Pi pi scattering lengths at O(p6): resonance estimates
Abstract
In a previous paper, some deviations were found in the O(p6) low-energy constants that contribute to the pi pi-scattering lengths. This work completes the study of all the relevant couplings (r1, ... r6, rS2). 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 aIJ. 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 aIJ 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(p6) contributions to the scattering lengths point out the limitation on further improvements unless the precision of the O(p6) low-energy couplings is properly increased.