Optimised Distillation for Nucleon Correlation Functions

The paper does exactly what it advertises: it applies Gaussian-weighted distillation profiles (previously used for charmonium and glueballs) to nucleon two- and three-point functions. The results on the A653 ensemble are clean, the method is cheap (no extra inversions), and the excited-state suppression in the two-point function looks comparable to tuned Wuppertal smearing. For the three-point axial charge, the ratio shows flatter plateaus, which is a real improvement in data quality.

What it does well: the methodology is clearly described, the GEVP treatment is standard, and the fits are appropriate. The reduction in curvature in the three-point ratio is visible and credible. The authors explicitly note that this is work in progress.

Soft spots: - Single ensemble, heavy pion mass (429 MeV). The method may behave differently at physical masses or on finer lattices. - The extracted gA = 1.146(18) agrees within error with the flat-profile result 1.147(18). The excited-state contamination was apparently small already; the profiles mainly flatten the plateau rather than change the answer. That is useful but not transformative. - The three-point rotation uses the two-point GEVP eigenvectors without independent cross-check. The stress-test concern about this assumption is reasonable—it is standard practice but untested here. - No systematic scan over N_v or profile widths. The choice of 50 eigenvectors is motivated but not justified as optimal. - The paper is a proceedings contribution (4 pages), so depth is limited.

Who this is for: lattice practitioners working on nucleon structure, especially those already using distillation. It shows that a known trick works for nucleons at rest and with small momenta on a coarse ensemble.

Recommendation: This deserves a serious referee if submitted to a lattice-specific proceedings or a journal supplement. The work is honest and the method is plausible, but it is too narrow to be a standalone journal article. I would accept a peer review invitation for this paper.

The central claim that optimised distillation profiles reduce excited state contamination in three-point functions (Figure 4) rests on an untested assumption: that the eigenvectors obtained from the two-point GEVP (Eq.6) are also optimal for rotating three-point functions. The paper states in §3.2: 'We take the eigenvectors calculated from the two-point correlation function and use these to rotate the three-point function to the same basis.' This assumes the same linear combination that projects onto the nucleon ground state in the two-point sector also suppress excited state in the presence of a current insertion. While standard in the variational literature, the paper does not provide internal validation by, e.g., solving a separate GEVP on the three-point correlation matrix. If the current couples differently to excited states, the optimised profile basis may not be truly optimal, and the apparent reduction in curvature could arise from a different cancellation. The extracted gA being consistent with the flat profile result does not rule out a common systematic error.

The reader's weakest assumption inclued both the eigenvector assumption and the single-ensmble limitation. Both are valid concerns, but I identify the eigenvector assumption as most directly load-bearing for the central claim within this single ensemble: if it fails, the three-point results could be misleading even on A653. The concrete test is feasible with existing data and would settle whether the optimised profile method requires separate three-point GEVP or whether the cheaper two-point eigenvectors are sufficient. The verdict remains UNCHANGED because the conditional verdict already accounts for this uncertainty; the stress-test adds a specific, testable condition.

If robust, the method offers a cost-effective improvement in excited-state control for nucleon structure calculations within the distillation framework, requiring no additional inversions. The demonstration is on a single ensemble with a heavy pion mass, so general significance to physical-point calculations remains to be shown. The consistency of the extracted g_A between flat and optimised profiles is reassuring, but the central claim of 'considerable reduction' in three-point contamination rests on an assumption that is standard but not validated here. The paper is a clear progress report and will be of interest to the lattice QCD community.

Distillation is a technique in lattice QCD that projects quark propagators onto the low eigenmodes of the gauge-covariant Laplacian, effectively smoothing the quark fields. The number of eigenmodes kept acts as a smearing parameter, but the choice is not always optimal. This paper applies Gaussian profiles to reweight each eigenmode, placing higher weight on lower modes and suppressing higher ones. A variational basis is built from several such profiles with different widths, and a generalised eigenvalue problem (GEVP) is solved to find the linear combination that best overlaps with the nucleon ground state. The method is implemented entirely at the contraction level, requiring no new inversions. On a single lattice ensemble with a pion mass of 429 MeV, the optimised operators give ground state dominance as early as tuned conventional Wuppertal smearing, with slower noise growth. For boosted nucleons the excited state suppression weakens with increasing momentum. In three-point functions with an axial current, the eigenvectors from the two-point GEVP are used to rotate the correlator to the optimised basis; the resulting ratio shows heavily reduced curvature in the insertion time and source-sink separation. A two-state fit yields the isovector axial charge gA = 1.146(18), consistent with the value from flat profiles (1.147(18)). Residual excited state contamination remains but is smaller than in the flat case.

Core claim. The excited state suppression from optimised distillation profiles is comparable to that of tuned Wuppertal smearing for a nucleon at rest, and the statistical noise is better controlled. For the nucleon isovector axial charge, the optimised profiles yield a considerable reduction in excited state contamination, giving gA = 1.146(18) consistent with the flat profile result 1.147(18) (see §3.2 and Figure 4).

The premise it rests on. The method's efficacy depends on the chosen number of Laplacian eigenvectors (N_v = 50) and the set of Gaussian widths; the paper notes that for flat profiles this choice gave suboptimal smearing (see b45). The authors assume the eigenvectors obtained from the two-point GEVP are optimal for rotating the three-point functions, which is standard but not independently validated here. The demonstration is on a single lattice ensemble (A653) with a heavy pion mass of 429 MeV, so the generalizability to finer lattices, lighter quarks, and different volumes is unproven.

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