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

TL;DR

This paper performs a one-loop analysis of scalar and pseudoscalar form factors within U(3) chiral perturbation theory, extending meson-meson scattering calculations, and explores spectral sum rules and duality, providing insights into scalar meson dynamics.

Contribution

It introduces a comprehensive one-loop calculation of form factors with resonance exchanges and extends scattering analysis, offering new constraints on scalar meson spectroscopy and dynamics.

Findings

Spectral functions satisfy sum rules and duality constraints.

Resonance content aligns with scattering data.

Results depend on Nc, revealing scalar meson behavior.

Abstract

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.