On pion and kaon decay constants and chiral SU(3) extrapolations

TL;DR

This paper investigates how pion and kaon decay constants depend on quark masses in QCD, emphasizing the role of vector mesons and using lattice data to accurately reproduce decay constants across different ensembles.

Contribution

It introduces an effective chiral Lagrangian including vector mesons and demonstrates its ability to match lattice QCD decay constants at unphysical quark masses.

Findings

Accurate reproduction of decay constants across multiple lattice ensembles.

Insights into vector meson masses and mixing angles.

Determination of quark mass ratios from lattice data.

Abstract

We consider the dependence of the pion and kaon decay constants on the up, down and strange quark masses in QCD with strict isospin symmetry. The role of dynamical vector meson degrees of freedom is scrutinized in terms of an effective chiral Lagrangian for vector mesons. Applying a set of low-energy parameters as determined previously from QCD lattice data on the masses of the light vector mesons from PACS-CS, QCDSF-UKQCD and HSC we compute its implications on the pion and kaon decay constants for QCD lattice ensembles of HPQCD, CLS and ETMC. It is shown that with Gasser-Leutwyler L_4 and L_5 parameters fixed to the empirical decay constants an accurate reproduction of their values at unphysical quark masses as computed by HPQCD, CLS and ETMC is achieved. Results for the masses of the light vector meson, the \omega -\phi mixing angles and the quark mass ratios for the ensembles used by HPQCD, CLS and ETMC are discussed.