Leading order mesonic and baryonic SU(3) low energy constants from $N_f = 3$ lattice QCD

TL;DR

This paper determines key low energy constants of SU(3) chiral perturbation theory from lattice QCD simulations with three degenerate quark flavors, providing controlled extrapolations to physical limits.

Contribution

It provides the first comprehensive lattice QCD determination of both mesonic and baryonic SU(3) low energy constants with controlled systematic uncertainties.

Findings

SU(3) chiral condensate smaller than SU(2)

F_0 smaller than F_pi

F/D ratio approximately 0.612

Abstract

We determine the leading order mesonic~($B_0$ and $F_0$) and baryonic~($m_0$, $D$ and $F$) SU(3) chiral perturbation theory low energy constants from lattice QCD. We employ gauge ensembles with $N_f=3$ (i.e., $m_u=m_d=m_s$) non-perturbatively improved Wilson fermions at six distinct values of the lattice spacing in the range $a\approx (0.039 - 0.098)$ fm, which constitute a subset of the Coordinated Lattice Simulations (CLS) gauge ensembles. The pseudoscalar meson mass $M_\pi$ ranges from around $430$ MeV down to $240$ MeV and the linear spatial lattice extent $L$ from $6.4\,M_{\pi}^{-1}$ to $3.3\,M_{\pi}^{-1}$, where $ L M_\pi \geq 4$ for the majority of the ensembles. This allows us to perform a controlled extrapolation of all the low energy constants to the chiral, infinite volume and continuum limits. We find the SU(3) chiral condensate and $F_0$ to be smaller than their SU(2) counterparts while the Gell-Mann--Oakes--Renner parameters $B_0\approx B$ are similar. Regarding baryonic LECs, we obtain $F/D = 0.612^{(14)}_{(12)}$.