{"id":"eebfd2c9-c93b-41de-81ff-40c1b7fca179","arxiv_id":"2412.00892","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The fitted intrinsic-kT width obtained from CASCADE3 Drell-Yan simulations is independent of the pair invariant mass at LHC energies, consistent with the slow scale dependence of the non-perturbative Sudakov form factor in the measured range.","lead":"Using the Parton Branching method and the CASCADE3 event generator, this paper studies how the random sideways motion of quarks inside protons and soft gluon emission shape very low momentum Drell-Yan lepton pairs. It finds that the fitted intrinsic-kT width is flat in the pair mass at LHC energies, and traces this to the weak scale dependence of the non-perturbative Sudakov form factor.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The q0-cut/Delta_NP equivalence in Sec. 2 is asserted rather than demonstrated; without it, flat qs(m_ll) does not establish weak mu-dependence of the non-perturbative Sudakov form factor.","rationale":"The reader's conditional verdict is already driven by the same foundational premise: the paper's interpretation of the q0-cut as equivalent to neglecting Delta(NP). I agree with the reader's weakest_assumption, and my stress-test does not move the verdict: the central result remains a non-confirmation, as the paper itself states, but the explanatory story built on it depends on an equivalence that is asserted rather than checked. This is the single most load-bearing concern because all subsequent steps—the mass independence of qs, the attribution to the weak mu dependence of Delta(NP), and the low-mass prediction via integrated PDFs—inherit this identification. A numerical demonstration using the actual evolution code would settle it. The paper otherwise deserves credit for presenting the null result explicitly, for giving scale-uncertainty bands, and for a cautious wording of the conclusion. The QED discussion is separate and does not carry the main argument. Therefore, the appropriate verdict remains CONDITIONAL, with the condition being verification of the zM=zdyn equivalence and, if possible, a direct evaluation of Delta(NP)'s scale dependence.","tokens_in":13278,"tokens_out":6880,"duration_ms":68297,"concrete_test":"Run CASCADE3 for the Z-peak bin at sqrt(s)=13 TeV under two prescriptions: (A) the current q0-veto applied to emissions from full PB-NLO Set2 TMDs (zM->1), and (B) TMDs re-evolved with zM=zdyn(q0) for the same q0, so Delta(NP) is removed from the Sudakov exponent before generation, with no additional veto. Compare the predicted dsigma/dpT(ll) and, after the chi2(qs) fit, the resulting qs. If (A) and (B) differ by more than the 5-10% transition-region discrepancy quoted in Sec. 2, or if the fitted qs changes, the Section 2 identification fails and the flat-qs interpretation is not established. A complementary analytic check is to evaluate Delta(NP) from Eq. (3) at mu=100 and 500 GeV and compare its fractional change with the qs uncertainties in Fig. 2.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2 states: \"In the PB Method zM -> 1 while in shower-based event generators zM = zdyn. This implies that when mimicking shower-based MC event generators, the non-perturbative part of the Sudakov form factor, Delta(NP), is neglected through the integral in z.\" This implication is the load-bearing premise: if a qT>q0 veto in CASCADE3 does not actually remove Delta(NP) from the Sudakov exponent, then the growth of qs with q0 and its flatness with m_ll (Fig. 2) are not evidence about the scale dependence of the non-perturbative Sudakov form factor. The concern is concrete. Equation (3) is a decomposition of the full Sudakov into Delta(P) and Delta(NP); setting zM=zdyn deletes the second factor from the exponent. But applying a cut on emissions in the Monte Carlo is not the same operation. CASCADE3 uses PB-NLO Set2 TMDs that contain the full zM->1 Sudakov; vetoing generated branchings with qTq0 cutoff on generated branchings. These are not obviously identical operations: a veto on real emissions below q0 does not by itself remove the corresponding virtual contributions from the TMD normalization. The manuscript should either provide a derivation that the q0 cut in CASCADE3 realizes zM=zdyn in the exponent, or validate the equivalence by comparing CASCADE3 with q0>0 against a shower-based generator (the paper itself lists this as a future step in Section 5). Without such support, the flatness of qs(m_ll) in Fig. 2 cannot be uniquely attributed to the scale dependence of the non-perturbative Sudakov form factor.","section":"Section 2, Eq. (3)"},{"comment":"The main quantitative result, namely the absence of qs dependence on m_ll within uncertainties, rests entirely on the chi-squared minimization and on the quoted error bars, but neither the minimization procedure nor the uncertainty derivation is documented here; the reader is