Enhanced non-quark-antiquark and non-glueball N-c behavior of light scalar mesons

Abstract

We show that the latest and very precise dispersive data analyses require a large and very unnatural finetuning of the 1/N_c expansion at N_c = 3if the f_o(600) and K(800) light scalar mesons are to be considered predominantly q̅q states, which is not needed for light vector mesons. For this, we use scattering observables whose 1/N_c corrections are suppressed further than one power of 1/N_c for q̅q or glueball states, thus enhancing contributions of other nature. This is achieved without using unitarized ChPT, but if it is used we can also show that it is not just that the coefficients of the 1/N_c expansion are unnatural, but that the expansion itself does not even follow the expected 1/N_c scaling of a glueball or a q̅q meson.