Pi pi scattering lengths at O(p^6): resonance estimates

TL;DR

This paper refines the estimates of pi pi scattering lengths at order p^6 by completing the analysis of relevant couplings, reanalyzing inputs, and assessing uncertainties, confirming previous results with improved reliability.

Contribution

It provides a comprehensive and more precise estimation of O(p^6) low-energy constants and their impact on pi pi scattering lengths, including uncertainty analysis and resonance input reanalysis.

Findings

Good agreement with previous estimates

More solid and slightly larger error bounds

Uncertainties limit further precision improvements

Abstract

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.