Constraints on low energy QCD parameters from $\eta \to 3\pi$ and $\pi\pi$ scattering

Understand

The $\eta \to 3\pi$ decays are a valuable source of information on low energy QCD.

• Yet they were not used for an extraction of the three flavor chiral symmetry breaking order parameters until now.
• We use a Bayesian approach in the framework of resummed chiral perturbation theory to obtain constraints on the quark condensate and pseudoscalar decay constant in the chiral limit.
• We compare our results with recent CHPT and lattice QCD fits and find some tension, as the $\eta \to 3\pi$ data seem to prefer a larger ratio of the chiral order parameters.