{"id":"61b04271-8a74-4142-ab4f-51a689146491","arxiv_id":"2501.08806","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A review showing unpolarized quark TMD fits now reach collinear-PDF-like precision, while polarized and gluon TMDs remain less constrained.","lead":"This paper is a conference proceedings review of how physicists map the 3D momentum structure of protons using transverse-momentum-dependent parton distributions. It explains where TMD extractions are already precise and where future electron-ion colliders are expected to close the gaps.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'precision era' claim rests on perturbative resummation order and chi2/N, but Eq. (3)'s nonperturbative fNP and b* prescription are not systematically improvable; without a robustness test of fNP, the claimed N3LL/N4LL accuracy can overstate the true precision of extracted TMDs.","rationale":"The reader's verdict CONDITIONAL already captures the central risk: the precision-era claim is a phenomenological claim about real accuracy, not just about the formal order of perturbative ingredients. Eq. (3) separates the perturbative kernel from fNP, and Sec. 2 explicitly says the b* procedure introduces power corrections that for qT near Lambda_QCD must be absorbed by fNP. The table in Fig. 1 quotes resummation order and chi2/N, but neither quantity carries information about the bias or limited flexibility of the chosen fNP form or about bmax. Thus the evidence shown does not by itself establish the comparison with collinear PDF extractions, which include systematic parametrization and scale uncertainties. I agree with the reader's weakest assumption and would keep the verdict CONDITIONAL: the paper can stand as an overview, but the 'precision era' statement should be tempered or accompanied by a robustness test. The proposed test—rerunning the MAPTMD24 fit with alternative fNP forms and varying bmax and checking whether extracted flavor-separated f1(kT) moves outside the quoted bands—is concrete and would settle the concern. No internal inconsistency is identified; the issue is evidential support for the headline claim.","tokens_in":19028,"tokens_out":4077,"duration_ms":46549,"concrete_test":"Take the MAPTMD24 global fit (Ref. [17], arXiv:2405.13833) and rerun it with two modifications: (a) an alternative fNP functional form with the same number of parameters but different large-bT asymptotic behavior, and (b) a different bmax choice, e.g. 1.5 GeV^-1 and 3 GeV^-1. Compare the extracted flavor-separated f1^q(kT) at Q = 2 GeV and the fit chi2/N. If central values at kT ~ 0.5 GeV shift by more than the quoted 1-sigma uncertainty band, or if chi2/N changes by more than ~0.1, the 'precision era' claim overstates the robustness of the extraction. If the shifts are within the quoted bands, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim in Sec. 5 is that unpolarized quark TMD extractions have entered a 'precision era' with accuracy comparable to collinear PDF extractions. The evidence in Fig. 1 is the perturbative resummation order and the fit chi2/N. But Eq. (3) factorizes the TMD into a perturbative evolution kernel, a matching coefficient evaluated at mu_b* = 2e^{-gamma_E}/b*, and a fitted nonperturbative term fNP. As Sec. 2 explicitly states, the b* prescription introduces power corrections of order (Lambda_QCD/qT)^m that for qT near Lambda_QCD must be absorbed into fNP. The quoted N3LL/N4LL orders therefore describe only the perturbative ingredients Evo and C; they do not quantify the uncertainty from the functional form of fNP or from the choice of bmax. A chi2/N near unity shows only that the chosen fNP form can fit the data, not that alternative forms would give the same TMDs. Collinear PDF extractions include systematic uncertainties from parametrization and scale choices; this manuscript shows no analogous uncertainty for the TMD nonperturbative input. The claim of comparability with PDF extractions is thus not yet established by the evidence presented. This is not an internal inconsistency, but it is the weakest load-bearing link: the headline precision claim is quantified on the perturbative side while the dominant uncertainty in the relevant small-qT region is nonperturbative.