ππ–scattering lengths at O(p6) revisited

This article completes a former work where part of the O(p6) low-energy constants entering in the ππ scattering were estimated. Some resonance contributions were missed in former calculations and appreciable differences appeared with respect to our outcome. Here, we provide the full results for all the contributing O(p6) 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 aJ . Our outcome is found in agreement with former works though with slightly larger errors. However, the effect in the final values of the aJ 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 theO(p6) LECs quite under control. Nevertheless, the uncertainties found in the present work point out the limitation on further improvements unless the precision of the O(p6) couplings is properly increased.