Large [Formula Presented] and chiral dynamics

We study the dependence on the number of colors of the leading [Formula Presented] scattering amplitude in chiral dynamics. We demonstrate the existence of a critical number of colors for and above which the low energy [Formula Presented] scattering amplitude computed from the simple sum of the current algebra and vector meson terms is crossing symmetric and unitary at leading order in a truncated and regularized [Formula Presented] expansion. The critical number of colors turns out to be [Formula Presented] and is insensitive to the explicit breaking of chiral symmetry. Below this critical value, an additional state is needed to enforce the unitarity bound; it is a broad one, most likely of a “four quark” nature. © 2004 The American Physical Society.