Constraints on the low-energy ππ isospin 0 s-wave from elastic π N scattering

Abstract

We show that the behaviour of the reduced πN d-waves close to the physical threshold is very sensitive to the value of the low-energy isospin 0 s-wave ππ phase. The slopes of the d-waves at threshold favour a ππ scattering length a 0 0 ∼ 0.10, the errors being small enough to rule out a scattering length as large as 0.60. We reach similar conclusions by considering a fixed v dispersion relation at v = 0 for the amplitude C (+).