-
Internal algebra/logic of what cancels in the ratio $R_b(\ell)$ is not made explicit, leading to inconsistent interpretation of beam-driven effects (Secs. 3.3, 4.2, 5.2). As defined (Eqs. (1) and (4)), any multiplicative factor applied identically to both numerator and denominator (e.g., the ACT beam deconvolution $1/b_\ell^{(b)}$, or a common transfer function) should largely cancel in $R_b(\ell)$. However, the text attributes the pa4\_f220 high-$\ell$ excursion to ACT beam-deconvolution amplification using $A_b(\ell)$, without clearly specifying which non-cancelling terms differ between NILC(std) and NILC(deproj) (e.g., different NILC effective beams, different transfer functions, different beam handling in the estimator).
Recommendation: Add an explicit expression for $R_b(\ell)$ obtained by substituting Eq. (1) into Eq. (4), and show term-by-term which factors cancel and which remain. Then align the interpretation in Secs. 4.2 and 5.2 with that expression: if the driver is a difference in $b_\ell^{({\rm NILC,std})}$ vs $b_\ell^{({\rm NILC,deproj})}$, or configuration-dependent $F_\ell$, state this clearly and quantify its expected size. If instead some steps apply different effective deconvolution/transfer corrections between the two configurations, document exactly where that asymmetry enters the pipeline.
-
Beam-uncertainty propagation for $R_b(\ell)$ appears incorrect/incomplete as written (Sec. 3.6, Eq. (7)) and is in tension with the cancellation structure of $R_b(\ell)$. Eq. (7) propagates ACT channel beam uncertainty into the ratio with a $\sqrt{2}$ factor, but the ACT beam is common to both spectra entering $R_b(\ell)$ and should be highly correlated (and potentially cancel), while uncertainty in the NILC effective beam—more likely to differ between std/deproj—does not appear explicitly.
Recommendation: Re-derive $\sigma_{\rm beam}[R_b(\ell)]$ from the explicit expanded form of $R_b(\ell)$, including correlated-error assumptions. If ACT beam factors are common, treat their uncertainty as (nearly) fully correlated and show the residual sensitivity (if any). If NILC effective beams differ between std and deproj, propagate $\delta b_\ell^{({\rm NILC,std})}$ and $\delta b_\ell^{({\rm NILC,deproj})}$ (and their covariance) explicitly. Justify or remove the $\sqrt{2}$ factor by stating the assumed correlation structure. Update Sec. 4.5’s error-budget discussion accordingly.
-
Transfer-function definition and application are not sufficiently specified to verify that corrections are applied exactly once and consistently across configurations (Sec. 3.2; Eqs. (1)–(2)). Eq. (2) states the MC output spectrum includes “beam convolution,” while Eq. (1) separately divides by beam transfer functions; it is therefore unclear whether beams (and/or pixel windows) are absorbed into $F_\ell$ or deconvolved separately, and whether $F_\ell$ is calibrated per channel and per NILC configuration (std vs deproj) or shared—an important point because shared corrections would largely cancel in $R_b(\ell)$.
Recommendation: Rewrite Sec. 3.2 to define precisely: (i) whether $F_\ell$ is computed from beam-convolved maps, beam-deconvolved maps, or maps smoothed to a common target beam; (ii) whether pixel window functions are included in $F_\ell$ or in the beam terms; (iii) whether $F_\ell \equiv F_\ell^{(b\times X)}$ depends on ACT channel $b$ and NILC configuration $X\in \{{\rm std,deproj}\}$. Ensure the estimator in Eq. (1) and the calibration in Eq. (2) are consistent so that each correction (mask/filters/beams/pixels) is applied once. If a common $F_\ell$ is used for both NILC configurations, state this explicitly and explain why configuration dependence is negligible.
-
Simulation suite description is insufficient for reproducibility and to support sub-percent claims (Sec. 3.2, Sec. 5.5). The paper states $N_{\rm MC}=480$ signal-only simulations but does not fully specify the input cosmology/$C_\ell$, whether any noise/foreground components are included, how channel/NILC-specific beams and filtering are implemented, and whether the same simulation realizations are used for both NILC configurations (which affects covariance and cancellation in the ratio). In addition, the reliance on Gaussian, CMB-only simulations leaves unquantified the potential impact of non-Gaussian foregrounds on pseudo-$C_\ell$ mode coupling and transfer functions at the $\leq 1\%$ level being tested.
