Controlling excited-state contributions with distillation in lattice QCD calculations of nucleon isovector charges gSu−d , gAu−

Abstract

We investigate the application of the distillation smearing approach, and the use of the variational method with an extended basis of operators facilitated by this approach, on the calculation of the nucleon isovector charges g u−d S , g u−d A , and g u−d T . We find that the better sampling of the lattice enabled through the use of distillation yields a substantial reduction in the statistical uncertainty in comparison with the use of alternative smearing methods, and furthermore, appears to offer better control over the contribution of excited-states compared to use of a single, local interpolating operator. The additional benefit arising through the use of the variational method in the distillation approach is less dramatic, but nevertheless significant given that it requires no additional Dirac inversions.A routinely come up short. Recent work by [1] employs a methodology inspired by the Feynman-Hellman theorem to control excited-state effects by summing over all current insertion times, engendering extrapolation in a single Euclidean temporal variable rather than two -agreement was found to within arXiv:1810.09991v1 [hep-lat]

Excited-state effects in nucleon structure on the lattice using hybrid interpolators

“…[5][6][7][8][9], which used bases of interpolators with different smearing widths and different site-local spin structures, and Ref. [10], which used the distillation method to enable the use of interpolators with a variety of local structures including covariant derivatives. In these cases, the variational setup was more computationally expensive than a standard calculation because of the need for additional quark propagators with different smeared sources 1 .…”

Controlling Excited-State Contributions to Nucleon Isovector Charges using Distillation

“…T . A complete accounting of g u−d S , g u−d A and g u−d T can be found in [12]. We show distillation provides a significant reduction in statistical uncertainty and appears to have a better control over excited-state effects in nucleon matrix elements, when compared to local interpolators smeared in a conventional manner.…”

“…The reader is referred to [12] for explicit construction of these interpolators. Due to the high Wick contraction costs of distillation, we applied the variational method to a correlation matrix of two-point functions, fixingP 3/7 for use in the three-point calculations.…”

“…For brevity we present results for the isovector charges where t fit 2pt ∈ [2, 16] and τ fit ∈ 2,t sep − 2 . The reader is referred to [12] for a complete analysis of the dependence of our results on the fitting windows chosen, as well as results for the scalar and vector charges, and a complete listing of our fitted parameters. We define an effective charge g eff Γ (t, τ) = C 3pt Γ (t, τ) /C 2pt fit (t) to quantify the amount of excited-state contamination, where C 2pt fit (t) is the best fit applied to the two-point function and C 3pt Γ (t, τ) the three-point function of the same source-sink separation and interpolator constructions.…”

Systematics in nucleon matrix element calculations

“…In Ref. [37] 4 , such a basis was used, employing the distillation method to efficiently construct the correlators. In general, a larger basis was more effective at removing excited-state contributions, with the largest effect seen in the tensor charge.…”