Pi pi scattering lengths at O(p⁶): resonance estimates

In a previous paper, some deviations were found in the O(p^6) low-energy constants that contribute to the pi pi-scattering lengths. This work completes the study of all the relevant couplings (r_1, ... r_6, r_S2). We also perform a reanalysis of the hadronical inputs used for the estimation (resonance masses, widths...), checking the impact of the input uncertainties on the determinations of the chiral couplings and the scattering lengths a^I_J. A good agreement is found with respect to former works, though our detailed analysis produces a more solid estimate of these couplings and slightly larger errors. The effect in the final values of the a^I_J is negligible after combining them with the other uncertainties, being the previous scattering length determinations sound and reliable. Nevertheless, the uncertainties derived here for the O(p^6) contributions to the scattering lengths point out the limitation on further improvements unless the precision of the O(p^6) low-energy couplings is properly increased.