ππ, Kπand πN potential scattering and a prediction of a narrow σmeson resonance

Abstract

Low energy scattering and bound state properties of the πN, ππand Kπsystems 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. Secondly, predictions of the model for pionium lifetime and shift confirm a well known and widely used effective range expression. Thirdly, as extension of this confirmation, we predict an unexpected medium effect of the pionium lifetime which shortens by several orders of magnitude. The σmeson 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 Kπsystem. To support our findings we present also results for the ρmeson and the Δ(1232) resonance.