Rigorous pion-pion scattering lengths from threshold pi N --> pi pi N data

A new evaluation of the universal $\pi \pi$ scattering length relation is used to extract the $\pi \pi$ $s$-wave scattering lengths from threshold pion production data. Previous work has shown that the chiral perturbation series relating threshold pion production to $\pi \pi$ scattering lengths appears to converge well only for the isospin-2 case, giving $a_2 = -0.031\pm 0.007 m_\pi^{-1}$. A model-independent and data-insensitive universal curve then implies $a_0=0.235\pm 0.03m_{\pi }^{-1}$ for the isospin-0 scattering length.