QCD with light Wilson quarks on fine lattices (I): first experiences and physics results

Abstract

Recent conceptual, algorithmic and technical advances allow numerical simulations of lattice QCD with Wilson quarks to be performed at significantly smaller quark masses than was possible before. Here we report on simulations of two-flavour QCD at sea-quark masses from slightly above to approximately 1/4 of the strange-quark mass, on lattices with up to 64×32 3 points and spacings from 0.05 to 0.08 fm. Physical sea-quark effects are clearly seen on these lattices, while the lattice effects appear to be quite small, even without O(a) improvement. A striking result is that the dependence of the pion mass on the sea-quark mass is accurately described by leading-order chiral perturbation theory up to meson masses of about 500 MeV. † Our notation and normalization conventions coincide with those of ref. [17]. As usual we quote the values of β = 6/g 2 0 and κ = 8 + 2m 0 instead of the bare coupling g 0 and sea-quark mass m 0 .

Determination of low-energy constants of Wilson chiral perturbation theory

“…The statistical error in M π 0 is dominated by the contribution of disconnected diagrams. 2 We observe that the precise form of the light-quark mass dependence of the mass-splittings related to W 6 and c 2 -see e.g. figures 1(b) and 2(b) -cannot be addressed within the present uncertainties.…”

“…Lattice QCD simulations employing a discretisation of the Dirac operator based on the original proposal by Wilson [1] are currently being performed with light dynamical fermions [2][3][4][5][6][7][8][9]. When decreasing the light quark mass at a fixed value of the lattice spacing, a subtle interplay between mass and discretisation effects can take place due to the explicit breaking of chiral symmetry by the Wilson term.…”

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

“…3 It is clear that the variance reduction is much more effective for the sectors with lower topological charge, which are dominated by infrared contributions. Nevertheless with LMA we still obtain a variance reduction of a factor ∼ 2 up to ν = 5 in all our runs.…”

Low energy constants ofχPTfrom the instanton vacuum model

“…Using our results (69, 86), we can obtain (m is given in GeV ) (118) were taken as input when we fixed the parameters ρ, R in (4). Our values of (l 3 ,l 4 ) should be compared with the phenomenological estimates [22,23] as well as lattice predictions [38,39] given in Table I. …”

“…al. [39] [42] prediction l3 2.9 ± 2.4 0.6 ± 1.2 3.0 ± 0.5 3.62 ± 0.12 1.84 l4 4.4 ± 0.2 3.9 ± 0.5 -4.52 ± 0.06 4.98 Γ ef f . First of all, we should notice that we are making not just a chiral expansion, but a double expansion over the 1/N c in large-N c limit and the chiral expansion over the quark mass m. We must take this fact into account when checking the theorems-we should keep only LO and the NLO corrections.…”