Pi pi scattering lengths at O(p⁶) revisited

This article completes a former work where part of the O(p^6) low-energy constants entering in the pi pi scattering were estimated. Some resonance contributions were missed in former calculations and slight differences appeared with respect to our outcome. Here, we provide the full results for all the contributing O(p^6) couplings. We also perform a reanalysis of the hadronic inputs used for the estimation (resonance masses, widths...). Their reliability was checked together with the impact of the input uncertainties on the determinations of the chiral couplings and the scattering lengths a^I_J. Our outcome is found in agreement with former works though with slightly larger errors. However, the effect in the final values of the a^I_J is negligible after combining them with the other uncertainties. Based on this consistency, we conclude that the previous scattering length determinations seem to be rather solid and reliable, with the cO(p^6) low-energy constants quite under control. Nevertheless, the uncertainties found in the present work point out the limitation on further improvements unless the precision of the O(p^6) couplings is properly increased.