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

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arxiv 1009.6204 v2 pith:322GBPQH submitted 2010-09-30 hep-ph nucl-th

classification hep-phnucl-th
keywords sigmabehaviourchiralperturbationtheorydualityloopmeson
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

The leading $1/N_c$ behaviour of Unitarised Chiral Perturbation Theory distinguishes the nature of the $\rho$ and the $\sigma$. At one loop order the $\rho$ is a ${\bar q}q$ meson, while the $\sigma$ 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 $\sigma$ 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 $\sigma$ 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.

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    New global, dispersion-constrained parametrizations for the S2, P, D, F, and G pion-pion partial waves, valid to roughly 1.8 to 2.1 GeV.

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