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

Abstract

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. The results also disfavor a very large value of the pseudoscalar decay constant in the chiral limit, which was found by some recent works. In addition, we present results of a combined analysis including $\eta \to 3\pi$ decays and $\pi \pi$ scattering and though the picture does not changed appreciably, we find some tension between the data we use. We also try to extract information on the mass difference of the light quarks, but the uncertainties prove to be large.

23 pages, 8 figures

References in corpus (9)

• Mesonic low-energy constants
• $\eta \to 3\pi$ at Two Loops In Chiral Perturbation Theory
• Lattice simulations with eight flavors of domain wall fermions in SU(3) gauge theory
• The decay $\eta \to 3\pi$: study of the Dalitz plot and extraction of the quark mass ratio $Q$
• Measurement of the Matrix Elements for the Decays $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ and $\eta /{\eta }^{\prime }\to {\pi }^0{\pi }^0{\pi }^0$
• Three-body final state interaction in $\eta \to 3\pi$ updated
• Dispersive Approach to Chiral Perturbation Theory
• Low-energy pi-pi and pi-K scatterings revisited in three-flavour resummed chiral perturbation theory
• Convergence properties of $\eta \to 3\pi$ decays in chiral perturbation theory

Cited by in corpus (4)

• ${\eta }^{\prime }\to \eta \pi \pi$ decays in unitarized resonance chiral theory
• Dispersive construction of two-loop $P\to \pi \pi \pi$ $(P=K,\eta )$ amplitudes
• Chiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation
• Subthreshold parameters of $\pi \pi$ scattering revisited