The I = 1 p-wave and I = 2 s-wave elastic π-π scattering amplitudes are calculated from a first-principles lattice QCD simulation using a single ensemble of gauge field configurations with N f = 2 + 1 dynamical flavors of anisotropic clover-improved Wilson fermions. This ensemble has a large spatial volume V = (3.7fm) 3 , pion mass m π = 230MeV, and spatial lattice spacing a s = 0.11fm. Calculation of the necessary temporal correlation matrices is efficiently performed using the stochastic LapH method, while the large volume enables an improved energy resolution compared to previous work. For this single ensemble we obtain m ρ /m π = 3.350(24), g ρππ = 5.99(26), and a clear signal for the I = 2 s-wave. The success of the stochastic LapH method in this proof-of-principle large-volume calculation paves the way for quantitative study of the lattice spacing effects and quark mass dependence of scattering amplitudes using state-of-the-art ensembles.
We calculate charmonium correlators on the lattice with 2+1-flavors of sea quarks and charm valence quark both described by the Möbius domain-wall fermion. Temporal moments of the correlators are calculated and matched to perturbative QCD formulae to extract the charm quark mass m c (µ) and strong coupling constant α s (µ). Lattice data at three lattice spacings, 0.044, 0.055, and 0.080 fm, are extrapolated to the continuum limit. The correlators in the vector channel are confirmed to be consistent with the experimental data for e + e − → cc, while the pseudo-scalar channel is used to extract m c (µ) and α s (µ). We obtain m c (3 GeV) = 1.003(10) GeV and α MS(4) s (3 GeV) = 0.253(13). Dominant source of the error is the truncation of perturbative expansion at α 3
Multi-hadron operators are crucial for reliably extracting the masses of excited states lying above multi-hadron thresholds in lattice QCD Monte Carlo calculations. The construction of multi-hadron operators with significant coupling to the lowest-lying multi-hadron states of interest involves combining single hadron operators of various momenta. The design and implementation of large sets of spatially-extended single-hadron operators of definite momentum and their combinations into two-hadron operators are described. The single hadron operators are all assemblages of gaugecovariantly-displaced, smeared quark fields. Group-theoretical projections onto the irreducible representations of the symmetry group of a cubic spatial lattice are used in all isospin channels. Tests of these operators on 24 3 × 128 and 32 3 × 256 anisotropic lattices using a stochastic method of treating the low-lying modes of quark propagation which exploits Laplacian Heaviside quark-field smearing are presented. The method provides reliable estimates of all needed correlations, even those that are particularly difficult to compute, such as ηη → ηη in the scalar channel, which involves the subtraction of a large vacuum expectation value. A new glueball operator is introduced, and the evaluation of the mixing of this glueball operator with a quark-antiquark operator, ππ, and ηη operators is shown to be feasible.
We determine the renormalization constants for flavor non-singlet fermion bilinear operators of Möbius domain-wall fermions. The renormalization condition is imposed on the correlation functions in the coordinate space, such that the non-perturbative lattice calculation reproduces the perturbatively calculated counterpart at short distances. The perturbative expansion is precise as the coefficients are available up to O(α 4 s ). We employ 2 + 1-flavor lattice ensembles at three lattice spacings in the range 0.044-0.080 fm. * tomii@post.kek.jp
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