Recommendation: Expand Sec. 3.2 (and/or add an appendix) to document: fiducial cosmology and CMB spectrum; map-level processing (beams, filtering, reprojection, masks) applied to each simulated product; whether $F_\ell$ is calibrated separately for std/deproj; and whether the same realizations are shared between the two pipelines. Add at least one quantitative bound on non-Gaussian foreground impact: e.g., a small ensemble with foregrounds (dust/CIB/point sources; optionally tSZ) passed through the same pipeline and the resulting shift in $F_\ell$ and/or $R_b(\ell)$, or a literature-supported validation argument tied specifically to the $\ell$-range $200$–$1500$ used for conclusions.
-
The pa4\_f220 high-$\ell$ excursion is plausibly beam/deconvolution related but is not yet demonstrated to be uniquely (or “unambiguously”) beam-driven (Secs. 4.2, 4.5, 5.2). Other channel- and configuration-dependent effects could contribute (e.g., differences in NILC effective beam or weights between std and deproj, or frequency-dependent foreground leakage that changes under tSZ deprojection). The current evidence is mainly qualitative correlation with $A_b(\ell)$ and the prominence of beam-envelope errors.
Recommendation: Either soften language in Sec. 5.2 (e.g., “strongly consistent with a beam/deconvolution origin”) or add targeted quantitative checks. Examples: (i) perturb the pa4\_f220 beam within its envelope/eigenmodes in simulations and show the induced spread in $R_b(\ell)$ matches the observed excursion; (ii) repeat the measurement after smoothing all maps to a common resolution (or computing spectra without deconvolution but with forward-modeling) and show the feature is reduced/removed; (iii) vary masking (more aggressive point-source/cluster masking; different sky regions) to bound a foreground-driven contribution. Report the resulting changes in the highest-$\ell$ bins and in $\bar{R}_b$.
-
Physical interpretation of “$R_b(\ell) \approx 1$” under tSZ deprojection is not fully articulated in the bigger-picture sense (Secs. 1, 5.1, 5.5). Since NILC(deproj) explicitly alters the map by nulling tSZ, one might expect a predictable differential effect on cross-spectra—especially at higher frequencies—depending on residual foreground correlations, masking, and the extent to which the cross-spectrum is CMB-dominated over $200\leq\ell\leq 1500$. Without a short expectation argument, it is harder to interpret unity as a meaningful validation rather than an accidental cancellation.
Recommendation: Add a brief discussion (Sec. 5.1 or 5.5) of the expected sign/magnitude of the change in $b\times {\rm NILC}$ TT cross-spectra when tSZ is deprojected: why the effect should be small over $200$–$1500$ (primary CMB dominance; tSZ subdominant in cross with a CMB-cleaned map; masking), and what residual foreground terms (CIB/radio/dust/kSZ) could in principle change under the deprojection constraint. If possible, include an order-of-magnitude estimate or a simple simulation/analytic forecast for $\Delta C_\ell/C_\ell$ to contextualize the measured constraints.
-
Scale-cut recommendations are useful but the cosmological/analysis impact is not quantified (Secs. 5.1, 5.4, 6). The paper recommends $\ell_{\rm max}=1500$ (and possible extensions) and notes a $\approx 4\%$ effect for pa4\_f220 at high $\ell$, but does not translate these into expected parameter shifts, information loss, or robustness impact for representative downstream use cases (e.g., TT-only parameter constraints or TT-based lensing).
Recommendation: Augment Secs. 5.1/5.4/6 with a quantitative impact estimate. Even a simple Fisher-style calculation or a pipeline-based reweighting that answers: (i) how much pa4\_f220 contributes to total TT information in current DR6 analyses; (ii) the parameter impact of a constant $1$–$4\%$ multiplicative distortion over a given $\ell$-range; and (iii) the net effect of excluding pa4\_f220 or cutting at $\ell=1500$ vs $2000$. Approximate numbers (with clear assumptions) are sufficient and would make the recommendations substantially more actionable.
-
Null-test reporting is not fully comprehensive across channels/configurations (Secs. 3.5, 4.3; Fig. 2). Figure 2 shows only a representative channel while the text states similar results hold for all channels; however, readers cannot easily assess whether any borderline PTEs exist, nor whether null consistency is equally strong for both NILC(std) and NILC(deproj) cross-spectra.
Recommendation: Add a compact table (Sec. 4.3 or an appendix) listing $\chi^2/{\rm dof}$ and PTEs for the split-difference null spectra for all six channels (and clarify whether they are computed for both NILC configurations or for the ratio pipeline specifically). This can replace the need for many extra plots while making the null-test claim verifiable.