Determination of Chiral Perturbarion Theory low energy constants from a precise description of pi-pi scattering threshold parameters

TL;DR

This paper precisely determines the low energy constants in Chiral Perturbation Theory for pi-pi scattering by using sum rules and effective range expansion, providing new coefficients up to third order.

Contribution

It introduces new sum rules and calculates third order coefficients, enhancing the precision of low energy constant determination in Chiral Perturbation Theory.

Findings

Results are consistent with previous determinations using scattering lengths and slopes.

Higher order contributions are necessary to fit third order coefficients.

Provides a more comprehensive set of coefficients for pi-pi scattering analysis.

Abstract

We report on our determination of the values of the one and two loop low energy constants appearing in the Chiral Perturbation Theory calculation of the pi-pi scattering amplitude. For this we use a precise sum rule determination of scattering lengths and slopes that appear in the effective range expansion. In addition we provide new sum rules and the values for these coefficients up to third order in the expansion. Our results when using only the scattering lengths and slopes of the S, P, D and F waves are consistent with previous determinations, but seem to require higher order contributions if they are to accommodate the third order coefficients of the effective range expansion.