Abstract: fBased on the picture that the f(0)(1370), f(0)(1710), f(2)(1270), f(2)'(1525), (K) over bar (2)*(0) (1430) resonances are dynamically generated from the vector-vector interaction, we study the decays J/psi -> phi(omega) f(0)(1370)[f(0)(1710)], J/psi ->phi(omega) f(2)(1270)[f(2)'(1525)], and J/psi -> K*(0)(K) over bar (2)*(0) (1430) and make predictions for seven independent ratios that can be done among them. The starting mechanism is that the J/psi decays into three vectors, followed by the final state interaction of a pair of them. The weights of the different three vector primary channels are obtained from the basic assumption that the J/psi (c (c) over bar) is an SU(3) singlet. By means of only one free parameter we predict four ratios in fair agreement with experiment, make two extra predictions for rates yet unmeasured, and disagree on one data for which only upper bounds are reported. Further measurements are most welcome to complete the information required for these ratios which test the nature of these resonances as dynamically generated.

Abstract: We study the tau -> nu(tau). A decay, with A an axialvector meson. We produce the a(1) (1260) and b(1) (1235) resonances in the Cabibbo favored mode and two K-1 (1270) states in the Cabibbo suppressed mode. We take advantage of previous chiral unitary approach results where these resonances appear dynamically from the vector and pseudoscalar meson interaction in s-wave. Actually two different poles were obtained associated to the K-1(1270) quantum numbers. We find that the unmeasured rates for b(1)(1235) production are similar to those of the a(1)(1260) and for the two K-1 states we suggest to separate the present information on the (K) over bar pi pi invariant masses into (K) over bar*pi and rho K modes, the channels to which these two resonances couple most strongly, predicting that thesemodes peak at different energies and have different widths. These measurements should shed light on the existence of these two K-1 states. In addition, we have gone one step further making a comparison with experimental results of three meson decay channels, letting the vector mesons of our approach decay into pseudoscalars, and we find an overall good agreement with experiment.

Abstract: We recall the predictions made ten years ago about a bound state of J(P) = 0(+) in I = 0 of the D*(K) over bar* system, which is manifestly exotic, and we associate it to the X-0(2866) state reported in the recent LHCb experiment. Fine tuning the parameters to reproduce exactly the mass and width of the X-0(2866) state, we report two more states stemming from the same interaction, one with 1(+) and the other with 2(+). For reasons of parity, the 1(+) state cannot be observed in D (K) over bar decay, and we suggest to observe it in the D*(K) over bar spectrum. On the other hand, the 2(+) state can be observed in D (K) over bar decay but the present experiment has too small statistics in the region of its mass to make any claim. We note that measurements of the D*(K) over bar spectrum and of the D (K) over bar with more statistics should bring important information concerning the nature of the X-0(2866) and related ones that could be observed.

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: .We perform a calculation of the -M1M2, with M1,M2 either pseudoscalar or vector mesons using the basic weak interaction and angular momentum algebra to relate the different processes. The formalism also leads to a different interpretation of the role played by G-parity in these decays. We also observe that, while PPp-wave production is compatible with chiral perturbation theory and experiment, VP and VVp-wave production is clearly incompatible with experiment and we develop the formalism also in this case, producing the VP or VV pairs in s-wave. We compare our results with experiment and other theoretical approaches for rates and invariant mass distributions and make predictions for unmeasured decays. We show the value of these reactions, particularly if the M1M2 mass distribution is measured, as a tool to learn about the meson-meson interaction and the nature of some resonances, coupling to two mesons, which are produced in such decays.