Chiral perturbation theory, the1/Ncexpansion and Regge behavior determine the structure of the lightest scalar meson
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Abstract
The leading $1/{N}_{c}$ behavior of unitarized chiral perturbation theory distinguishes the nature of the $\ensuremath{\rho}$ and the $\ensuremath{\sigma}$: The $\ensuremath{\rho}$ is a $\overline{q}q$ meson, while the $\ensuremath{\sigma}$ is not. However, semilocal duality between resonances and Regge behavior cannot be satisfied for larger ${N}_{c}$, if such a distinction holds. While the $\ensuremath{\sigma}$ at ${N}_{c}=3$ is inevitably dominated by its di-pion component, unitarized chiral perturbation theory also suggests that as ${N}_{c}$ increases above 6--8, the $\ensuremath{\sigma}$ may have a subdominant $\overline{q}q$ fraction up at 1.2 GeV. Remarkably this ensures semilocal duality is fulfilled for the range of ${N}_{c}\ensuremath{\lesssim}15--30$, where the unitarization procedure adopted applies.