Constraints on 3-flavor QCD order parameters and light quark mass difference from η → 3pi decays

The η → 3pi decays are a valuable source of information on low energy QCD. Yet they were not used for an extrac-tion of the 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, as well as the mass difference of light quarks. We compare our results with recent χPT and lattice QCD fits and find some tension, as the η → 3pi data seem to prefer a larger ratio of the chiral order parameters. The results also seem to exclude a large value of the chiral decay constant, which was found by some recent works. Spontaneous breaking of chiral symmetry (SBχS) is a prominent feature of the QCD vacuum and thus its char-acter has been under discussion for a long time [1, 2]. The principal order parameters are the quark conden-sate and the pseudoscalar decay constant in the chiral limit Σ(N f) = − 〈 0 | q̄q | 0 〉 |mq→0, (1) F(N f) = FaP |mq→0, ipµ FaP = 〈 0 | Aaµ | P 〉, (2) where N f is the number of quark flavors q considered light, mq collectively denotes their masses. Aaµ are the QCD axial vector currents, FaP the decay constants of the light pseudoscalar mesons P. Chiral perturbation theory (χPT) [3–5] is constructed as a general low energy parameterization of QCD based on its symmetries and the discussed order parameters appear at the lowest order of the chiral expansion as low energy constants (LECs). Interactions of the light pseu-doscalar meson octet, the pseudo-Goldstone bosons of the broken symmetry, directly depend on the pattern of SBχS and thus can provide information about the values of these observables. A convenient reparameterization of the order parame-ters, relating them to physical quantities connected with pion two point Green functions, can be introduced [1] Z(N f) = F(N f)