Continuum Limit Physics from 2+1 Flavor Domain Wall QCD

Abstract

We present physical results obtained from simulations using 2+1 flavors of domain wall quarks and the Iwasaki gauge action at two values of the lattice spacing $a$, ($a^{-1}$=\,1.73\,(3)\,GeV and $a^{-1}$=\,2.28\,(3)\,GeV). On the coarser lattice, with $24^3\times 64\times 16$ points, the analysis of ref.[1] is extended to approximately twice the number of configurations. The ensembles on the finer $32^3\times 64\times 16$ lattice are new. We explain how we use lattice data obtained at several values of the lattice spacing and for a range of quark masses in combined continuum-chiral fits in order to obtain results in the continuum limit and at physical quark masses. We implement this procedure at two lattice spacings, with unitary pion masses in the approximate range 290--420\,MeV (225--420\,MeV for partially quenched pions). We use the masses of the $\pi$ and $K$ mesons and the $\Omega$ baryon to determine the physical quark masses and the values of the lattice spacing. While our data are consistent with the predictions of NLO SU(2) chiral perturbation theory, they are also consistent with a simple analytic ansatz leading to an inherent uncertainty in how best to perform the chiral extrapolation that we are reluctant to reduce with model-dependent assumptions about higher order corrections. Our main results include $f_{\pi }=124(2{)}_{\mathrm{stat}}(5{)}_{\mathrm{syst}}$\,MeV, $f_K/f_{\pi }=1.204(7)(25)$ where $f_K$ is the kaon decay constant, $m_s^{\overline{\text{MS}}}(2\text{GeV})=(96.2\pm 2.7)$\,MeV and $m_{ud}^{\overline{\text{MS}}}(2\text{GeV})=(3.59\pm 0.21)$\,MeV\, ($m_s/m_{ud}=26.8\pm 1.4$) where $m_s$ and $m_{ud}$ are the mass of the strange-quark and the average of the up and down quark masses respectively, $[Σ^{\msbar}(2 {\rm GeV})]^{1/3} = 256(6)\; {\rm MeV}$, where $\Sigma$ is the chiral condensate, the Sommer scale $r_0=0.487(9)$\,fm and $r_1=0.333(9)$\,fm.

129 pages, 59 figures, Published version containing an extended discussion of reweighting and including a new appendix (Appendix C)

References in corpus (11)

• Ab-initio Determination of Light Hadron Masses
• Non-perturbative renormalization of quark bilinear operators and B_K using domain wall fermions
• Reweighting towards the chiral limit
• Kl3 semileptonic form factor from 2+1 flavour lattice QCD
• Neutral kaon mixing from 2+1 flavor Domain Wall QCD
• Proton lifetime bounds from chirally symmetric lattice QCD
• Two-loop matching factors for light quark masses and three-loop mass anomalous dimensions in the RI/SMOM schemes
• Localization and chiral symmetry in 2+1 flavor domain wall QCD
• K->pi form factors with reduced model dependence
• Precise MS-bar light-quark masses from lattice QCD in the RI/SMOM scheme
• First results from 2+1-Flavor Domain Wall QCD: Mass Spectrum, Topology Change and Chiral Symmetry with $L_s=8$

Cited by in corpus (6)

• Lattice QCD at the physical point: light quark masses
• Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD
• Step Scaling with off-shell renormalisation
• Matching factors for Delta S=1 four-quark operators in RI/SMOM schemes
• Progress in Lattice QCD Relevant for Flavor Physics
• Light Meson Distribution Amplitudes