Different unitarization approaches that all lead to the two-pole structure have been considered in the mean time, showing some spread in the pole positions. This fact is now part of the PDG book, though it is not yet listed in the summary tables. Here, I will discuss the open ends and critically review approaches that can not deal with this issue. In the meson sector some excited charm mesons are good candidates for such a two-pole structure. Next, I consider in detail the $D_0^*(2300)$, that is another candidate for this scenario. Combining lattice QCD with chiral unitary approaches in the finite volume, the precise data of the Hadron Spectrum Collaboration for coupled-channel $D\pi$, $D\eta$, $D_s\bar{K}$ scattering in the isospin $I=1/2$ channel indeed reveal its two-pole structure. Further states in the heavy meson sector with $I=1/2$ exhibiting this phenomenon are predicted, especially in the beauty meson sector. I also discuss the relation of these two-pole structures and the possible molecular nature of the states under consideration.