Pion Scalar Form Factor and the Sigma Meson

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.

Comments: 6 pages, 3 figs, REVTeX, to appear in Phys. Rev. D