Abstract
A new method of stochastically estimating the low-lying effects of quark propagation is proposed which allows accurate determinations of temporal correlations of single-hadron and multihadron operators in lattice QCD. The method is well suited for calculations in large volumes. Contributions involving quark propagation connecting hadron sink operators at the same final time can be handled in a straightforward manner, even for a large number of final time slices. The method exploits Laplacian Heaviside (LapH) smearing. ${Z}_{N}$ noise is introduced in a novel way, and variance reduction is achieved using judiciously-chosen noise-dilution projectors. The method is tested using isoscalar mesons in the scalar, pseudoscalar, and vector channels, and using the two-pion system of total isospin $I=0$, 1, 2 on large anisotropic ${24}^{3}\ifmmode\times\else\texttimes\fi{}128$ lattices with spatial spacing ${a}_{s}\ensuremath{\sim}0.12\text{ }\text{ }\mathrm{fm}$ and temporal spacing ${a}_{t}\ensuremath{\sim}0.034\text{ }\text{ }\mathrm{fm}$ for pion masses ${m}_{\ensuremath{\pi}}\ensuremath{\approx}390$ and 240 MeV.
Highlights
N mesons in the scalar, pseudoscalar, and vector channels, and using the two-pion system of total isospin I = 0, 1, 2 on large anisotropic 243 × 128 lattices with spatial spacing as ∼ 0.12 fm and temporal spacing at ∼ 0.034 fm for pion masses mπ ≈ 390 and 240 MeV
We focus on the problem of incorporating multi-hadron operators into finite-volume excitedstate spectrum calculations in lattice quantum chromodynamics (QCD)
Keep in mind that the number of Laplacian eigenvectors needed doubles in going from the smaller to the larger volume. These results show that once a sufficient number of dilution projectors are used, the number of inversions required by the stochastic Laplacian Heaviside (LapH) method does not increase with the lattice volume and are sufficient to essentially reach the gauge noise limit
Summary
The use of smeared fields is crucial for successfully extracting the spectrum of QCD in our Monte Carlo computations. Keep in mind that the number of Laplacian eigenvectors needed doubles in going from the smaller to the larger volume These results show that once a sufficient number of dilution projectors are used, the number of inversions required by the stochastic LapH method does not increase with the lattice volume and are sufficient to essentially reach the gauge noise limit. Different dilution schemes were explored using 163, 203, and 243 spatial lattices with spacing as ∼ 0.12 fm and light quark masses yielding pion masses ranging from 240 MeV to 500 MeV, and we have found that the scheme (TF, SF, LI8) produces variances near that of the gauge noise limit for correlators which involve only quark lines that connect the source and sink time slices.
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