{"id":"b128d79c-d0df-4890-9827-5a10f5c2fd70","arxiv_id":"1908.08524","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Dynamical soft-gluon resolution scales make parton-branching TMD predictions differ from single-emission KMRW at low and high transverse momentum, affecting LHC Z pT spectra.","lead":"This paper studies how the resolution scale for soft-gluon emissions changes with the branching scale in transverse momentum dependent parton evolution, and rewrites the evolution equations in terms of transverse momentum. It shows that the parton branching and KMRW approaches differ strongly at very low and very high pT, and that low-pT Z boson spectra at the LHC are sensitive to this difference.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central-value comparison conflates single-vs-multiple emission with different intrinsic-kT inputs and q0=1 GeV; with no uncertainty bands, the low-pT differences are not uniquely attributable to multiple emission.","rationale":"The paper's formal PB construction and the phase-space mapping in Sec. 3 are internally consistent, and the analytic comparison in Sec. 4 correctly identifies structural differences between the PB and KMRW evolution equations: different scale arguments in the Sudakov factor and collinear density, and different phase-space cutoffs. The 'PB-last-step' diagnostic is a sensible internal check for isolating multiple-emission effects. However, the numerical evidence for the paper's strongest empirical claims is not controlled in the same way. The low-k⊥ behavior of MRW-CT10nlo is generated using a different intrinsic-k⊥ parametrization from the PB calculation, and both the dynamical resolution scale q0 and the intrinsic width k0 are inputs inherited from earlier fits rather than varied here. The paper's own final caveat in Sec. 5.2—only central values are shown, TMD uncertainties for dynamical zM not yet available—marks the comparison with ATLAS data as indicative, not quantitative. A single 'good agreement' without uncertainty bands cannot establish that p⊥<5–10 GeV measurements probe dynamical resolution scales, because the same data would likely be compatible with a range of q0 and k0 choices. This is precisely the conditional-acceptance issue: the central mechanism is plausible and internally coherent, but the headline empirical claim is underdetermined by the presented comparison. The reader's q0/angular-ordering concern is valid; I would extend it to the intrinsic-k⊥ parametrization and the lack of uncertainty estimates, so my read does not change the CONDITIONAL verdict.","tokens_in":11538,"tokens_out":6124,"duration_ms":63407,"concrete_test":"Re-run the Fig. 7 comparison with controlled inputs: (1) generate MRW-CT10nlo with the same Gaussian intrinsic-k⊥ input as PB (k0=0.5 GeV) instead of the flat k⊥<1 GeV parametrization; (2) vary q0 over 0.5, 1, and 2 GeV while holding k0 fixed; (3) add a rough theory-uncertainty band by scanning k0 and renormalization-scale choices. If the low-p⊥ kink and the PB/MRW separation below 10 GeV persist under (1) and (2) outside the band, the multiple-emission interpretation is supported. If they shrink or disappear, the central claim as stated is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Most load-bearing is the numerical support for the empirical claim, not the qualitative multiple-vs-single-emission distinction (which is well motivated). In Sec. 5.1 PB is evaluated with a Gaussian intrinsic-k⊥ distribution of width k0/√2, k0=0.5 GeV, while MRW-CT10nlo is used as published in TMDlib, which uses a flat intrinsic-k⊥ distribution for k⊥<1 GeV [27]. Thus Fig. 4's low-k⊥ kink in MRW and its absence in PB may reflect different nonperturbative inputs rather than the number of emissions. Additionally, the dynamical resolution scale is fixed by q0=1 GeV in Eq. (8), and Sec. 5.2 states only central values are shown because TMD uncertainties for dynamical zM are not yet available. The claim that high-resolution Z-boson measurements with p⊥≲5–10 GeV can quantitatively probe dynamical resolution-scale effects therefore rests on an uncontrolled comparison: q0, the intrinsic-k⊥ shape, and the multiple-emission mechanism are varied together. The analytic comparison in Sec. 4 also sets q0≈µ0 to match KMRW, while the numerics use q0=1 GeV, so the analytic identification of the differences with single vs multiple emission is not directly the one realized in Figs. 4–7.