Pi pi scattering lengths at O(p^6) revisited

TL;DR

This paper revisits pi pi scattering lengths at order p^6, correcting previous calculations by including missed resonance contributions, reanalyzing inputs, and confirming the robustness of earlier results with slightly larger uncertainties.

Contribution

It provides complete results for all O(p^6) couplings in pi pi scattering and reassesses the impact of resonance inputs and uncertainties on scattering length determinations.

Findings

Results agree with previous studies but with larger errors.

The effect of uncertainties on scattering lengths is negligible.

Previous determinations of scattering lengths are reliable and well-understood.

Abstract

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.