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
No abstract
We report on progress applying the stochastic LapH method to estimate all-to-all propagators required in correlation functions of multi-hadron operators relevant for pion-pion scattering. Largevolume results for I = 2 and I = 1 pion-pion scattering phase shifts with good statistical precision are obtained from an N f = 2 + 1 anisotropic Wilson clover ensemble with m π = 240MeV. We also present a preliminary determination of the I = 1 pion-pion scattering phase shift and timelike pion form factor on an isotropic N f = 2 + 1 flavour ensemble generated by the Coordinated Lattice Simulation (CLS) community effort.Pion-pion scattering and the timelike pion form factor Lattice QCD simulations are inevitably carried out in finite volume and euclidean time, which complicates scattering calculations [1]. Since most excited hadrons are unstable resonances which appear experimentally as features in scattering cross sections, first-principles calculation of hadronhadron scattering amplitudes is desirable. The relation between finite-volume two-hadron spectra and infinite-volume elastic scattering amplitudes was formulated by Lüscher [2, 3] more than two decades ago and extended to moving frames in Ref. [4]. However, only recently have algorithmic advances in lattice QCD spectroscopy enabled finite-volume spectra to be calculated efficiently in large volume with light pion masses.These advances concern the treatment of all-to-all propagators, which are required to give definite momenta to all hadrons and to treat valence-quark-line-disconnected Wick contractions. Laplacian-Heaviside (LapH) quark smearing projects the quark propagator onto the subspace spanned by the lowest-lying N v eigenmodes of the three-dimensional covariant Laplace operator [5]. Stochastic noise introduced only in the LapH subspace results in more efficient estimators for allto-all quark propagators compared to noise on the entire lattice [6].The spatial profile of the LapH subspace projector is approximately Gaussian, as with other quark smearing procedures. In order to maintain a constant physical smearing radius, N v must increase proportionally to the spatial volume. However, in Ref. [6] it was demonstrated that with a moderate amount of dilution in the LapH subspace, the number of quark matrix inversions can be held constant as the spatial volume is increased without increasing the stochastic estimation error relative to the gauge noise. This enables all-to-all quark propagators to be estimated efficiently in large spatial volumes for a reasonable cost.The efficient treatment of all-to-all quark propagators in turn enables precision calculation of correlation functions containing multi-hadron interpolating operators with definite momenta and/or disconnected Wick contractions. From these correlation functions, finite-volume energies can be precisely extracted, which then yield elastic scattering amplitudes. The application of these techniques to extract elastic pion-pion scattering amplitudes from large volume ensembles is the subject of this work. Se...
We report results of masses and decay constants of light and charmed pseudo-scalar mesons using lattice QCD with Möbius domain-wall fermions. Using this formulation we are able to compute pseudo-scalar decay constants through the pseudo-scalar density operator as well as with the axial-vector current. Results are shown from several lattice spacings and pion masses between 230 MeV and 500 MeV. We present an analysis of these results at different quark masses to show the chiral properties of the light mesons masses and decay constants.
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