Quark mass dependence of pseudoscalar masses and decay constants on a lattice

TL;DR

This study investigates how pseudoscalar meson masses and decay constants depend on quark masses using lattice QCD, confirming NLO ChPT predictions and highlighting the need for NNLO terms in valence quark analysis.

Contribution

The paper extends previous lattice QCD calculations with a larger lattice, providing improved data on quark mass dependence and confirming the applicability of NLO and NNLO ChPT in this context.

Findings

Sea quark mass dependence matches NLO ChPT with chiral logs.

Valence quark dependence requires NNLO contributions.

Lattice artifacts are minimal.

Abstract

Our previous calculations of the sea- and valence-quark mass dependence of the pseudoscalar meson masses and decay constants is repeated on a 16^3x32 lattice which allows for a better determination of the quantities in question. The conclusions are similar as before on the 16^4 lattice [1]. The two light dynamical quark flavours we simulate have masses in the range 1/4 m_s < m_{u,d} < 2/3 m_s. The sea quark mass dependence of f_pi and m_pi^2/m_q is well described by the next-to-leading order (NLO) Chiral Perturbation Theory (ChPT) formulas and clearly shows the presence of chiral logarithms. The valence quark mass dependence requires the presence of NNLO contributions in Partially Quenched ChPT (PQChPT) -- in addition to the NLO terms. The O(a) lattice artifacts in these quantities turn out to be small.