Rigorous pion-pion scattering lengths from threshold πN → ππN data

A new evaluation of the universal ππ scattering length relation is used to extract the ππ s-wave scattering lengths from threshold pion production data. Previous work has shown that the chiral perturbation series relating threshold pion production to ππ scattering lengths appears to converge well only for the isospin-2 case, giving a₂ = −0.031 ± 0.007m_π⁻¹. A model-independent and data-insensitive universal curve then implies a₀ = 0.235 ± 0.03m_π⁻¹ for the isospin-0 scattering length.