Abstract: We study the decay mode of the a(1)(1260) into a pi(+) in p wave and the f(0)(980) that decays into pi(+)pi(-) in s wave. The mechanism proceeds via a triangular mechanism where the a(1)(1260) decays into K*K-, the K* decays to an external pi(+) and an internal K that fuses with the (K) over bar producing the f(0)(980) resonance. The mechanism develops a singularity at a mass of the a(1)(1260) around 1420 MeV, producing a peak in the cross section of the pp reaction, used to generate the mesonic final state, which provides a natural explanation of all the features observed in the COMPASS experiment, where a peak observed at this energy is tentatively associated to a new resonance called a(1)(1420). On the other hand, the triangular singularity studied here gives rise to a remarkable feature, where a peak is seen for a certain decay channel of a resonance at an energy about 200 MeV higher than its nominal mass.

Abstract: We make a theoretical study of the eta(1405) -> pi(0)f(0)(980) and eta(1405) -> pi(0)a(0)(980) reactions with an aim to determine the isospin violation and the mixing of the f(0)(980) and a(0)(980) resonances. We make use of the chiral unitary approach where these two resonances appear as composite states of two mesons, dynamically generated by the meson-meson interaction provided by chiral Lagrangians. We obtain a very narrow shape for the f(0)(980) production in agreement with a BES experiment. As to the amount of isospin violation, or f(0)(980) and a(0)(980) mixing, assuming constant vertices for the primary eta(1405) -> pi K-0 (K) over bar and eta(1405) -> pi(0)pi(0)eta production, we find results which are much smaller than found in the recent experimental BES paper, but consistent with results found in two other related BES experiments. We have tried to understand this anomaly by assuming an I = 1 mixture in the eta(1405) wave function, but this leads to a much bigger width of the f(0)(980) mass distribution than observed experimentally. The problem is solved by using the primary production driven by eta' -> K*(K) over bar followed by K* -> K pi, which induces an extra singularity in the loop functions needed to produce the f(0)(980) and a(0)(980) resonances. Improving upon earlier work along the same lines, and using the chiral unitary approach, we can now predict absolute values for the ratio Gamma(pi(0), pi(+)pi(-))/Gamma(pi(0), pi(0)eta) which are in fair agreement with experiment. We also show that the same results hold if we had the eta(1475) resonance or a mixture of these two states, as seems to be the case in the BES experiment.

Abstract: In this paper we present the connection between scattering amplitudes in momentum space and wave functions in coordinate space, generalizing previous work done for s-waves to any partial wave. The relationship to the wave function of the residues of the scattering amplitudes at the pole of bound states or resonances is investigated in detail. A sum rule obtained for the couplings provides a generalization to coupled channels, any partial wave and bound or resonance states, of Weinberg's compositeness condition, which was only valid for weakly bound states in one channel and s-wave. An example, requiring only experimental data, is shown for the rho meson indicating that it is not a composite particle of pi pi and K (K) over bar but something else.