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.

Abstract: We use the local hidden gauge approach in order to study the B (B) over bar* and B*(B) over bar* interactions for isospin I = 1. We show that both interactions via one light meson exchange are not allowed by the Okubo-ZweigIizuka rule and, for that reason, we calculate the contributions due to the exchange of two pions, interacting and noninteracting among themselves, and also due to the heavy vector mesons. Then, to compare all these contributions, we use the potential related to the heavy vector exchange as an effective potential corrected by a factor which takes into account the contribution of the other light meson exchanges. In order to look for poles, this effective potential is used as the kernel of the Bethe-Salpeter equation. As a result, for the B (B) over bar* interaction we find a loosely bound state with mass in the range 10587-10601 MeV, very close to the experimental value of the Z(b)(10610) reported by the Belle Collaboration. For the B*(B) over bar* case, we find a cusp at 10650 MeV for all spin J = 0, 1, 2 cases.

Abstract: We investigate the decay of f(1) (1285) > pi K (K) over bar with the assumption that the f(1) (1285) is dynamically generated from the K*(K) over bar – cc interaction. In addition to the tree level diagrams that proceed via f(1)(1285) -> K*(K) over bar – cc -> pi K (K) over bar, we take into account also the final state interactions of K (K) over bar -> K (K) over bar and pi K -> pi K. The partial decay width and mass distributions of f(1) (1285) -> pi K (K) over bar are evaluated. We get a value for the partial decay width which, within errors, is in fair agreement with the experimental result. The contribution from the tree level diagrams is dominant, but the final state interactions have effects in the mass distributions. The predicted mass distributions are significantly different from phase space and tied to the K*(K) over bar – cc nature of the f(1) (1285) state.

Abstract: We have analyzed the singularities of a triangle loop integral in detail and derived a formula for an easy evaluation of the triangle singularity on the physical boundary. It is applied to the Lambda(b) -> J/psi K(-)p process via Lambda*-charmonium-proton intermediate states. Although the evaluation of absolute rates is not possible, we identify the chi(c1) and the psi(2S)as the relatively most relevant states among all possible charmonia up to the psi(2S). The Lambda(1890)chi(c1)p loop is very special, as its normal threshold and triangle singularities merge at about 4.45 GeV, generating a narrow and prominent peak in the amplitude in the case that the chi(c1)p is in an S wave. We also see that loops with the same charmonium and other Lambda* hyperons produce less dramatic peaks from the threshold singularity alone. For the case of chi(c1)p -> J/psi p and quantum numbers 3/2(-) or 5/2(+), one needs P and D waves, respectively, in the chi(c1)p, which drastically reduce the strength of the contribution and smooth the threshold peak. In this case, we conclude that the singularities cannot account for the observed narrow peak. In the case of 1/2(+), 3/2(-) quantum numbers, where chi(c1)p -> J/psi p can proceed in an S wave, the Lambda(1890)chi(c1)p triangle diagram could play an important role, though neither can assert their strength without further input from experiments and lattice QCD calculations.

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.