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

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

Aspects of Strangeness -1 Meson-Baryon Scattering

We consider meson-baryon interactions in S-wave with strangeness -1. This is a sector populated by plenty of resonances interacting in several two-body coupled channels. We consider a large set of experimental data, where the recent experiments are remarkably accurate. This requires a sound theoretical description to account for all the data and we employ Unitary Chiral Perturbation Theory up to and including O(p^2). The spectroscopy of our solutions is studied within this approach, discussing the rise from the pole content of two \Lambda(1405) resonances and of the \Lambda(1670), \Lambda(1800), \Sigma(1480), \Sigma(1620) and \Sigma(1750). We finally argue about our preferred fit.Comment: 6 figures, 3 figures, talk given in the IVth International Conference on Quarks and Nuclear Physics (QNP06), Madrid June 5th and 10th, 2006. One reference is update

Chiral unitary meson-baryon dynamics in the presence of resonances: Elastic pion-nucleon scattering

We develop a novel approach to chiral meson-baryon dynamics incorporating unitarity constraints and explicit resonance fields. It is based on the most general structure of any pion-nucleon partial wave amplitude neglecting the unphysical cuts as derived from the N/D method. This amplitude is then matched to the one-loop heavy baryon chiral perturbation theory result at third order and to tree level exchanges of baryon- and meson states in the s,t and u channels. This generates the left-hand cuts. The unitarization procedure does not involve form factors or regulator functions. The resonance parameters are determined from fits to the S- and P-wave pion-nucleon partial wave amplitudes for energies up to 1.3 GeV. In particular, the $\Delta (1232)$ is accurately reproduced whereas scalar and vector meson couplings are less precisely pinned down. We also obtain a satisfactory description of the $\pi$N threshold parameters. Further extensions of this method to coupled channels and the three-flavor case are briefly discussed.Comment: 23 pp, LaTeX2e, 10 fig

Nucleon-Nucleon Interactions from Effective Field Theory

We have established a new convergent scheme to treat analytically nucleon-nucleon interactions from a chiral effective field theory. The Kaplan-Savage-Wise (KSW) amplitudes are resummed to fulfill the unitarity or right hand cut to all orders below pion production threshold. This is achieved by matching order by order in the KSW power counting the general expression of a partial wave with resummed unitarity cut, with the inverses of the KSW amplitudes. As a result, a new convergent and systematic KSW expansion is derived for an on-shell interacting kernel \cR in terms of which the partial waves are computed. The agreement with data for the S-waves is fairly good up to laboratory energies around 350 MeV and clearly improves and reestablishes the phenomenological success of the KSW amplitudes when treated within this scheme.Comment: 30 pages, 8 figures, enlarged and more detailed version, new results, version to be published in Nucl. Phys.

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