Light scalar mesons: comments on their behavior in the 1/Nc expansion near Nc=3 versus the Nc --> infinity limit

TL;DR

This paper reviews the behavior of light scalar mesons in the 1/Nc expansion, showing they are not predominantly quark-antiquark states near Nc=3 but may have a subdominant component, and discusses limitations of the Nc --> infinity limit.

Contribution

It clarifies the Nc dependence of light scalar mesons and highlights the limitations of using the Nc --> infinity limit to infer their nature.

Findings

Light vectors follow Nc behavior of q̄q mesons near Nc=3

Light scalars do not behave as q̄q mesons near Nc=3

The Nc --> infinity limit is unreliable for understanding scalar mesons

Abstract

We briefly review how light meson resonances are described within one and two-loop Unitarized Chiral Perturbation Theory amplitudes and how, close to Nc=3, light vectors follow the Nc behavior of $q\bar q$ mesons whereas light scalars do not. This supports the hypothesis that the lightest scalar is not predominantly a $q\bar q$ meson, although a subdominant $q\bar q$ component is suggested around 1 GeV at somewhat larger Nc. In contrast, when Nc is very far from 3, like in the Nc --> infinity limit, we explain again in detail why unitarization is not, a priori, reliable nor robust and why this limit should not be used to drag any conclusions about the dominant nature of physical light scalar mesons.