Determination of Low Energy Constants and testing Chiral Perturbation Theory at Next to Next to Leading Order

TL;DR

This paper investigates relations between physical observables in meson scattering and decay processes that are independent of NNLO low-energy constants in Chiral Perturbation Theory, testing its predictive power.

Contribution

It identifies observable relations independent of NNLO LECs and evaluates their numerical validity using previous NLO fits, advancing ChPT testing.

Findings

Discovered relations between $bla\u00f1etaeta$ scattering and decay observables.

Numerical evaluation confirms some relations are consistent with existing fits.

Provides a basis for testing ChPT without dependence on NNLO LECs.

Abstract

We present the results of a search for relations between observables that are independent of the Chiral Pertubation Theory (ChPT) Next-to-Next-to-Leading Order (NNLO) Low-Energy Constants (LECs). We have found some relations between observables in $\pi\pi$, $\pi K$ scattering and $K_{l4}$ decay which have been evaluated numerically using the old fit (fit 10 in [1] of the NLO LECs.