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This is a short proceedings contribution reviewing the current phenomenological status of transverse-momentum-dependent parton distributions (TMD PDFs). The paper summarizes the factorized cross sections for Drell-Yan and SIDIS, the b*-prescription for TMD evolution, and a table of recent global extractions of the unpolarized quark TMD f1. It then discusses selected results: an EIC pseudodata impact study on flavor-dependent f1, the Sivers sign-change prediction and its possible connection to the spin Odderon, the transversity/tensor-charge comparison with lattice QCD, and a spectator-model calculation of gluon TMDs. The central claim, stated in the abstract and in Section 5, is that unpolarized quark TMD extractions have reached a 'precision era' with accuracy comparable to collinear PDF extractions, while polarized quark and gluon TMDs remain much less constrained.","tokens_in":19379,"tokens_out":7667,"duration_ms":77240,"significance":"The paper is a useful, compact status report on TMD phenomenology. Its main value is synthetic: it collects the recent f1 extractions in one table, states the standard factorization equations clearly, and identifies key open questions (Sivers sign change, spin Odderon, transversity-lattice tension, and the scarcity of gluon TMD data). It also makes testable predictions, most notably the SIDIS/DY sign change of the Sivers function and the small-x connection to the spin Odderon. The paper does not present new derivations or new numerical fits, but as a proceedings overview it serves a legitimate purpose. The main risk is that the 'precision era' wording overstates the certainty of the extracted TMDs, since the nonperturbative input fNP is not subjected to the same systematic scrutiny as the perturbative ingredients.","major_comments":[{"comment":"The central claim that unpolarized quark TMD extractions have entered a 'precision era' with accuracy 'comparable to state-of-art extractions of PDFs' is supported only by the perturbative resummation order and by the fit quality chi2/N listed in Fig. 1. However, as Section 2 correctly states after Eq. (3), the b*-prescription introduces power corrections that for qT near Lambda_QCD must be absorbed into the fitted nonperturbative function fNP. The paper gives no test of the sensitivity of the extracted f1 to the functional form of fNP or to the choice of bmax, and no comparison of the spread among the different extractions in Fig. 1 as a proxy for systematic uncertainty. Without such an assessment, the claim of comparability with collinear PDF extractions, which typically include parametrization and scale uncertainties, is not fully established. I recommend either adding a robustness test (e.g., varying the fNP parametrization and bmax, or quantifying the spread among the fits in Fig. 1) or explicitly limiting the claim to the perturbative accuracy of the theoretical framework rather than to the total precision of the extracted TMDs.","section":"Section 5 and Abstract"}],"minor_comments":[{"comment":"The quantitative statements that EIC pseudodata reduce the f1 uncertainty 'by a factor 2 overall' and 'by a factor 3 for d and dbar' are based on 'L. Rossi, Ph.D. Thesis, in preparation' and are labelled 'Preliminary'. For a published proceedings, these numbers should be backed by a citable preprint or by an appendix describing the pseudodata assumptions; otherwise the claims should be presented as qualitative illustrations.","section":"Section 3.1 and Fig. 2"},{"comment":"Both panels of Fig. 4 are 'adapted from' conference talks by C. Alexandrou and D. Pitonyak (QCD Evolution 24). The figure caption should cite the primary publications [66,67,51,59,58] so that readers can verify the numerical comparison and the claimed 3-4 sigma tension.","section":"Section 3.3 and Fig. 4"},{"comment":"The sentence 'In this limit, the function b*(bT) saturates to a fixed bmin value' is unclear. In the standard b* prescription, b*(bT) saturates to bmax at large bT; the role of bmin, if any, should be defined explicitly. Please give the explicit definition of b*(bT) or correct the statement.","section":"Section 2, after Eq. (3)"},{"comment":"The typeset version contains a duplicated block of text from the EIC Yellow Report (the paragraph beginning 'ments will also play a key role...' appears twice in the text surrounding Fig. 3). This editing artifact