referred to references [1,3]. Since Figures 2 and 6 present new results, the paper should at least summarize the fitting procedure, the definition of the uncertainties (for example, Delta chi-squared = 1 or scale-variation bands), and whether the same qs value is used for all mass bins in the ratio predictions of Figure 3. This information is necessary to judge whether the flatness is a genuine null result or an artifact of the fitting procedure.","section":"Section 3, Figure 2"},{"comment":"There is a direct inconsistency between the text and the figures: the text states that the integrated PDFs are shown for mu = 100 and 500 GeV, while the Figure 4 caption and axes show mu = 70 and 400 GeV; Figure 5 is described in the text as showing mu = 4 and 20 GeV, but its caption says mu = 70 and 400 GeV. The argument that the relative change of the PDFs is nearly scale-independent over the LHC range and differs at low mu depends on the correct scales. Please correct the captions and axis labels, and ensure the text matches the figures.","section":"Section 3, Figures 4 and 5"}],"minor_comments":[{"comment":"There are numerous typographical errors, including \"pronaunced\", \"Comparisson\", \"od the\", \"ilustrate\", and \"resovable\". A careful proofreading pass is needed.","section":"Throughout"},{"comment":"The text says \"transverse momentum distribution in 4.2 < m(ll) < 8 GeV measured at 38.8 GeV [22]\", but the right panel of Figure 8 is labeled \"E605 sqrt(s)=38.8 GeV, Z/gamma* -> l+l-, 7 < m_ll < 8 GeV\", while the middle panel is at sqrt(s)=200 GeV with 4.8 < m_mu+mu- < 8.2 GeV. Please clarify which mass interval and dataset correspond to each panel.","section":"Section 4, Figure 8"},{"comment":"The E605 panel shows a visible trend of qs with m_ll, while the text says only a \"weak dependence\" and that no firm conclusion can be drawn. It would be helpful to state explicitly whether this trend is seen for q0 = 1 GeV, q0 = 2 GeV, or both, and whether it is consistent with the quoted uncertainties.","section":"Section 3, Figure 6"},{"comment":"The left panel of Figure 9 is described as showing the invariant mass distribution, but the axis label appears to read \"M (GeV)\" with a ratio panel; please verify that the labels and captions correctly identify the plotted quantities.","section":"Section 4, Figure 9"}],"recommendation":"major_revision","confidential_remarks":"This is a conference proceedings contribution that relies heavily on references [1,3] for the methodology behind the chi-squared fits and the q0-cut interpretation. The editor may wish to consider whether the journal expects the load-bearing equivalence between the q0 cutoff and the neglect of the non-perturbative Sudakov factor to be self-contained; if not, the major comments above can be addressed by explicit references plus a short summary of the derivation. The self-citation pattern is natural for a group's line of work and is not a concern in itself. The novel content is modest, but the null result on qs versus m_ll is useful for the community."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this proceedings paper gives you the first scan of the fitted intrinsic width qs against DY pair invariant mass at finite q0, a PDF-level diagnostic of the q0 cut, and clean QED checks down to 200 GeV. The LHC scan is a solid null result. But the paper's explanation of why qs is flat leans on an equivalence between a qT>q0 veto in CASCADE3 and dropping the non-perturbative Sudakov factor, and that equivalence is stated, not demonstrated.\n\nThe new material is genuinely new: Figure 2 and Figure 6 show qs versus m_ll at q0 = 1 and 2 GeV for LHC and fixed-target energies, and Figure 9 gives QED-only predictions at 200 GeV that are testable. The paper is honest: the conclusion is a non-confirmation, not a claim of discovery. The QED section cleanly separates effects above pT ~ 8 GeV, which is useful for anyone fitting low-pT Drell-Yan.\n\nThe soft spot is the one flagged by the stress-test. Section 2 argues that because shower generators use zM = zdyn, mimicking them with a q0 cut automatically neglects Delta(NP). That is an assertion about how the Monte Carlo veto relates to the Sudakov decomposition in Eq. (3). A veto on real emissions does not obviously delete the corresponding virtual terms from the TMD normalization. The paper supplies no test that the two prescriptions are equivalent. If they are not, the flatness of qs could just mean the fit is insensitive to the mass-dependent soft contribution, not that Delta(NP) is scale-independent over 100-500 GeV. The PDF ratio in Figures 4-5 does not repair this, because it addresses the integrated PDF, not the Delta(NP)-removal equivalence.\n\nA smaller annoyance: the figure captions are inconsistent. Figure 5's caption lists 70 and 400 GeV while the text says 4 and 20 GeV. That kind of sloppiness makes verification harder than it needs to be.