Abstract: We study the isospin breaking in the reactions chi(c1) -> pi(0)pi(+)pi(-) and chi(c1) -> pi(0)pi(0)eta and its relation to the a(0)(980) – f(0)(980) mixing, which was measured by the BESIII Collaboration. We show that the same theoretical model previously developed to study the chi(c1) -> eta pi(+)pi(-) reaction (also measured by BESIII), and further explored in the predictions to the eta(c) -> eta pi(+)pi(-), can be successfully employed in the present study. We assume that the chi(c1) behaves as an SU(3) singlet to find the weight in which trios of pseudoscalars are created, followed by the final state interaction of pairs of mesons to describe how the a(0)(980) and f(0)(980) are dynamically generated, using the chiral unitary approach in coupled channels. The isospin violation is introduced through the use of different masses for the charged and neutral kaons, either in the propagators of pairs of mesons created in the chi(c1) decay, or in the propagators inside the T matrix, constructed through the unitarization of the scattering and transition amplitudes of pairs of pseudoscalar mesons. We find that violating isospin inside the T matrix makes the pi(0)eta -> pi(+)pi(-) amplitude nonzero, which gives an important contribution and also enhances the effect of the K (K) over bar term. We also find that the most important effect in the total amplitude is the isospin breaking inside the T matrix, due to the constructive sum of pi(0)eta -> pi(+)pi(-) and K (K) over bar -> pi(+)pi(-), which is essential to get a good agreement with the experimental measurement of the mixing.

Abstract: Stimulated by the new experimental LHCb findings associated with the Omega(c) states, some of which we have described in a previous work as being dynamically generated through meson-baryon interaction, we have extended this approach to make predictions for new Xi(cc) molecular states in the C = 2, S = 0, and I = 1/2 sector. These states manifest themselves as poles in the solution of the Bethe-Salpeter equation in coupled channels. The kernels of this equation were obtained using general Lagrangians coming from the hidden local gauge symmetry or massive Yang-Mills theory, and the interactions are dominated by the exchange of light vector mesons. The extension of this approach to the heavy sector stems from the realization that the dominant interaction corresponds to having the heavy quarks as spectators, which implies the preservation of the heavy quark symmetry. As a result, we get several states: three states from the pseudoscalar meson-baryon interaction with J(P) = 1/2(-), and masses around 3840, 4080 and 4090 MeV, and two at 3920 and 4150 MeV for J(P) = 3/2(-). Furthermore, from the vector meson-baryon interaction we get three states degenerate with J(P) 1/2(-) and 3/2(-) from 4220 MeV to 4290 MeV, and two more states around 4280 and 4370 MeV, degenerate with J(P) = 1/2(-), 3/2(-), and 5/2(-).