should be removed.","section":"Section 3.2"},{"comment":"The variables xA and xB and the hard factor H_DY are used in Eq. (1) but not defined in the surrounding text. Please define them explicitly for the non-specialist reader.","section":"Equation (1)"},{"comment":"The 'printed on' page headers and the 'Preliminary' watermarks in the figures should be cleaned before publication.","section":"General formatting"}],"recommendation":"major_revision","confidential_remarks":"This is a proceedings contribution, so the bar for novelty is appropriately low. The main issue is that the headline 'precision era' claim, which is the paper's central message, needs either a systematic-uncertainty caveat or an explicit restriction to perturbative accuracy. The EIC impact figure is based on unpublished thesis work, which is a provenance concern for a published proceedings. Both issues are fixable with modest revisions; I do not see a fundamental problem with the science as reported."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a competent, well-organized conference review, and the only genuinely new element — the EIC impact projection in Fig. 2 — is clearly labeled \"Preliminary\" and comes from a thesis in preparation. Take the paper as a status summary, not a source of new results, and it does its job.\n\nThe paper does well: the table in Fig. 1 is a handy compilation of recent unpolarized-f1 extractions, the factorization formulas in Sec. 2 are correct and standard, and the gluon-TMD section gives a fair picture of a field that is still mostly model-driven. The author's reliance on his own fits (MAPTMD24, Radici/Bacchetta transversity) is not a problem in itself; those are published global analyses of external data with published uncertainty estimates.\n\nThe soft spot is the \"precision era\" claim in Sec. 5. The evidence on the table is resummation order and chi2/N, which are perturbative credentials. But as Sec. 2 itself says, the b* prescription and the fitted fNP must absorb power corrections near qT ~ Lambda_QCD. A chi2/N near one shows the chosen fNP form fits the data; it does not show that a different, equally reasonable fNP would give the same TMDs. So \"comparable to state-of-art extractions of PDFs\" is not yet established, because collinear PDF fits do include parametrization and scale systematics. That is a caveat on the claim, not a fatal flaw for a review, but it belongs in the summary.\n\nTwo provenance items need attention: Fig. 2 uses unpublished EIC pseudodata (\"Ph.D. Thesis, in preparation\") and Fig. 4 is adapted from conference talks. The quantitative impact numbers in Fig. 2 are therefore not traceable. Either link them to a public source or label them explicitly as the author's preliminary estimate.\n\nThe math in the formalism is clean and the citation pattern looks fine. The review is aimed at relative newcomers or experimental colleagues who want a quick map of the TMD pheno landscape; it would be a legitimate entry point.\n\nFor peer review: I'd send it, not because it breaks new ground but because the field-level precision claim is load-bearing and deserves a referee's check. The referee should ask for a softer summary statement and traceable sources for the preliminary figures.","headline":"Solid status review whose 'precision era' headline is slightly ahead of the evidence: perturbative accuracy is high, but fNP uncertainty is not quantified.","tokens_in":19884,"tokens_out":3260,"would_cite":false,"duration_ms":33250,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper argues that unpolarized quark transverse-momentum-dependent distributions have reached a precision comparable to collinear PDFs, while polarized and gluon TMDs remain far less constrained.","keywords":["transverse-momentum-dependent distributions","unpolarized quark TMDs","TMD factorization","global fits","Drell-Yan and SIDIS","Sivers effect","transversity and tensor charge","gluon TMDs"],"falsifier":"Fit $f_1^q$ to the same data set with two different $b_{\\max}$ values or two different functional forms of $f_{\\rm NP}$; if the extracted TMDs disagree by more than the quoted uncertainty band, the precision-era claim is overstated. Alternatively, compute the large-$b_T$ TMD on the lattice and compare with the fitted $f_{\\rm NP}$; a significant mismatch would show that the