Constraints on 3-flavor QCD order parameters from eta to pi+pi-pi0 decay width

TL;DR

This paper uses statistical analysis of eta decay data within resummed chiral perturbation theory to constrain three-flavor QCD order parameters, including the quark condensate and decay constant, and explores the isospin violating parameter R.

Contribution

It introduces a novel approach combining statistical methods with resummed chiral perturbation theory to better constrain QCD order parameters from eta decay data.

Findings

Constraints on quark condensate and decay constant in the three-flavor case.

Estimates of the isospin violating parameter R from decay data.

Insights into the difference between u and d quark masses.

Abstract

Quark condensate and pseudoscalar decay constant in the chiral limit are the principal order parameters of spontaneous chiral symmetry breaking in QCD. Yet their three flavor values are still only weakly constrained by analyses using experimental data. We try to obtain such constraints by statistical methods from the decay width of the eta to pi+pi-pi0 decay in the framework of resummed chiral perturbation theory. We rely on recent estimates of the isospin violating parameter R, which is proportional to the difference of the u and d quark masses. Alternatively, we relax the assumption and try to extract information on R as well.