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

摘要

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