nonperturbative term is not absorbing the true power corrections.","tokens_in":18818,"feed_emoji":"⚛️","tokens_out":12360,"duration_ms":102170,"temperature":0.7,"pith_summary":"This short review argues that transverse-momentum-dependent (TMD) distributions, the functions that map how quarks and gluons move sideways inside a fast-moving nucleon, have reached very different levels of maturity. For unpolarized quarks, the field has entered what the author calls a precision era: the TMD PDF $f_1^q$ for each flavor can now be extracted from global fits of semi-inclusive deep-inelastic scattering, Drell-Yan, and $Z$-boson data, with resummation accuracies up to N4LL and $\\chi^2/N$ values near one, comparable to state-of-the-art collinear PDF extractions. That matters because $f_1^q$ is the denominator of every asymmetry used to extract polarized TMDs and because it feeds flavor-sensitive precision observables such as the $W$-boson mass. The same precision does not yet exist for polarized quark TMDs like the Sivers function and transversity, nor for gluon TMDs, where experimental information is scarce and model calculations carry the discussion. The paper also highlights a persistent 3 to 4$\\sigma$ tension between the tensor charge extracted from phenomenology and from lattice QCD, and the still-unconfirmed prediction that the Sivers function changes sign between SIDIS and Drell-Yan processes.","feed_headline":"Unpolarized quark TMDs now rival collinear PDFs","feed_subtitle":"Global fits of scattering data now extract quark transverse motion at collinear-level precision","key_machinery":"The object that carries the argument is the $b_T$-space factorization formula for the unpolarized TMD PDF, Eq. (3): $\\hat f_1(x,b_T^2;Q) = E_{\\rm evo}(Q\\leftarrow \\mu_{b_*})\\,[C\\otimes f_1](x,\\mu_{b_*})\\, f_{\\rm NP}(x,b_T^2)$. The evolution operator $E_{\\rm evo}$ resums large soft-gluon logarithms, the Wilson coefficient $C$ matches the TMD onto the collinear PDF $f_1$ at small $b_T$, and the $b_*$ prescription freezes the scale $\\mu_{b_*}$ at large $b_T$ so the perturbative series does not hit the Landau pole. The fitted nonperturbative function $f_{\\rm NP}$, constrained by $f_{\\rm NP}\\to1$ as $b_T\\to0$, absorbs the power corrections $(\\Lambda_{\\rm QCD}/q_T)^m$ that the $b_*$ procedure introduces at low $q_T$. The 'Accuracy' column in Fig. 1 is the order to which $E_{\\rm evo}$ and $C$ are computed, and the rightmost column is the quality of the $f_{\\rm NP}$ fit; the claim of a precision era is exactly the claim that this pair of numbers now means what it appears to mean.","core_discovery":"The paper's central claim is that unpolarized quark TMDs have crossed from illustrative to precision phenomenology. The evidence is the table of recent extractions in Fig. 1: reading from the 2017 fits at NLL accuracy over 8059 points with $\\chi^2/N=1.5$ down to the 2023 N4LL fit and the 2024 flavor-dependent global fit at N3LL with $\\chi^2/N\\simeq1.06$, the trajectory mirrors what happened for collinear PDFs over the previous decades. The author states this directly in the summary: 'for unpolarized quark TMDs, we can assert that we entered a precision era.' On the other hand, polarized quark TMDs are based on smaller data sets with lower perturbative accuracy, and gluon TMDs, though completely classified at leading twist with proven factorization for several processes, remain dominated by model predictions rather than extractions.","pith_inferences":["Editorial inference: if the precision-era claim is correct, the limiting uncertainty in unpolarized TMD fits has shifted from resummation order to the parametric form of $f_{\\rm NP}$ and the choice of $b_{\\max}$; a direct check would be to fit the same data with different $b_*$ prescriptions and compare the spread.","Editorial inference: the spectator-model gluon TMDs shown in Fig. 5 could be promoted from predictions to tests by feeding them into global fits of quarkonium or dijet production, where factorization has been proven, to see whether the model's T-odd patterns survive.","Editorial inference: the tensor-charge tension may not be purely statistical, because a handful of lattice points leave $\\chi^2$ almost unchanged yet shift the fitted values strongly; this points to non-Gaussian pulls or parameterization sensitivity rather than