We will study open and hidden charm scalar meson resonances within two different models. The first one is a direct application of a chiral Lagrangian already used to study flavor symmetry breaking in Skyrme models. In another approach to the problem a $SU(4)$ symmetric Lagrangian is built and the symmetry is broken down to $SU(3)$ by identifying currents where heavy mesons are exchanged and suppressing those. Unitarization in coupled channels leads to dynamical generation of resonances in both models, in particular, a new hidden charm resonance with mass 3.7 GeV is predicted. The small differences between these models and with previous works is discussed. We also perform an error analysis of the results, checking their stability and determining the uncertainties in masses and couplings of the heavy resonances.

We perform an analytical study of the scattering matrix and bound states in problems with many physical coupled channels. We establish the relationship of the couplings of the states to the different channels, obtained from the residues of the scattering matrix at the poles, with the wave functions for the different channels. The couplings basically reflect the value of the wave functions around the origin in coordinate space. In the concrete case of the $X(3872)$ resonance, understood as a bound state of $D^0{\overline{D}}^{*0}$ and $D^{+}{D}^{*-}$ (and $c.c.$ From now on, when we refer to $D^0{\overline{D}}^{*0}$ , $D^{+}{D}^{*-}$, or $D{\overline{D}}^{*}$ we are actually referring to the combination of these states with their complex conjugate in order to form a state with positive C-parity), with the $D^0{\overline{D}}^{*0}$ loosely bound, we find that the couplings to the two channels are essentially equal leading to a state of good isospin $I=0$ character. This is in spite of having a probability for finding the $D^0{\overline{D}}^{*0}$ state much larger than for $D^{+}{D}^{*-}$ since the loosely bound channel extends further in space. The analytical results, obtained with exact solutions of the Schrödinger equation for the wave functions, can be useful in general to interpret results found numerically in the study of problems with unitary coupled channels methods.

In this paper we study the effects of isospin breaking in the dynamical generation of the $X(3872)$ state. We also calculate the ratio of the branching fractions of the $X$ decaying into $J/\psi$ with two and three pions, which has been measured experimentally to be close to unity. Together with the $X(3872)$, of positive $C$ parity, we predict the existence of a negative $C$-parity state, and we comment on which decay channel is more promising to observe this state. The simultaneous investigation of the $X(3872)$ decay into $J/\psi \pi \pi$ and $D^0{\overline{D}}^{*0}$ show a preference for a slightly unbound, virtual state of $D{\overline{D}}^{*}$ and $\overline{D}{D}^{*}$.

We use a consistent SU(6) extension of the meson-baryon chiral Lagrangian within a coupled channel unitary approach in order to calculate the T matrix for meson-baryon scattering in the s wave. The building blocks of the scheme are the $\pi${} and N octets, the $\rho${} nonet and the $\Delta${} decuplet. We identify poles in this unitary T matrix and interpret them as resonances. We study here the nonexotic sectors with strangeness S=0, -1, -2, -3 and spin J=12, 32 and 52. Many of the poles generated can be associated with known N, $\Delta${}, $\Sigma${}, $\Lambda${}, $\Xi${} and $\Omega${} resonances with negative parity. We show that most of the low-lying three and four star odd-parity baryon resonances with spin 12 and 32 can be related to multiplets of the spin-flavor symmetry group SU(6). This study allows us to predict the spin-parity of the $\Xi${}(1620), $\Xi${}(1690), $\Xi${}(1950), $\Xi${}(2250), $\Omega${}(2250) and $\Omega${}(2380) resonances, which have not been determined experimentally yet.

A study of the $J/\psi \pi \pi$ and $J/\psi K\overline{K}$ systems, treating them as coupled channels, has been made by solving the Faddeev equations, with the purpose of investigating the possibility of generation of the $J^{\mathrm{PC}}=1^{--}$, $Y(4260)$ resonance due to the interaction between these three mesons. In order to do this, we start by solving the Bethe-Salpeter equation for the two pseudoscalar and for the vector-pseudocalar meson systems using the amplitudes obtained from the lowest order chiral Lagrangians as potentials. With the $t$- matrices generated from these potentials, which contain the poles of the $\sigma$, $f_0(980)$, and $a_0(980)$ resonances for the pseudoscalar-pseudoscalar system and the pole of the $X(3872)$, along with other new charmed resonant states, for the vector-pseudoscalar system, we solve the Faddeev equations. As a result, we get a peak around 4150 MeV with a width $\sim 90\mathrm{MeV}$ when the invariant mass of the two pseudoscalars is close to that of the $f_0(980)$.