Nature of the sigma meson as revealed by its softening process

TL;DR

This paper investigates the sigma meson in two-flavor chiral models, revealing that its nature and behavior during symmetry restoration depend on its origin, with distinct patterns for dynamically generated versus chiral partner scenarios.

Contribution

It compares different models of the sigma meson, showing the universal threshold enhancement pattern for dynamically generated sigma and its relation to chiral symmetry restoration.

Findings

Dynamically generated sigma shows threshold enhancement reflecting s-wave nature.

Behavior of sigma near threshold is universal if the bare sigma pole remains away from the threshold.

For zero pion mass, the dynamically generated sigma mimics the chiral partner, suggesting possible chiral partner identity.

Abstract

The pi pi scattering is studied in two-flavor chiral models with a finite pion mass to investigate the nature of the sigma meson which is observed as the lowest scalar-isoscalar resonance. We compare several models with different origins of the sigma meson, such as the chiral partner of the pion and the dynamically generated pi pi molecule. We find that the dynamically generated sigma meson exhibits a novel pattern of the threshold enhancement reflecting the s-wave nature of the resonance, which is qualitatively different from the softening of the chiral partner introduced as a bare field. This behavior around the threshold energy region is universal as far as the bare sigma pole stays away from the threshold throughout the symmetry restoration process. On the other hand, for m_pi=0, the dynamically generated sigma behaves similarly to the chiral partner in the symmetry restoration limit, implying the possibility of the dynamically generated chiral partner.