Pole structure and compositeness

We present in this talk a series of new results on the nature of a bound state or resonance based on the calculation of the expectation values of the number operators of the free particles in the state of interest. In this way, a new universal criterion for the elementariness of a bound state emerges. In the case of large particle wavelengths compared to the range of their interaction, a new closed formula for the compositeness of a bound state in a two-particle continuum is obtained. The extension of these results to resonances with respect to the open channels can be given by making use in addition of suitable phase-factor transformations as also reviewed here. We end with a discussion on the $X(3872)$ as possible double- or triple-pole virtual state, which would be the first case in particle phenomenology.Comment: 10 pages, 4 figures. Plenary talk at Hadron201

Final State Interactions in Hadronic D decays

We show that the large corrections due to final state interactions (FSI) in the D^+\to \pi^-\pi^+\pi^+, D^+_s\to \pi^-\pi^+\pi^+, and D^+\to K^-\pi^+\pi^+ decays can be accounted for by invoking scattering amplitudes in agreement with those derived from phase shifts studies. In this way, broad/overlapping resonances in S-waves are properly treated and the phase motions of the transition amplitudes are driven by the corresponding scattering matrix elements determined in many other experiments. This is an important step forward in resolving the puzzle of the FSI in these decays. We also discuss why the \sigma and \kappa resonances, hardly visible in scattering experiments, are much more prominent and clearly visible in these decays without destroying the agreement with the experimental \pi\pi and K\pi low energy S-wave phase shifts.Comment: 22 pages, 6 figures, 5 tables. Minor changes. We extend the discusion when quoting a reference and we include a new one. Some typos are fixe

Unitarization Technics in Hadron Physics with Historical Remarks

We review a series of unitarization techniques that have been used during the last decades, many of them in connection with the advent and development of current algebra and later of Chiral Perturbation Theory. Several methods are discussed like the generalized effective-range expansion, K-matrix approach, Inverse Amplitude Method, Pad\'e approximants and the N/D method. More details are given for the latter though. We also consider how to implement them in order to correct by final-state interactions. In connection with this some other methods are also introduced like the expansion of the inverse of the form factor, the Omn\'es solution, generalization to coupled channels and the Khuri-Treiman formalism, among others.Comment: 45 pages, 2 figures. Invited contribution to a special issue on "Effective Field Theories - Chiral Perturbation Theory and Non-relativistic QFT". Updated to match the published versio

Scalar Mesons and Chiral Symmetry

It is the purpose of the present manuscript to emphasize those aspects that make the scalar sector with vacuum quantum numbers rather unique. Chiral symmetry is the basic tool for our study together with a resummation of Chiral Perturbation Theory (CHPT) that stresses the role of unitarity but also allows one to include explicit resonance fields and to match with the CHPT expansion at low energies.Comment: 8 pages,2 figures. Invited talk at the $\sigma$-meson workshop, Kyoto, June 200

Identification of a Scalar Glueball

We have performed a coupled channel study of the meson-meson S-waves involving isospins (I) 0, 1/2 and 3/2 up to 2 GeV. For the first time the channels \pi\pi, K\bar{K}, \eta\eta, \sigma\sigma, \eta\eta', \eta'\eta', \rho\rho, \omega\omega, \omega\phi$, \phi\phi, a_1\pi and \pi^*\pi are considered. All the resonances with masses below 2 GeV for I=0 and 1/2 are generated by the approach. We identify the f_0(1710) and a pole at 1.6 GeV, which is an important contribution to the f_0(1500), as glueballs. This is based on an accurate agreement of our results with predictions of lattice QCD and the chiral suppression of the coupling of a scalar glueball to \bar{q}q. Another nearby pole, mainly corresponding to the f_0(1370), is a pure octet state not mixed with the glueball.Comment: 5 pages, 1 figure. More data are included and reproduced. Some discussions have been rephrase

Scalar-Pseudoscalar scattering and pseudoscalar resonances

The interactions between the f_0(980) and a_0(980) scalar resonances and the lightest pseudoscalar mesons are studied. We first obtain the interacting kernels, without including any ad hoc free parameter, because the lightest scalar resonances are dynamically generated. These kernels are unitarized, giving the final amplitudes, which generate pseudoscalar resonances, associated with the K(1460), \pi(1300), \pi(1800), \eta(1475) and X(1835). We also consider the exotic channels with I=3/2 and I^G=1^+ quantum numbers. The former could be also resonant in agreement with a previous prediction.Comment: 3 pages, 2 figures; Contributed oral presentation in (QCHS09) The IX International Conference on Quark Confinement and Hadron Spectrum - Madrid, Spain, 30 Aug 2010 - 03 Sep 201

Two Meson Scattering Amplitudes and their Resonances from Chiral Symmetry and the N/D Method

We study the vector and scalar meson-meson amplitudes up to \sqrt{s}\lesssim 1.4 GeV and their associated spectroscopy. The study has been done considering jointly the N/D method, Chiral Symmetry and implications from large N_c QCD. The N/D method provides us with the way to unitarize the tree level amplitudes constructed in agreement with Chiral Symmetry and its breaking (explicit and spontaneous). These amplitudes are calculated making use of the lowest order Chiral Perturbation Theory (\chiPT) Lagrangians and the exchanges of resonances compatible with Chiral Symmetry as given in. On the other hand the large N_c considerations allow us to distinguish between elementary (as elementary as the pions, for instance) and compound (meson-meson) states. Making use of this formalism one observes that the \sigma, \kappa and a_0(980) resonances are meson-meson states originating from the unitarization of the lowest order \chiPT amplitudes. On the other hand, the f_0(980) is a combination of a strong S-wave meson-meson unitarity effect and of a preexisting singlet resonance with a mass around 1 GeV.Comment: 4 pages, LaTeX, Talk given at PANIC99, Uppsala (Sweden), June 10-16, 199