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 Λ b → J/ψK − p process via Λ * -charmonium-proton intermediate states. Although the evaluation of absolute rates is not possible, we identify the χ c1 and the ψ(2S) as the relatively most relevant states among all possible charmonia up to the ψ(2S). The Λ(1890) χ 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 χ c1 p is in an S-wave. We also see that loops with the same charmonium and other Λ * hyperons produce less dramatic peaks from the threshold singularity alone. For the case of χ c1 p → J/ψ p and quantum numbers 3/2 − or 5/2 + one needs Pand D-waves, respectively, in the χ 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 χ c1 p → J/ψ p can proceed in an S-wave, the Λ(1890) χ c1 p triangle diagram could play an important role, though can neither assert their strength without further input from experiments and lattice QCD calculations. 1 I. INTRODUCTIONTriangle singularities in physical processes were introduced by Landau [1] and stem from Feynman diagrams involving three intermediate particles when the three particles can be placed simultaneously on shell and the momenta of these particles are collinear (parallel or antiparallel) in the frame of an external decaying particle at rest. In one of the cases (we call it parallel), two of the particles in the loop will go in the same direction and might fuse into other external outgoing particle(s) [2], so that the rescattering process can even happen as a classical process. In this case, the decay amplitude has a singularity close to the physical region 1 and, thus, can produce an enhancement. One of the classical cases would be given when the two on shell particles move in the same direction and with similar velocities. In the center-of-mass frame of the rescattering particles, these two particles would also be at rest and the triangle singularity is then located around the threshold.One very successful example of effects of the triangle singularity was shown in the decay of η(1405) → πa 0 (980) and η(1405) → πf 0 (980) in Refs. [3,4]. The second reaction breaks isospin symmetry. However, the process η(1405) → K * K followed by K * → Kπ and the fusion of KK → f 0 (980) enhances drastically the rate of η(1405) → πf 0 (980) relative to other isospin violating processes. Experimentally the ratio of rates for η(1405), a huge number for an isospin breaking magnitude. The work of [3,4] was continued in [6] where the precise rates, as well as the shapes of the two reactions, are well described.Another striking example of triangle singularities is the one ...

From a picture of the X(3872) where the resonance is a bound state ofDD * − c.c., we evaluate the decay width into the J/ψγ channel, which is sensitive to the internal structure of this state.For this purpose we evaluate the loops through which the X(3872) decays into its components, and the J/ψ and the photon are radiated from these components. We use the local hidden gauge approach extrapolated to SU (4) with a particular SU (4) breaking. The radiative decay involves anomalous couplings and we obtain acceptable values which are compared to experiments and results of other calculations.Simultaneusly, we evaluate the decay rate for the X(3872) into J/ψω and J/ψρ, and the results obtained for the ratio of these decay widths are compatible with the experiment.We also show the grossly unacceptable results that come from taking only theD 0 D * 0 + c.c. component.

We study here the interaction of DD * in the isospin I = 1 channel in the light of recent theoretical advances that allow to combine elements of the local hidden gauge approach with heavy quark spin symmetry. We find that the exchange of light qq is OZI suppressed and, thus, we concentrate on the exchange of heavy vectors and of two pion exchange. The latter is found to be small compared to the exchange of heavy vectors, which then determines the strength of the interaction. A barely DD * bound state decaying into η c ρ and πJ/ψ is found. At the same time we reanalyse the data of the BESIII experiment on e + e − → π ± (DD * ) ∓ , from where a Z c (3885) state was claimed, associated to a peak in the (DD * ) ∓ invariant mass distribution close to threshold, and we find the data compatible with a resonance with mass around 3875 MeV and width around 30 MeV. We discuss the possibility that this and the Z c (3900) state found at BESIII, reconfirmed at 3894 MeV at Belle, or 3885 MeV at CLEO, could all be the same state and correspond to the one that we find theoretically.

Abstract. We extend the Weinberg compositeness condition to partial waves of L = 1 and resonant states to determine the weight of meson-baryon component in theWe obtain an appreciable weight of N in the (1232) wave function, of the order of 60 % and we also show that, as we go to higher energies in the members of the decuplet, the weights of meson-baryon component decrease and they already show a dominant part for a genuine component in the wave function. We interpret the meaning of the Weinberg sum-rule extended to complex energies.