J. Ruiz de Elvira

Chiral dynamics in form factors, spectral-function sum rules, meson-meson scattering and semi-local duality

In this work, we perform the one-loop calculation of the scalar and pseudoscalar form factors in the framework of U(3) chiral perturbation theory with explicit tree level exchanges of resonances. The meson-meson scattering calculation from Ref.[1] is extended as well. The spectral functions of the nonet scalar-scalar (SS) and pseudoscalar-pseudoscalar (PP) correlators are constructed by using the corresponding form factors. After fitting the unknown parameters to the scattering data, we discuss the resonance content of the resulting scattering amplitudes. We also study spectral-function sum rules in the SS-SS, PP-PP and SS-PP sectors as well as semi-local duality from scattering. The former relate the scalar and pseudoscalar spectra between themselves while the latter mainly connects the scalar spectrum with the vector one. Finally we investigate these items as a function of Nc for Nc > 3. All these results pose strong constraints on the scalar dynamics and spectroscopy that are discussed. They are successfully fulfilled by our meson-meson scattering amplitudes and spectral functions.

Chiral Perturbation Theory, the 1/N_c expansion and Regge behavior determine the structure of the lightest scalar meson

The leading 1/N{sub c} behavior of Unitarized Chiral Perturbation Theory distinguishes the nature of the {rho} and the {sigma}. At one loop order the {rho} is a {bar q}q meson, while the {sigma} is not. However, semi-local duality between resonances and Regge behaviour cannot be satisfied for larger N{sub c}, if such a distinction holds. While the {sigma} at N{sub c}= 3 is inevitably dominated by its di-pion component, Unitarised Chiral Perturbation Theory beyond one loop order reveals that as N{sub c} increases above 6-8, the {sigma} has a sub-dominant {bar q}q fraction up at 1.2 GeV. Remarkably this ensures semi-local duality is fulfilled for the range of N{sub c} {approx}< 15-30, where the unitarization procedure adopted applies.

On the

Abstract.We present an improved determination of the

\pi\pi

\pi\pi

continuum in the nucleon form factors and the proton radius puzzle

ππ continuum contribution to the isovector spectral functions of the nucleon electromagnetic form factors. Our analysis includes the most up-to-date results for the

Chiral dynamics in U(3) unitary chiral perturbation theory

\pi\pi\rightarrow\bar{N} N

Reconciling threshold and subthreshold expansions for pion–nucleon scattering

ππ→N¯N partial waves extracted from Roy-Steiner equations, consistent input for the pion vector form factor, and a thorough discussion of isospin-violating effects and uncertainty estimates. As an application, we consider the

Scalar susceptibilities and four-quark condensates in the meson gas within chiral perturbation theory

\pi\pi

Nonfactorization of four-quark condensates at low energies within chiral perturbation theory

ππ contribution to the isovector electric and magnetic radii by means of sum rules, which, in combination with the accurately known neutron electric radius, are found to slightly prefer a small proton charge radius.

Chiral symmetry restoration and scalar-pseudoscalar partners in QCD

Abstract We perform a complete one-loop calculation of meson–meson scattering, and of the scalar and pseudoscalar form factors in U ( 3 ) chiral perturbation theory with the inclusion of explicit resonance fields. This effective field theory takes into account the low-energy effects of the QCD U A ( 1 ) anomaly explicitly in the dynamics. The calculations are supplied by non-perturbative unitarization techniques that provide the final results for the meson–meson scattering partial waves and the scalar form factors considered. We present thorough analyses on the scattering data, resonance spectroscopy, spectral functions, Weinberg-like sum rules and semi-local duality. The last two requirements establish relations between the scalar spectrum with the pseudoscalar and vector ones, respectively. The N C extrapolation of the various quantities is studied as well. The fulfillment of all these non-trivial aspects of the QCD dynamics by our results gives a strong support to the emerging picture for the scalar dynamics and its related spectrum.