Abstract: We apply an extension of the Weinberg compositeness condition on partial waves of L = 1 and resonant states to determine the weight of the meson-baryon component in the Delta(1232) resonance and the other members of the baryon decuplet. We obtain an appreciable weight of pi N in the Delta(1232) wave function, of the order of 60%, which looks more natural when one recalls that experiments on deep inelastic and Drell Yan give a fraction of pi N component of 34% for the nucleon. We also show that, as we go to higher energies in the members of the decuplet, the weights of the meson-baryon component decrease and they already show a dominant part for a genuine, non-meson-baryon, component in the wave function. We write a section to interpret the meaning of the Weinberg sum rule when it is extended to complex energies and another one for the case of an energy-dependent potential.

Abstract: Assuming that the recently observed hidden-charm pentaquark state, P-c(4450), is of molecular nature as predicted in the unitary approach, we propose to study the decay of Xi(-)(b) -> J/psi K-Lambda to search for the strangeness counterpart of the P-c(4450). There are three ingredients in the decay mechanism: the weak decay mechanism, the hadronization mechanism, and the final state interactions in the meson-baryon system of strangeness S = -2 and isospin I = 1/2 and of the J/psi Lambda. All these have been tested extensively. As a result, we provide a genuine prediction of the invariant mass distributions where a strangeness hidden-charm pentaquark state, the counterpart of the P-c(4450), can be clearly seen. The decay rate is estimated to be of similarmagnitude as the Lambda(0)(b) -> J/psi K(-)p measured by the LHCb Collaboration.

Abstract: Based on a spin-flavor extension of chiral symmetry, a novel s-wave meson-meson interaction involving members of the rho nonet and of the pi octet is introduced, and its predictions are analyzed. The starting point is the SU(6) version of the SU(3)-flavor Weinberg-Tomozawa Lagrangian. SU(6) symmetry-breaking terms are then included to account for the physical meson masses and decay constants in a way that preserves (broken) chiral symmetry. Next, the T-matrix amplitudes are obtained by solving the Bethe-Salpeter equation in a coupled-channel scheme, and the poles are identified with their possible Particle Data Group counterparts. It is shown that most of the low-lying even-parity Particle Data Group meson resonances, especially in the J(P) = 0(+) and 1(+) sectors, can be classified according to multiplets of SU(6). The f(0)(1500), f(1)(1420), and some 0(+)(2(++)) resonances cannot be accommodated within this scheme, and thus they would be clear candidates to be glueballs or hybrids. Finally, we predict the existence of five exotic resonances (I >= 3/2 and/or vertical bar Y vertical bar = 2) with masses in the range of 1.4-1.6 GeV, which would complete the 27(1), 10(3), and 10(3)* multiplets of SU(3) circle times SU(2).

Abstract: In this paper we present an approach to study the radiative decay modes of the J/psi into a photon and one of the tensor mesons f (2)(1270) , f' (2)(1525) , as well as the scalar ones f (0)(1370) and f (0)(1710) . Especially, we compare predictions that emerge from a scheme where the states appear dynamically in the solution of vector meson-vector meson scattering amplitudes to those from a (admittedly naive) quark model. We provide evidence that it might be possible to distinguish amongst the two scenarios, once improved data are available.

Abstract: We examine in detail a recent work (D. Gulmez, U. G. Meibner and J. A. Oller, Eur. Phys. J. C, 77: 460 (2017)), where improvements to make rho rho scattering relativistically covariant are made. The paper has the remarkable conclusion that the J=2 state disappears with a potential which is much more attractive than for J=0, where a bound state is found. We trace this abnormal conclusion to the fact that an “on-shell” factorization of the potential is done in a region where this potential is singular and develops a large discontinuous and unphysical imaginary part. A method is developed, evaluating the loops with full rho propagators, and we show that they do not develop singularities and do not have an imaginary part below threshold. With this result for the loops we define an effective potential, which when used with the Bethe-Salpeter equation provides a state with J=2 around the energy of the f(2)(1270). In addition, the coupling of the state to is evaluated and we find that this coupling and the T matrix around the energy of the bound state are remarkably similar to those obtained with a drastic approximation used previously, in which the q(2) terms of the propagators of the exchanged rho mesons are dropped, once the cut-off in the rho rho loop function is tuned to reproduce the bound state at the same energy.