Machine learning unveils the quark mass dependence of the pseudoscalar meson decay constants in three-flavour N$^2$LO ChPT
The quark mass dependence of the pseudoscalar meson decay consntants, $f_π, f_K$ and $f_η$, are determined from three-flavor N$^2$LO ChPT till pion masses around $780$ MeV, near the SU(3) limit. This is done by conducting an analysis of recent LQCD data using the LASSO method, a machine-learning technique which allows to pin down the relevant low-energy-constants with high precision. Since the pion decay constant is a fundamental quantity which usually appears in relevant phenomenological lagrangians or Effective Field Theories based on QCD at low energies, this analysis can be used as input to evaluate the quark mass dependence of hadronic states. As an example, we predict the masses of the octect baryons in the SU(3) limit within covariant Baryon Chiral Perturbation Theory.