\n\nWho is this for? People working on TMD phenomenology and event-generator tunes. If you already know the previous CASCADE papers, you will read this as a status update; if you do not, the self-citation is heavy but not inappropriate. The paper deserves a serious referee, because the scans are useful and the interpretive premise deserves scrutiny. I would suggest the author document or reference the chi2 fits more explicitly, fix the captions, and either test the zM = zdyn equivalence or flag it as a model assumption rather than an implication.","headline":"A useful null result with a load-bearing interpretation that the paper asserts rather than proves.","tokens_in":14237,"tokens_out":2643,"would_cite":true,"duration_ms":25875,"reading_group":"yes","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 the intrinsic transverse-momentum width extracted from Drell-Yan pair spectra is independent of the pair invariant mass at LHC energies, because the non-perturbative Sudakov form factor is only weakly scale dependent.","keywords":["Drell-Yan production","parton branching method","intrinsic transverse momentum","Sudakov form factor","soft gluon emission","transverse momentum dependent PDF","CASCADE3","low transverse momentum"],"falsifier":"A concrete experiment would be to measure the Drell-Yan transverse-momentum spectrum for pair masses around 4 to 20 GeV at a low-energy facility; the paper's own Figure 5 predicts the $q_0$-induced change in integrated PDFs varies rapidly with $\\mu$ there, so $q_s$ should show a visible mass dependence. If $q_s$ stays flat in that region, the weak-scale-dependence explanation would be falsified.","tokens_in":12840,"feed_emoji":"⚛️","tokens_out":12939,"duration_ms":99654,"temperature":0.7,"pith_summary":"Using the Parton Branching method and the CASCADE3 event generator, this paper tries to establish that the intrinsic transverse-momentum width $q_s$ extracted from Drell-Yan pair transverse-momentum spectra is independent of the pair invariant mass for soft-gluon cutoffs up to $q_0 = 2$ GeV over the LHC range, and that this flatness follows from the weak scale dependence of the non-perturbative Sudakov form factor. A sympathetic reader should care because this explains a long-standing discrepancy: shower-based generators see intrinsic-$k_T$ growing with collision energy, while CASCADE3 does not. The paper argues that shower generators effectively drop the non-perturbative part of the Sudakov form factor, so the energy dependence they see is a proxy for missing soft gluons rather than a property of the proton. The paper also shows that final-state QED radiation does not affect the low-$p_T$ region where these non-perturbative effects dominate, so the extraction is not contaminated.","feed_headline":"Drell-Yan transverse-momentum width stays flat in pair mass at LHC","feed_subtitle":"Weak Sudakov scale dependence explains why intrinsic-kT does not grow with energy in the parton branching method.","key_machinery":"The key object is the Sudakov form factor of the Parton Branching method, split into a perturbative and a non-perturbative part, $\\Delta(\\mu^2,\\mu_0^2) = \\Delta^{(\\mathrm{P})}(\\mu^2,\\mu_0^2,q_0^2) \\cdot \\Delta^{(\\mathrm{NP})}(\\mu^2,\\mu_0^2,q_0^2)$, where the separation is set by the dynamic-$z$ scale $z_{\\mathrm{dyn}} = 1 - q_0/q'$ defined by the transverse-momentum cutoff $q_0$. In the PB method $z_M \\to 1$, so all soft gluons are included, while shower generators use $z_M = z_{\\mathrm{dyn}}$, which drops $\\Delta^{(\\mathrm{NP})}$. Applying a $q_0$ cut in CASCADE3 mimics the shower generators, and the fitted width $q_s$ absorbs the missing soft-gluon contribution; the paper's quantitative evidence is the ratio of integrated TMD parton densities with and without the $q_0$ cut, which is nearly $\\mu$-independent in the LHC range but not at low scales.","core_discovery":"The central discovery is that the fitted width $q_s$ -- related to the Gaussian intrinsic-$k_T$ width by $\\sigma = \\sqrt{2}q_s$ -- is flat as a function of the Drell-Yan pair invariant mass $m_{\\ell\\ell}$ across the LHC measurements, for both $q_0 = 1$ GeV and $q_0 = 2$ GeV. The paper explains this flatness by showing that the change in the integrated parton densities induced by the $q_0$ cut is nearly identical at evolution scales $\\mu = 100$ GeV and $\\mu = 500$ GeV, whereas at $\\mu = 4$ GeV and $\\mu = 20$ GeV the change differs strongly. Since the pair mass is identified with the evolution scale $\\mu$ of the Sudakov form factor, the flatness of $q_s$ reflects the insensitivity of the non-perturbative Sudakov factor $\\Delta^{(\\mathrm{NP})}(\\mu^2,\\mu_0^2,q_0^2)$ over the LHC-accessible scale range. The paper therefore concludes that the relative soft-gluon contribution to low-$p_T$ Drell-Yan production is similar across mass bins, and that the energy dependence seen in shower generators is caused