Yang-Mills Fields and theππInteraction

Abstract

Starting from a Lagrangian where the $\rho$ meson is treated as a Yang-Mills field, we calculate $\pi \pi$ scattering amplitudes in the one-loop approximation. The summation of the strong-coupling perturbation series is performed with a unitary-rational-function approximation, and the $\rho$ appears as a true resonance. We show that the interaction generates the $d$-wave $f_0$ resonance, and a very broad $s$-wave $\sigma$ resonance. The model yields a version of the Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation, which agrees very well with experiment, and our $s$-wave amplitudes are close to the current-algebra predictions. We draw some conclusions on $\pi \pi$ dynamics.