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: We investigate the Schmid theorem, which states that if one has a tree level mechanism with a particle decaying to two particles and one of them decaying posteriorly to two other particles, the possible triangle singularity developed by the mechanism of elastic rescattering of two of the three decay particles does not change the cross section provided by the tree level. We investigate the process in terms of the width of the unstable particle produced in the first decay and determine the limits of validity and violation of the theorem. One of the conclusions is that the theorem holds in the strict limit of zero width of that resonance, in which case the strength of the triangle diagram becomes negligible compared to the tree level. Another conclusion, on the practical side, is that for realistic values of the width, the triangle singularity can provide a strength comparable or even bigger than the tree level, which indicates that invoking the Schmid theorem to neglect the triangle diagram stemming from elastic rescattering of the tree level should not be done. Even then, we observe that the realistic case keeps some memory of the Schmid theorem, which is visible in a peculiar interference pattern with the tree level.

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(-).

Abstract: We have investigated Omega(c) states that are dynamically generated from the meson-baryon interaction. We use an extension of the local hidden gauge to obtain the interaction from the exchange of vector mesons. We show that the dominant terms come from the exchange of light vectors, where the heavy quarks are spectators. This has as a consequence that heavy quark symmetry is preserved for the dominant terms in the (1/m(Q)) counting, and also that the interaction in this case can be obtained from the SU(3) chiral Lagrangians. We show that for a standard value for the cutoff regulating the loop, we obtain two states with J(P) = 1/2(-) and two more with J(P) = 3/2(-), three of them in remarkable agreement with three experimental states in mass and width. We also make predictions at higher energies for states of vector-baryon nature.

Abstract: We perform calculations for the eta(c) -> eta pi(+)pi(-) decay using elements of SU(3) symmetry to see the weight of different trios of pseudoscalars produced in this decay, prior to the final state interaction of the mesons. After that, the interaction of pairs of mesons, leading finally to eta pi(+)pi(-), is done using the chiral unitary approach. We evaluate the pi(+)pi(-) and pi eta mass distributions and find large and clear signals for f(0)(500), f(0)(980) and a(0)(980) excitation. The reaction is similar to the chi(c1) -> eta pi(+)pi(-), which has been recently measured at BESIII and its implementation and comparison with these predictions will be very valuable to shed light on the nature of the low mass scalar mesons.