Structure of the lightest scalar meson from the 1/Nc expansion of Unitarized Chiral Perturbation Theory and Regge Theory

TL;DR

This paper investigates the nature of the lightest scalar meson using unitarized chiral perturbation theory and Regge theory, revealing the necessity of a subdominant quark-antiquark component to satisfy local duality.

Contribution

It demonstrates that a subdominant q-qbar component in the sigma meson is essential for maintaining local duality, reconciling different theoretical approaches.

Findings

Sigma becomes broader with Nc, unlike rho

A subdominant q-qbar component around 1.2 GeV is necessary

Ensures consistency between UChPT and local duality

Abstract

One-loop unitarized Chiral Perturbation Theory (UChPT) calculations, suggest a different Nc behaviour for the sigma or f_0(600) and rho(770) mesons: while the rho meson becomes narrower with Nc, as is expected for a q-qbar meson, the sigma becomes broader, and its contribution to the total cross section is less and less important. On the other hand, local duality requires a cancellation between the sigma and rho amplitudes, but if there is a different Nc behaviour for them, there is a possible contradiction between the Inverse Amplitude Method (IAM) and local duality for large Nc. However, next to next to leading order UChPT calculations suggested a subdominant q-qbar component for the sigma with a mass around 1.2 GeV. In this work, we show that this subdominant q-qbar component is indeed needed to ensure local duality.