PADE APPROXIMANTS IN STRONG INTERACTIONS . 2-BODY PION AND KAON SYSTEMS

We construct the Padé approximants to the S-matrix starting from a formal perturbation series. Starting with a first-order «germ» we calculate the higher-order terms by repeatedly applying unitarity and crossing in the Mandelstam representation. The germ is chosen to be compatible with crossing and analyticity requirements, and to lead to a nonincreasing number of subtraction constants. We consider meson-meson scattering in which case the germs are simply constants. We have studied systems involving pions and kaons. In that case, there are only three parameters. Resonances and Regge trajectories have been computed. The seven lowest-lying two-body resonances (ρ, K*(890), φ{symbol}, K*(1420), f0, f 0 ′, A2) are obtained within a few percent of their actual masses. Also, the intercepts of the ρ and f0 trajectories agree very well with present estimates. Some degeneracies between channels with different quantum numbers appear and are discussed. The comparison with a pure π-π calculation shows promising improvement. We explain the further extensions of the model to compute meson states, and also baryon-meson and baryon-baryon amplitudes. In the course of this work, we have studied many mathematical and practical aspects of Padé approximants and their application to various fields. © 1969 Società Italiana di Fisica.