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

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 $6.4M_{\pi }^{-1}$ to $3.3M_{\pi }^{-1}$, where $L{M}_{\pi }\ge 4$ 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 $F/D=0.612_{(12)}^{(14)}$.

17 pages, 12 figures, minor typos corrected, references added, 2 figures updated