Experimental status of the ππ\pi\pi isoscalar S wave at low energy: f0(600)f_0(600) pole and scattering length

The experimental results obtained in the last few years on kaon decays (K$\to2\pi$ and, above all, Ke4 decays) allow a reliable, model independent determination of low energy $\pi\pi$ scattering in the S0 wave. Using them and, eventually, other sets of data, it is possible to give a precise parametrization of the S0 wave as well as to find the scattering length and effective range parameter. One can also perform an extrapolation to the pole of the "$\sigma$ resonance" [$f_0(600)$]. We obtain the results $$a_0^{(0)}=0.233\pm0.013 M^{-1}_\pi,\quad b_0^{(0)}=0.285\pm0.012 M^{-3}_\pi$$ and, for the $\sigma$ pole, M_\sigma=484\pm17 \mev,\quad\gammav_\sigma/2= 255\pm10 {\rm MeV}.Comment: Plain TeX;4 figures; improved data used; version to appear in Phys. Rev.

Scalar resonances: scattering and production amplitudes

Scattering and production amplitudes involving scalar resonances are known, according to Watson's theorem, to share the same phase $\delta(s)$. We show that, at low energies, the production amplitude is fully determined by the combination of $\delta(s)$ with another phase $\omega(s)$, which describes intermediate two-meson propagation and is theoretically unambiguous. Our main result is a simple and almost model independent expression, which generalizes the usual $K$-matrix unitarization procedure and is suited to be used in analyses of production data involving scalar resonances.Comment: 10 pages, 4 figures. Minor changes, references added, version to appear in Phys. Rev.

η→π0γγ\eta \to \pi^0 \gamma \gamma decay within unitarized chiral perturbation theory

We improve the calculations of the $\eta \to \pi^0 \gamma \gamma$ decay within the context of meson chiral lagrangians. We use a chiral unitary approach for the meson-meson interaction, thus generating the $a_0(980)$ resonance and fixing the longstanding sign ambiguity on its contribution. This also allows us to calculate the loops with one vector meson exchange, thus removing a former source of uncertainty. In addition we ensure the consistency of the approach with other processes. First, by using vector meson dominance couplings normalized to agree with radiative vector meson decays. And, second, by checking the consistency of the calculations with the related $\gamma \gamma \to \pi^0 \eta$ reaction. We find an $\eta \to \pi^0 \gamma \gamma$ decay width of $0.47\pm 0.10$ eV, in clear disagreement with published data but in remarkable agreement with the most recent measurement.Comment: 15 pages, 10 figures, published versio

Enhanced non-quark-antiquark and non-glueball Nc behavior of light scalar mesons

We show that the latest and very precise dispersive data analyses require a large and very unnat- ural fine-tuning of the 1/Nc expansion at Nc = 3 if the f_0(600) and K(800) light scalar mesons are to be considered predominantly quark-antiquark states, which is not needed for light vector mesons. For this, we use scattering observables whose 1/Nc corrections are suppressed further than one power of 1/Nc for quark-antiquark or glueball states, thus enhancing contributions of other nature. This is achieved without using unitarized ChPT, but if it is used we can also show that it is not just that the coefficients of the 1/Nc expansion are unnatural, but that the expansion itself does not even follow the expected 1/Nc scaling of a glueball or a quark-antiquark meson.Comment: Discussion disfavoring a glueball interpretation added. Version published in Phys. Rev.

Light scalars as tetraquarks or two-meson states from large Nc and unitarized Chiral Perturbation Theory

By means of unitarized Chiral Perturbation Theory it is possible to obtain a remarkable description of meson-meson scattering amplitudes up to 1.2 GeV, and generate poles associated to scalar and vector resonances. Since Chiral Perturbation Theory is the QCD low energy effective theory, it is possible then to study its large Nc limit where qqbar states are easily identified. The vectors thus generated follow closely a qqbar behavior, whereas the light scalar poles follow the large Nc behavior expected for a dominant tetraquark or two-meson structure.Comment: Invited Brief Report to appear in Modern Physcis Letters A. 15 page

Chiral Perturbation Theory and the f2(1270) resonance

Within Chiral Perturbation Theory, we study elastic pion scattering in the I=0, J=2, channel, whose main features are the f2(1270) resonance and the vanishing of the lowest order. By means of a chiral model that includes an explicit resonance coupled to pions, we describe the data and calculate the resonance contribution to the O(p^4) and O(p^6) chiral parameters. We also generalize the Inverse Amplitude Method to higher orders, which allows us to study channels with vanishing lowest order. In particular, we apply it to the I=0,J=2 case, finding a good description of the f2(1270) resonance, as a pole in the second Riemann sheet.Comment: 4 pages,1 figur

Chiral Symmetry and light resonances in hot and dense matter

We present a study of the $\pi\pi$ scattering amplitude in the $\sigma$ and $\rho$ channels at finite temperature and nuclear density within a chiral unitary framework. Meson resonances are dynamically generated in our approach, which allows us to analyze the behavior of their associated scattering poles when the system is driven towards chiral symmetry restoration. Medium effects are incorporated in three ways: (a) by thermal corrections of the unitarized scattering amplitudes, (b) by finite nuclear density effects associated to a renormalization of the pion decay constant, and complementarily (c) by extending our calculation of the scalar-isoscalar channel to account for finite nuclear density and temperature effects in a microscopic many-body implementation of pion dynamics. Our results are discussed in connection with several phenomenological aspects relevant for nuclear matter and Heavy-Ion Collision experiments, such as $\rho$ mass scaling vs broadening from dilepton spectra and chiral restoration signals in the $\sigma$ channel. We also elaborate on the molecular nature of $\pi\pi$ resonances.Comment: 14 pages, 14 figures. Contribution to Hard Probes 2008, Illa de A Toxa, Spain, June 8th-14th 200

The S-wave \Lambda\pi phase shift is not large

We study the strong interaction S-wave \Lambda\pi phase shift in the region of the \Xi mass in the framework of a relativistic chiral unitary approach based on coupled channels. All parameters have been previously determined in a fit to strangeness S= -1 S-wave kaon-nucleon data. We find 0^\circ \le \delta_0 \le 1.1^\circ in agreement with previous chiral perturbation theory calculations (or extensions thereof). We also discuss why a recent coupled channel K-matrix calculation gives a result for \delta_0 that is negative and much bigger in magnitude. We argue why that value should not be trusted.Comment: 3 pages, REVTe