Leading order mesonic and baryonic SU(3) low energy constants from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:math> lattice QCD
Gunnar Bali, Sara Collins, Wolfgang Söldner, Simon Weishäupl
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., ${m}_{u}={m}_{d}={m}_{s}$) nonperturbatively improved Wilson fermions at six distinct values of the lattice spacing in the range $a\ensuremath{\approx}(0.039--0.098)\text{ }\text{ }\mathrm{fm}$, which constitute a subset of the coordinated lattice simulations (CLS) gauge ensembles. The pseudoscalar meson mass ${M}_{\ensuremath{\pi}}$ ranges from around 430 MeV down to 240 MeV and the linear spatial lattice extent $L$ from $6.4{M}_{\ensuremath{\pi}}^{\ensuremath{-}1}$ to $3.3{M}_{\ensuremath{\pi}}^{\ensuremath{-}1}$, where $L{M}_{\ensuremath{\pi}}\ensuremath{\ge}4$ 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 ${B}_{0}\ensuremath{\approx}B$ are similar. Regarding baryonic LECs, we obtain $F/D=0.61{2}_{(12)}^{(14)}$.