simply more data.","Editorial inference: a natural testable extension is to use the same EIC pseudodata framework to project uncertainties for the Sivers function at small $x$; the existing impact studies are for $f_1^q$, and the analogous projection for the T-odd sector would show how quickly the sign-change prediction could be confirmed."],"forward_implications":["Flavor-sensitive LHC measurements such as the $W$-boson mass can now be analyzed with genuine flavor-dependent intrinsic transverse momentum from $f_1^q$, including a quantified nonperturbative uncertainty.","Projections with EIC pseudodata show the relative uncertainty on $f_1^q$ shrinking by about a factor 2 at $x=0.001$, and by a factor 3 for $d$ and $\\bar d$, making 3D flavor tomography of the proton testable.","The predicted sign change of the Sivers function between SIDIS and Drell-Yan remains one of the sharpest unconfirmed predictions of QCD; future data could either confirm it or expose a breakdown of the TMD factorization assumptions.","A confirmed small-$x$ Sivers effect with the predicted C-odd behavior would provide indirect evidence for the spin Odderon, tying TMD phenomenology to the high-energy color-glass-condensate picture.","If the tensor-charge tension between phenomenology and lattice QCD survives future SoLID and EIC data, it would signal missing theoretical input in one of the two extractions, a key input for searches for new tensor interactions beyond the Standard Model."],"supporting_citations":[{"why":"supplies the TMD factorization framework and the $b_T$-space formula that Eq. (3) is built on.","marker":"[13]"},{"why":"the source of the $(\\Lambda_{\\rm QCD}/q_T)^m$ power corrections that the $b_*$ prescription and $f_{\\rm NP}$ must control.","marker":"[18]"},{"why":"the first global fit of SIDIS, Drell-Yan and $Z$ data, the baseline 'PV 2017' entry in Fig. 1.","marker":"[11]"},{"why":"the N3LL extraction from Drell-Yan data that raised the perturbative accuracy of the unpolarized TMD fit.","marker":"[16]"},{"why":"the global SIDIS+DY fit at N3LL(-) that forms the 'MAPTMD 2022' row and produces $\\chi^2/N=1.06$.","marker":"[14]"},{"why":"the first global fit with flavor-dependent intrinsic transverse momentum, the 'MAPTMD24' baseline used for the EIC impact study.","marker":"[17]"}],"fun_headline_variants":["Unpolarized quark TMDs enter precision era","Quark TMDs match collinear PDF precision","TMD precision: quarks ahead, gluons lag","Gluon TMDs remain model-bound, quarks precise"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The precision-era claim rests on the assumption that the $b_*$ prescription and the fitted nonperturbative function $f_{\\rm NP}(x,b_T^2)$ capture all power corrections of order $(\\Lambda_{\\rm QCD}/q_T)^m$ near $q_T\\simeq\\Lambda_{\\rm QCD}$; if that function is too rigid or misses genuine large-$b_T$ physics, the quoted N3LL or N4LL accuracy overstates the real precision of the extracted TMDs.","fun_headline_variants_meta":{"raw":{"variants":["Unpolarized quark TMDs enter precision era","Quark TMDs match collinear PDF precision","TMD precision: quarks ahead, gluons lag","Gluon TMDs remain model-bound, quarks precise"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000243,"raw_usage":{"total_tokens":1464,"prompt_tokens":816,"completion_tokens":648,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":432,"completion_tokens_details":{"reasoning_tokens":581}},"tokens_in":432,"tokens_out":648,"duration_ms":6485,"temperature":1.0,"reasoning_tokens":581,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:17:25.079087+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Fit $f_1^q$ to the same data set with two different $b_{\\max}$ values or two different functional forms of $f_{\\rm NP}$; if the extracted TMDs disagree by more than the quoted uncertainty band, the precision-era claim is overstated. Alternatively, compute the large-$b_T$ TMD on the lattice and compare with the fitted $f_{\\rm NP}$; a significant mismatch would show that the nonperturbative term is not absorbing the true power corrections.","supporting_citations":[{"cited_title":"Collins, Foundations of perturbative QCD , vol","cited_arxiv_id":null,"evidence_quote":"supplies the TMD factorization framework and the $b_T$-space formula that Eq. (3) is built on."}],"review_version":1}