Pion Scalar Form Factor and the Sigma Meson

TL;DR

This paper analyzes the pion scalar form factor using unitarity, dispersion relations, and chiral perturbation theory, providing strong evidence for the existence of the broad and light sigma meson through resonance pole identification.

Contribution

It offers a novel analysis of the pion scalar form factor in the complex energy plane, supporting the sigma meson existence with a resonance pole.

Findings

Resonance pole at √s=445-i235 MeV supports sigma meson existence.

Analysis agrees with empirical data in the elastic region.

Provides theoretical evidence for the sigma meson based on form factor analysis.

Abstract

From recent analysis of the $\pi\pi$ scattering amplitude, it has been claimed that there exists a broad and light $\sigma$ meson. However, if this meson really exists, it must also appear in other observables such as the pion scalar form factor. With the use of unitarity and dispersion relations together with chiral perturbation theory, this form factor is analyzed in the complex energy plane. The result agrees well with the empirical information in the elastic region and reveals a resonance pole at $\sqrt{s}=445-i235$ MeV. This gives further strong evidence for the existence of the $\sigma$ meson.