Chiral Perturbation Theory, the ${1/N_c}$ expansion and Regge behaviour determine the structure of the lightest scalar meson

Abstract

The leading $1/N_c$ behaviour of Unitarised Chiral Perturbation Theory distinguishes the nature of the $ρ$ and the $σ$. At one loop order the $ρ$ is a ${\bar q}q$ meson, while the $σ$ is not. However, semi-local duality between resonances and Regge behaviour cannot be satisfied for larger $N_c$, if such a distinction holds. While the $σ$ at $N_c=3$ is inevitably dominated by its di-pion component, Unitarised Chiral Perturbation Theory beyond one loop order reveals that as $N_c$ increases above 6-8, the $σ$ has a sub-dominant ${\bar q}q$ fraction up at 1.2 GeV. Remarkably this ensures semi-local duality is fulfilled for the range of $N_c \lesssim 15$, where the unitarisation procedure adopted applies.