pi pi, K pi, and pi N potential scattering and a prediction of a narrow sigma meson resonance

Low energy scattering and bound state properties of the pi N, pi pi, and K pi systems are studied as coupled channel problems using inversion potentials of phase shift data. In a first step we apply the potential model to explain recent measurements of pionic hydrogen shift and width. Second, predictions of the model for the pionium lifetime and shift confirm a well-known and widely used effective range expression. Third, as an extension of this confirmation, we predict an unexpected medium effect of the pionium lifetime which shortens by several orders of magnitude. The sigma meson shows a narrow resonance structure as a function of the medium-modified mass with the implication of being essentially energy independent. Similarly, we see this medium resonance effect realized for the K pi system. To support our findings we present also results for the rho meson and the Delta(1232) resonance.