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Continuing our previous work(JHEP 0706:030,2007), large--$N_C$ techniques andpartial wave dispersion relations are used to discuss $\pi\pi$ scatteringamplitudes. We get a set of predictions for $O(p^6)$ low-energy chiralperturbation theory couplings. They are provided in terms of the masses anddecay widths of scalar and vector mesons.

$O(p^6)$ extension of the large--$N_C$ partial wave dispersion relations