Companion poles: from the $a_0(980)$ to the $X(3872)$

Abstract

When an unstable ordinary quark-antiquark state couples strongly to other low-mass mesons (such as pions, kaons, $D$-mesons, etc.), the quantum fluctuations generated by the decay products dress the bare `seed' $\bar{q}q$ state and modify its spectral functions. The state is associated to a pole on the complex plane. When the coupling to the decay products is sufficiently large, a remarkable and interesting phenomenon takes place: dynamically generated companion states (or poles) might emerge. Some resonances listed in the PDG , such as the $a_0(980),$ the $K_0^{\ast }(700),$ and the $X(3872),$ can be well understood by this mechanism, that we briefly review in these proceedings. On the other hand, we show that the $Y(4008)$ and $Y(4260)$ are not independent resonances (or poles), but manifestations of $\psi (4040)$ and $\psi (4160),$ respectively.

Comments: Prepared for the proceedings of the workshop "Excited QCD 2019", 30/1/2019-3/2/2019, Schladming, Austria