Padé and K-matrix approximations to the O(2N) model for large N

The Padé approximation and the K matrix are techniques for constructing perturbative amplitudes which satisfy two-body unitarity exactly. We apply these approximations to the Goldstone-boson scattering amplitude in a spontaneously broken O(2N) model, in the large-N limit, and compare with the exact amplitude (to leading order in 1N). The [r, r] Padé approximation reproduces the exact large-N amplitude for all r. The K matrix, at any finite order, yields an amplitude which is qualitatively similar to, but not identical to, the exact amplitude.