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Register a new userChiral perturbation theory for lattice QCD including O(a^2)
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The O(a^2) contributions to the chiral effective Lagrangian for lattice QCD with Wilson fermions are constructed. The results are generalized to partially quenched QCD with Wilson fermions as well as to the mixed lattice theory with Wilson sea quarks and Ginsparg-Wilson valence quarks.
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We apply chiral perturbation theory to the pseudoscalar meson mass and decay constant data obtained in the PACS-CS Project toward 2+1 flavor lattice QCD simulations with the O(a)-improved Wilson quarks. We examine the existence of chiral logarithms in the quark mass range from m_{ud}=47 MeV down to 6 MeV on a (2.8 fm)^3 box with the lattice spacing a=0.09 fm. Several low energy constants are determined. We also discuss the magnitude of finite size effects based on chiral perturbation theory.
We perform a detailed, fully-correlated study of the chiral behavior of the pion mass and decay constant, based on 2+1 flavor lattice QCD simulations. These calculations are implemented using tree-level, O(a)-improved Wilson fermions, at four values of the lattice spacing down to 0.054 fm and all the way down to below the physical value of the pion mass. They allow a sharp comparison with the predictions of SU(2) chiral perturbation theory (chi PT) and a determination of some of its low energy constants. In particular, we systematically explore the range of applicability of NLO SU(2) chi PT in two different expansions: the first in quark mass (x-expansion), and the second in pion mass (xi-expansion). We find that these expansions begin showing signs of failure around M_pi=300 MeV for the typical percent-level precision of our N_f=2+1 lattice results. We further determine the LO low energy constants (LECs), F=88.0 pm 1.3pm 0.3 and B^msbar(2 GeV)=2.58 pm 0.07 pm 0.02 GeV, and the related quark condensate, Sigma^msbar(2 GeV)=(271pm 4pm 1 MeV)^3, as well as the NLO ones, l_3=2.5 pm 0.5 pm 0.4 and l_4=3.8 pm 0.4 pm 0.2, with fully controlled uncertainties. We also explore the NNLO expansions and the values of NNLO LECs. In addition, we show that the lattice results favor the presence of chiral logarithms. We further demonstrate how the absence of lattice results with pion masses below 200 MeV can lead to misleading results and conclusions. Our calculations allow a fully controlled, ab initio determination of the pion decay constant with a total 1% error, which is in excellent agreement with experiment.
We present a comprehensive study of the electromagnetic form factor, the decay constant and the mass of the pion computed in lattice QCD with two degenerate O(a)-improved Wilson quarks at three different lattice spacings in the range 0.05-0.08fm and pion masses between 280 and 630MeV at m_pi L >~ 4. Using partially twisted boundary conditions and stochastic estimators, we obtain a dense set of precise data points for the form factor at very small momentum transfers, allowing for a model-independent extraction of the charge radius. Chiral Perturbation Theory (ChPT) augmented by terms which model lattice artefacts is then compared to the data. At next-to-leading order the effective theory fails to produce a consistent description of the full set of pion observables but describes the data well when only the decay constant and mass are considered. By contrast, using the next-to-next-to-leading order expressions to perform global fits result in a consistent description of all data. We obtain <r^2_pi>=0.481(33)(13)fm^2 as our final result for the charge radius at the physical point. Our calculation also yields estimates for the pion decay constant in the chiral limit, F_pi/F=1.080(16)(6), the quark condensate, Sigma^{1/3}_MSbar(2GeV)=261(13)(1)MeV and several low-energy constants of SU(2) ChPT.
We investigate the quark mass dependence of meson and baryon masses obtained from 2+1 flavor dynamical quark simulations performed by the PACS-CS Collaboration. With the use of SU(2) and SU(3) chiral perturbation theories up to NLO, we examine the chiral behavior of the pseudoscalar meson masses and the decay constants in terms of the degenerate up-down quark mass ranging form 3 MeV to 24 MeV and two choices of the strange quark mass around the physical value. We discuss the convergence of the SU(2) and SU(3) chiral expansions and present the results for the low energy constants. We find that the SU(3) expansion is not convergent at NLO for the physical strange quark mass. The chiral behavior of the nucleon mass is also discussed based on the SU(2) heavy baryon chiral perturbation theory up to NNLO. Our results show that the expansion is well behaved only up to m_pi^2 ~ 0.2 GeV^2.
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 $m_{s}^{bar{rm MS}}(2 {rm GeV}) = 107.3(4.4)_{rm stat}(9.7)_{rm ren}(4.9)_{rm syst} {rm MeV}$.
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