Abstract: We present a method to evaluate the (K) over bar absorption width in the bound (K) over bar N N system. Most calculations of this system ignore this channel and only consider the (K) over bar N -> pi Sigma conversion. Other works make a qualitative calculation using perturbative methods. Since the (1405) resonance is playing a role in the process, the same resonance is changed by the presence of the absorption channels andwe find that a full nonperturbative calculation is called for, which we present here. We employ the fixed center approximation to Faddeev equations to account for (K) over bar rescattering on the (NN) cluster and we find that the width of the states found previously for S = 0 and S = 1 increases by about 30 MeV due to the (K) over bar N N absorption, to a total width of about 80 MeV.

Abstract: We extend the Fixed Center Approximation (FCA) to the Faddeev equations for the (K) over bar N N system with S = 0, including the charge exchange mechanisms in the (K) over bar rescattering which have been ignored in former works within the FCA. We obtain similar results to those found before, but the binding is reduced by 6 MeV. At the same time we also evaluate the explicit contribution the pi N Sigma intermediate state in the three body system and find that it produces and additional small decrease in the binding of about 3 MeV. The system appears bound by about 35 MeV and the width omitting two body absorption, is about 50 MeV.

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.