Fast Fits for Lattice QCD Correlators

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• G. P. Lepage, B. Clark, C. T. H. Davies, K. Hornbostel, P. B. Mackenzie, C. Morningstar, H. Trottier, Nucl. Phys. Proc. Suppl. 106

  2002

  Earlier work this paper cites.

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• For a proof, see the appendix of C. McNeile, C. T. H. Davies, E. Follana, K. Hornbostel, G. P. Lepage, Phys. Rev. D82

  Original

  2010

  Cited alongside, same era.

• Lattice QCD simulations use Euclidean time and so − i ​ t -it is replaced by − t -t in the exponentials. Also simulations are for finite volumes in space, and therefore all states, including multi-hadron states, have discrete energy eigenvalues

  Cited in the paper.

• Again the covariance matrix for Δ ​ G a ​ b ​ ( t , n ) \Delta G_{ab}(t;n) is computed using standard error propagation — for example, f ⁡ ( x ¯ ± σ x ) = f ¯ ± σ f f(\overline{x}\pm\sigma_{x})\!=\!\overline{f}\pm\sigma_{f} with f ¯ ≈ f ⁡ ( x ¯ ) \overline{f}\!\approx\!f(\overline{x}) and σ f 2 ≈ f ′ ​ ( x ¯ ) 2 ​ σ x 2 \sigma^{2}_{f}\!\approx\!f^{\prime}(\overline{x})^{2}\sigma_{x}^{2} . We have compared this linearized analysis with Monte Carlo evaluations of Δ ​ G \Delta G (from normal distributions for the priors). We find the Monte Carlo results to be both much more expensive and also less robust for correlators that decay exponentially quickly. Note also that it is essential to retain the off-diagonal elements (correlations) in the covariance matrix for Δ ​ G a ​ b ​ ( t , n ) \Delta G_{ab}(t;n) ; correlations arise because, for example, the prior data used for a parameter is the same for all t t values

  Cited in the paper.

• The simulations used 0.09 fm lattices with n f = 4 n_{f}\!=\!4 sea quarks (HISQ discretization), and NRQCD dynamics for the b b quark. The gluon configurations were provided by the MILC collaboration. For further details see: R. J. Dowdall, et al

  Original

  Cited in the paper.

• The absolute computer times quoted here are obviously of little relevance since they depend upon specific details of hardware and software. What is relevant is the comparison between methods

  Cited in the paper.

• The simulations used 0.12 fm lattices with n f = 3 n_{f}\!=\!3 light sea quarks (ASQTAD discretization), and HISQ relativistic dynamics for valence quarks. The gluon configurations were provided by the MILC collaboration. For further details see (set C2): H. Na, C. T. H. Davies, E. Follana, J. Koponen, G. P. Lepage, J. Shigemitsu, arXiv:1109.1501 [hep-lat]

  Original

  Cited in the paper.

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