by neglecting $\\Delta^{(\\mathrm{NP})}$ through the truncation of the $z$ integral at $z_{\\mathrm{dyn}} = 1 - q_0/q'$.","pith_inferences":["Beyond the paper: if the weak scale dependence of $\\Delta^{(\\mathrm{NP})}$ is the real mechanism, a low-energy fixed-target Drell-Yan experiment at pair masses of a few GeV would be a direct discriminating test, since the paper's Figure 5 predicts $q_s$ should visibly rise with $m_{\\ell\\ell}$ there, unlike at the LHC.","Beyond the paper: the same logic suggests parton-shower generators could be made consistent with the PB results by restoring the non-perturbative Sudakov term rather than by tuning the intrinsic-$k_T$ distribution; a concrete check would be to run a shower generator with $z_M \\to 1$ and see if the fitted width flattens with collision energy.","Beyond the paper: the ratio of integrated PDFs with and without the $q_0$ cut could itself be treated as a quantitative observable $\\mathcal{R}(\\mu,q_0)$ and mapped over $\\mu$; the full curve would let other approaches compare their soft-gluon treatments directly."],"forward_implications":["If the flat $q_s$ is right, the intrinsic-$k_T$ width at $q_0 \\to 0$ (about $1.04 \\pm 0.08$ GeV) is a genuine hadronic property, not a scale-dependent artifact.","The energy dependence of intrinsic-$k_T$ seen in shower-based generators and in CMS data would be understood as a missing non-perturbative Sudakov contribution, not as new physics in the proton.","The relative soft-gluon fraction contributing to the lowest pair transverse momenta is the same in all measured LHC mass bins, so one set of non-perturbative parameters describes the whole mass range from about 50 to 1000 GeV.","At pair masses of a few GeV, where the evolution scale is small, the paper's integrated-PDF analysis predicts a visible change of $q_s$ with mass once such measurements become available."],"supporting_citations":[{"why":"Establishes the CASCADE3-based extraction of q_s and the earlier observation that intrinsic k_T does not depend on sqrt(s) or pair mass.","marker":"[1]"},{"why":"Provides the CMS observation that the intrinsic-kT width depends on collision energy in PYTHIA and HERWIG, the discrepancy this paper explains.","marker":"[2]"},{"why":"Introduces the q_0 cutoff that mimics shower generators and shows q_s grows with q_0, the starting point of this study.","marker":"[3]"},{"why":"Links the q_0 dependence to the role of soft gluons in collinear parton densities.","marker":"[4]"},{"why":"The CASCADE3 event generator used to compute all predictions compared with data.","marker":"[7]"},{"why":"Defines the Parton Branching QCD evolution equations with the soft-gluon resolution scale z_M.","marker":"[8]"},{"why":"Provides the PB-NLO-2018 Set2 TMD densities used for the integrated-PDF comparisons.","marker":"[10]"},{"why":"Supplies the 13 TeV CMS Drell-Yan transverse-momentum measurements across mass bins that yield the q_s values.","marker":"[17]"},{"why":"Supplies the 8 TeV ATLAS measurements used for the lower-mass q_s extraction and QED comparisons.","marker":"[18]"}],"fun_headline_variants":["Intrinsic-kT width flat across Drell-Yan mass at LHC","Sudakov scale dependence keeps Drell-Yan pT width constant","Parton branching: soft-gluon share unchanged with pair mass","Flat q_s in Drell-Yan via non-perturbative Sudakov stability","Drell-Yan mass insensitivity of intrinsic-kT explained"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that a shower generator's cutoff on the soft-gluon momentum fraction is exactly equivalent to omitting the non-perturbative part of the Sudakov form factor, and that the pair mass is the evolution scale.","fun_headline_variants_meta":{"raw":{"variants":["Intrinsic-kT width flat across Drell-Yan mass at LHC","Sudakov scale dependence keeps Drell-Yan pT width constant","Parton branching: soft-gluon share unchanged with pair mass","Flat q_s in Drell-Yan via non-perturbative Sudakov stability","Drell-Yan mass insensitivity of intrinsic-kT explained"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000262,"raw_usage":{"total_tokens":1715,"prompt_tokens":1184,"completion_tokens":531,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":800,"completion_tokens_details":{"reasoning_tokens":435}},"tokens_in":800,"tokens_out":531,"duration_ms":6165,"temperature":1.0,"reasoning_tokens":435,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T04:54:20.979676+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete experiment would be to measure the Drell-Yan transverse-momentum spectrum for pair masses around 4 to 20 GeV at a low-energy facility; the paper's own Figure 5 predicts the $q_0$-induced change in integrated PDFs varies rapidly with $\\mu$ there, so $q_s$ should show a visible mass dependence. If $q_s$ stays flat in that region, the weak-scale-dependence explanation would be falsified.","supporting_citations":[],"review_version":1}