Padé Approximant Calculation of p-Wave π–π Scattering with a σ Model Lagrangian

A π–π it interaction via a scalar I = 0, σ exchange is considered. The contribution of the t and u channel exchanges of the σ to the p-wave, I = 1 amplitude is calculated using Padé approximants. A p-wave resonance, interpreted as the p meson, the width of which depends on the mass of the input a meson, is found; for a certain range of values of the σ mass the ρ width compares not unfavorably with similar calculations using a [Formula: see text] interaction. However, for the range of masses considered the width is considerably smaller than the experimental value. The I = 0, d-wave channel is also considered and a resonance, interpreted as the ƒ0(1260), is found.