Jacobo Ruiz de Elvira

Pion-pion scattering amplitude. IV. Improved analysis with once subtracted Roy-like equations up to 1100 MeV

We improve our description of π π scattering data by imposing additional requirements on our previous fits, in the form of once-subtracted Roy-like equations, while extending our analysis up to 1100 MeV. We provide simple and ready to use parametrizations of the amplitude. In addition, we present a detailed description and derivation of these once-subtracted dispersion relations that, in the 450 to 1100 MeV region, provide an additional constraint which is much stronger than our previous requirements of forward dispersion relations and standard Roy equations. The ensuing constrained amplitudes describe the existing data with rather small uncertainties in the whole region from threshold up to 1100 MeV, while satisfying very stringent dispersive constraints. For the S0 wave, this requires an improved matching of the low and high energy parametrizations. Also for this wave we have considered the latest low energy K_(l4) decay results, including their isospin violation correction, and we have removed some controversial data points. These changes on the data translate into better determinations of threshold and subthreshold parameters which remove almost alldisagreement with previous chiral perturbation theory and Roy equation calculations below 800 MeV. Finally, our results favor the dip structure of the S0 inelasticity around the controversial 1000 MeV region.

Large-N-c naturalness in coupled-channel meson-meson scattering

The analysis of hadronic interactions with effective field theory techniques is complicated by the appearance of a large number of low-energy constants, which are usually fitted to data. On the other hand, the large-

Uncertainty estimates of the σ-pole determination by Padé approximants

N_c

Fock space expansion of σ meson in leading-Nc

limit imposes natural short-distance constraints on these low-energy constants, providing a parameter reduction. A Bayesian interpretation of the expected

Recent advances on chiral partners and patterns and the thermal f 0 ( 500 ) in chiral restoration

1/N_c

Recent advances on chiral partners and patterns and the thermal

accuracy allows for an easy and efficient implementation of these constraints, using an augmented

f_0(500)

\chi^2

in chiral restoration

. We apply this approach to the analysis of meson-meson scattering, in conjunction with chiral perturbation theory to one loop and coupled-channel unitarity, and show that it helps to largely reduce the many existing ambiguities and simultaneously provide an acceptable description of the available phase shifts.

Recent developments in U(3) \chi PT: meson-meson scattering and finite energy sum rules

We discuss the determination of the f0(500) (or σ) resonance by analytic continuation through Pade approximants of the ππ-scattering amplitude from the physical region to the pole in the complex energy plane. The aim is to analyze the uncertainties of the method, having in view the fact that analytic continuation is an ill-posed problem in the sense of Hadamard. Using as input a class of admissible parametrizations of the scalar-isoscalar ππ partial wave, which satisfy with great accuracy the same set of dispersive constraints, we find that the Roy-type integral representations lead to almost identical pole positions for all of them, while the predictions of the Pade approximants have a larger spread, being sensitive to features of the input parametrization that are not controlled by the dispersive constraints. Our conservative conclusion is that the σ-pole determination by Pade approximants is consistent with the prediction of Roy-type equations, but has an uncertainty almost a factor of 2 larger.

F_0(600) and f_0(980) pole positions from a dispersive π π scattering data analysis

We examine the leading- N c behavior of the masses and transition matrix elements of some low-lying, few-particle configurations in QCD. A truncation of the Fock space produces an effective, symmetric Hamiltonian that we diagonalize. The lowest eigenvalue is identified as the σ meson if the Hamiltonian is chosen to represent the scalar sector. As an application, the coefficients of the N c powers are then fit to two-loop Unitarized SU(2) Chiral Perturbation Theory results for the σ mass and width as a function of the number of colors, and we show that those results can be accommodated using the QCD N c dependence previously derived for matrix elements, without the need for unnatural parameters or fine tunings. Finally, we show a very preliminary good quality fit, estimating the proportion of tetraquark/molecule-like (dominant), q q ¯ -like (subdominant) and exotic-like (marginal) configurations in the σ .