G. Rios

Quark-Mass Dependence of the ρ and σ Mesons from Dispersion Relations and Chiral Perturbation Theory

We use the one-loop chiral perturbation theory π π -scattering amplitude and dispersion theory in the form of the inverse amplitude method to study the quark-mass dependence of the two lightest resonances of the strong interactions, the f_0(600) (σ) and the ρ meson. As the main results, we find that the rho π π coupling constant is almost quark mass independent and that the ρ mass shows a smooth quark-mass dependence while that of the σ shows a strong nonanalyticity. These findings are important for studies of the meson spectrum on the lattice.

Inverse amplitude method and Adler zeros

The inverse amplitude method is a powerful unitarization technique to enlarge the energy applicability region of effective Lagrangians. It has been widely used to describe resonances in hadronic physics, combined with chiral perturbation theory, as well as in the strongly interacting symmetry breaking sector. In this work we show how it can be slightly modified to also account for the subthreshold region, incorporating correctly the Adler zeros required by chiral symmetry and eliminating spurious poles. These improvements produce negligible effects on the physical region.

Chiral extrapolation of light resonances from one and two-loop unitarized chiral perturbation theory versus lattice results

We study the pion mass dependence of the {rho}(770) and f{sub 0}(600) masses and widths from one and two-loop unitarized chiral perturbation theory (ChPT). We show the consistency of one-loop calculations with lattice results for the M{sub {rho}}, f{sub {pi}}, and the isospin-2 scattering length a{sub 20}. Then, we develop and apply the modified inverse amplitude method formalism for two-loop ChPT. In contrast to the f{sub 0}(600), the {rho}(770) is rather sensitive to the two-loop ChPT parameters--our main source of systematic uncertainty. We thus provide two-loop unitarized fits constrained by lattice information on M{sub {rho}}, f{sub {pi}}, by the qq leading 1/N{sub c} behavior of the {rho} and by existing estimates of low-energy constants. These fits yield relatively stable predictions up to m{sub {pi}{approx_equal}3}00-350 MeV for the {rho} coupling and width as well as for all the f{sub 0}(600) parameters. We confirm, to two loops, the weak m{sub {pi}} dependence of the {rho} coupling and the Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation, and the existence of two virtual f{sub 0}(600) poles for sufficiently high m{sub {pi}}. At two loops one of these poles becomes a bound state when m{sub {pi}} is somewhat larger than 300 MeV.

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

We show that the latest and very precise dispersive data analyses require a large and very unnatural fine-tuning of the 1/N{sub c} expansion at N{sub c}=3 if the f{sub 0}(600) and K(800) light scalar mesons are to be considered predominantly qq states, which is not needed for light vector mesons. For this, we use scattering observables whose 1/N{sub c} corrections are suppressed further than one power of 1/N{sub c} for qq 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/N{sub c} expansion are unnatural, but that the expansion itself does not even follow the expected 1/N{sub c} scaling of a glueball or a qq meson.

Chiral extrapolation of the sigma and rho mesons from dispersion relations and chiral perturbation theory

We review our recent study of the pion mass dependence of the p and a resonances, generated from one-loop SU(2) Chiral Perturbation Theory (ChPT) with the Inverse Amplitude Method (IAM). In order to properly account for the Adler zero region, we also review the recently obtained modified version of the IAM; which is based on analyticity, elastic unitarity and ChPT at low energies, thus yielding the correct pion mass dependence of the resonance pole positions up to next-to-leading order in ChPT. As main results we find that the rho pi pi coupling constant is almost in, independent and that M(rho) shows a smooth m(pi) dependence while that of the sigma shows a strong non-analyticity. These findings are important for studies of the meson spectrum on the lattice.

Properties of light resonances from unitarized Chiral perturbation theory: Nc behavior and quark mass dependence

We review the unitarization of Chiral Perturbation Theory with dispersion relations and how it describes meson-meson scattering data, generating light resonances whose mass, width and nature can be related to QCD parameters like quark masses and the number of colors.

Unitarized Chiral Perturbation Theory and the meson spectrum

In this talk we briefly review how the unitarization of Chiral Perturbation Theory with dispersion relations can successfully describe the meson‐meson scattering data and generate light resonances, whose mass, width and nature can be related to QCD parameters like quark masses and the number of colors.

m{sub {pi}} and N{sub c} dependence of {rho} and {sigma} mesons from unitarized chiral perturbation theory

We review the N{sub c} and m{sub {pi}} dependence of the {rho}(770) and {sigma}(or f{sub 0}(600)) resonances generated with the Inverse Amplitude Method. The {sigma}N{sub c} behavior is at odds with being dominantly a q-barq state, but there is a hint of a subdominant q-barq component with a mass above 1 GeV. We find fair agreement with lattice results for the chiral extrapolation of the {rho} mass, and that the {rho}{pi}{pi} coupling is almost m{sub {pi}} independent whereas the {sigma}{pi}{pi} coupling depends strongly on m{sub {pi}}.

Chiral Extrapolations of light resonances from dispersion relations and Chiral Perturbation Theory

We review our recent study of the pion mass dependence of the ρ and σ resonances, generated from one-loop SU(2) Chiral Perturbation Theory (ChPT) with the Inverse Amplitude Method (IAM) which was modified to properly account for the Adler zer o. The method is based on analyticity, elastic unitarity and ChPT at low energies, th us yielding the pion mass dependence of the resonance pole positions from the ChPT series up to a given order. We find that the ρππ coupling constant is almost mπ independent and that our prediction compare well with some recent lattice results for the ρ mass. These findings may be relevant for studies of the meson spectrum and form factors on the lattice.

Determination of Chiral Perturbation Theory low energy constants from a precise description of pion-pion scattering threshold parameters

We report on our determination of the values of the one and two loop low energy constants appearing in the Chiral Perturbation Theory calculation of th e ππ scattering amplitude. For this we use a precise sum rule determination of scattering lengths a nd slopes that appear in the effective range expansion. In addition we provide new sum rules and the values for these coefficients up to third order in the expansion. Our results when using only t he scattering lengths and slopes of the S, P, D and F waves are consistent with previous determina tions, but seem to require higher order contributions if they are to accommodate the third ord er coefficients of the effective range expansion.