In the present paper we address the interaction of charmed mesons in hidden charm channels in a finite box. We use the interaction from a recent model based on heavy quark spin symmetry that predicts molecules of hidden charm in the infinite volume.
The energy levels in the box are generated within this model, and several methods for the analysis of these levels (inverse problem) are investigated.
The problem of scalar mesons still remains a challenging puzzle, for which we do not even know which are the right pieces to set up. The proliferation of resonances (some of them are very broad and appear on top of hadronic thresholds) and of coupled
channels that interact strongly among each other makes the study of this sector a hard task. Our objective is the study of the strongly interacting mesons in coupled channels with quantum numbers J^{PC} = 0^{++} and I=0 and I=1/2, up to a center of mass energy sqrt{s} < 2 GeV. Our framework is based on Unitary Chiral Perturbation Theory. We include for I=0 the channels: pipi, Kbar{K}, etaeta, sigmasigma, etaeta, rhorho, omegaomega, etaeta, omegaphi, phiphi, K^ast bar{K}^ast, a_1(1260)pi and pi^{star}(1300)pi. In addition, and in order to constrain our fits, we also study the I=1/2, 3/2 channels given by Kpi, Keta and Keta. We finally present the resonant content of our fits with the $sigma$, $f_0(980)$, $f_0(1310)$, $f_(1500)$, $f_0(1710)$ and $f_0(1790)$.
