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Register a new userLocalization and chiral symmetry in 2+1 flavor domain wall QCD
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We present results for the dependence of the residual mass of domain wall fermions (DWF) on the size of the fifth dimension and its relation to the density and localization properties of low-lying eigenvectors of the corresponding hermitian Wilson Dirac operator relevant to simulations of 2+1 flavor domain wall QCD. Using the DBW2 and Iwasaki gauge actions, we generate ensembles of configurations with a $16^3times 32$ space-time volume and an extent of 8 in the fifth dimension for the sea quarks. We demonstrate the existence of a regime where the degree of locality, the size of chiral symmetry breaking and the rate of topology change can be acceptable for inverse lattice spacings $a^{-1} ge 1.6$ GeV.
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We have simulated QCD using 2+1 flavors of domain wall quarks on a $(2.74 {rm fm})^3$ volume with an inverse lattice scale of $a^{-1} = 1.729(28)$ GeV. The up and down (light) quarks are degenerate in our calculations and we have used four values for the ratio of light quark masses to the strange (heavy) quark mass in our simulations: 0.217, 0.350, 0.617 and 0.884. We have measured pseudoscalar meson masses and decay constants, the kaon bag parameter $B_K$ and vector meson couplings. We have used SU(2) chiral perturbation theory, which assumes only the up and down quark masses are small, and SU(3) chiral perturbation theory to extrapolate to the physical values for the light quark masses. While next-to-leading order formulae from both approaches fit our data for light quarks, we find the higher order corrections for SU(3) very large, making such fits unreliable. We also find that SU(3) does not fit our data when the quark masses are near the physical strange quark mass. Thus, we rely on SU(2) chiral perturbation theory for accurate results. We use the masses of the $Omega$ baryon, and the $pi$ and $K$ mesons to set the lattice scale and determine the quark masses. We then find $f_pi = 124.1(3.6)_{rm stat}(6.9)_{rm syst} {rm MeV}$, $f_K = 149.6(3.6)_{rm stat}(6.3)_{rm syst} {rm MeV}$ and $f_K/f_pi = 1.205(0.018)_{rm stat}(0.062)_{rm syst}$. Using non-perturbative renormalization to relate lattice regularized quark masses to RI-MOM masses, and perturbation theory to relate these to $bar{rm MS}$ we find $ m_{ud}^{bar{rm MS}}(2 {rm GeV}) = 3.72(0.16)_{rm stat}(0.33)_{rm ren}(0.18)_{rm syst} {rm MeV}$ and $m_{s}^{bar{rm MS}}(2 {rm GeV}) = 107.3(4.4)_{rm stat}(9.7)_{rm ren}(4.9)_{rm syst} {rm MeV}$.
Nucleon-structure calculations of isovector vector- and axialvector-current form factors, transversity and scalar charge, and quark momentum and helicity fractions are reported from two recent 2+1-flavor dynamical domain-wall fermions lattice-QCD ensembles generated jointly by the RIKEN-BNL-Columbia and UKQCD Collaborations with Iwasaki $times$ dislocation-suppressing-determinatn-ratio gauge action at inverse lattice spacing of 1.378(7) GeV and pion mass values of 249.4(3) and 172.3(3) MeV.
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 $24^3times 64times 16$ points, the analysis of ref.[1] is extended to approximately twice the number of configurations. The ensembles on the finer $32^3times 64times 16$ 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 $f_pi=124(2)_{rm stat}(5)_{rm syst}$,MeV, $f_K/f_pi=1.204(7)(25)$ where $f_K$ is the kaon decay constant, $m_s^{bar{textrm{MS}}}(2,textrm{GeV})=(96.2pm 2.7)$,MeV and $m_{ud}^{bar{textrm{MS}}}(2,textrm{GeV})=(3.59pm 0.21)$,MeV, ($m_s/m_{ud}=26.8pm 1.4$) where $m_s$ and $m_{ud}$ are the mass of the strange-quark and the average of the up and down quark masses respectively, $[Sigma^{msbar}(2 {rm GeV})]^{1/3} = 256(6); {rm MeV}$, where $Sigma$ is the chiral condensate, the Sommer scale $r_0=0.487(9)$,fm and $r_1=0.333(9)$,fm.
We present results for the nucleon axial charge g_A at a fixed lattice spacing of 1/a=1.73(3) GeV using 2+1 flavors of domain wall fermions on size 16^3x32 and 24^3x64lattices (L=1.8 and 2.7 fm) with length 16 in the fifth dimension. The length of the Monte Carlo trajectory at the lightest m_pi is 7360 units, including 900 for thermalization. We find finite volume effects are larger than the pion mass dependence at m_pi= 330 MeV. We also find that g_A exhibits a scaling with the single variable m_pi L which can also be seen in previous two-flavor domain wall and Wilson fermion calculati ons. Using this scaling to eliminate the finite-volume effect, we obtain g_A = 1.20(6)(4) at the physical pion mass, m_pi = 135 MeV, where the first and second errors are statistical and systematic. The observed finite-volume scaling also appears in similar quenched simulations, but disappear when Vge (2.4 fm)^3. We argue this is a dynamical quark effect.
We present a study of chiral behavior of light meson form factors in QCD with three flavors of overlap quarks. Gauge ensembles are generated at single lattice spacing 0.12 fm with pion masses down to 300 MeV. The pion and kaon electromagnetic form factors and the kaon semileptonic form factors are precisely calculated using the all-to-all quark propagator. We discuss their chiral behavior using the next-to-next-to-leading order chiral perturbation theory.
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