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies transverse-momentum-dependent (TMD) parton distributions in the parton-branching (PB) formalism with a dynamical soft-gluon resolution scale, zM(µ′)=1−q0/µ′. It derives a phase-space mapping from branching scales to transverse momenta in Sec. 3, uses this to compare the PB formulation with the coherent-branching (CMW) and single-emission (KMRW) approaches in Sec. 4, and presents numerical TMDs and Z-boson p⊥ spectra in Sec. 5. The central qualitative claim is that PB builds the initial-state transverse momentum from multiple emissions whereas KMRW builds it from a single last emission, and that the differences are large at low and high k⊥ but small in the intermediate k⊥ region. The paper further claims that the PB calculation describes the ATLAS Z p⊥ spectrum well, while MRW-CT10nlo does not, and that high-resolution measurements with p⊥≲5–10 GeV can probe dynamical resolution-scale effects.","tokens_in":11774,"tokens_out":5987,"duration_ms":54962,"significance":"If established, the multi-emission versus single-emission distinction would be a useful clarification for TMD phenomenology, and the prediction of enhanced sensitivity in the low-p⊥ Z-boson region is falsifiable with high-resolution LHC data. The analytic mapping in Sec. 3 is a genuine contribution, and the use of public codes uPDFevolv and TMDplotter with the same CT10nlo collinear input for PB and KMRW makes the numerical comparison reproducible at the level of the collinear input. These strengths are partially offset by the uncontrolled differences in the nonperturbative inputs discussed below; the significance of the paper therefore depends on whether the authors can isolate the multiple-emission effect from the modeling of the intrinsic-k⊥ distribution and the choice of q0.","major_comments":[{"comment":"The central numerical comparison between PB and MRW-CT10nlo simultaneously varies the number of resolved emissions, the intrinsic-kT parametrization, and the resolution threshold: PB uses a Gaussian intrinsic-kT distribution with width k0/√2, k0=0.5 GeV, while MRW-CT10nlo uses a flat intrinsic-kT distribution for kT<1 GeV, and the PB dynamical scale is fixed by q0=1 GeV. The low-kT kink in MRW-CT10nlo and its absence in PB may therefore reflect the different nonperturbative inputs rather than the single-emission versus multiple-emission mechanism. Please provide a controlled comparison in which the intrinsic-kT distributions are matched (e.g., evaluate PB with a flat intrinsic-kT input, or convolve both TMDs with the same Gaussian smearing) and in which q0 is varied over a plausible range.","section":"Sec. 5.1, Fig. 4"},{"comment":"The analytic comparison with KMRW is made under the condition q0≈µ0 (text preceding Eq. (11)), whereas the numerical PB calculation uses q0=1 GeV and the PB starting scale µ0 from the uPDFevolv setup. Because zM(µ′)=1−q0/µ′ and the phase-space domains in Eqs. (11)–(13) depend on the ratio q0/µ0, the analytic identification of the numerical differences with single-emission versus multiple-emission physics is not the same parameter setting that is realized in Figs. 4–7. Please either repeat the analytic comparison at the numerical values of q0 and µ0, or demonstrate that the conclusions are insensitive to q0/µ0.","section":"Sec. 4 versus Sec. 5.1"},{"comment":"The empirical claim that PB describes the ATLAS Z-boson p⊥ spectrum while MRW-CT10nlo does not is based on central values only; the paper acknowledges that TMD uncertainties for dynamical zM are not yet available. Without uncertainty bands or a variation of q0 and k0, the reader cannot determine whether the differences in the low-p⊥ region are significant. Please add at least a sensitivity scan over q0 (and k0), or estimate the uncertainty by propagating PB Set-2 uncertainties with the dynamical resolution scale.","section":"Sec. 5.2, Fig. 7"},{"comment":"The statement that Eq. (10) agrees with the CMW result, citing Eqs. (42) and (49) of Ref. [9], is made by reference rather than by derivation. Since one of the paper's conclusions is that 'the PB formula coincides with CMW at the level of integrated distributions,' this is a load-bearing point. Please provide the explicit variable transformation and the main steps connecting Eq. (10) to the CMW branching equation, including the treatment of the resolution cut and the running-coupling scale.","section":"Sec. 4, CMW comparison"}],"minor_comments":[{"comment":"The notation ∫ d2µ′/πµ′2 is non-standard; it should be ∫ dµ′^2/µ′^2 (or explicitly defined), since µ′ is a single scale.","section":"Eq. (1)"},{"comment":"The inequality 'q⊥>q 0' should be typeset as q⊥>q0, and q0∼>ΛQCD should be q0≳ΛQCD.","section":"Sec. 2, Eq. (7)"},{"comment":"The definition of PB-last-step should state explicitly whether the intrinsic-kT distribution is included in the transverse momentum assigned to the last emission; otherwise the comparison in Fig. 4 is ambiguous.","section":"Sec. 5.1"},{"comment":"The text alternates between 'MRW-CT10nlo' and 'MRW-ct10nlo'; use one form throughout.","section":"Sec. 5.1"},{"comment":"The notation 'p⊥∼< 5 - 10 GeV' should be written as p⊥≲5–10 GeV.","section":"Sec. 5.2"},{"comment":"Reference [19] is incomplete: it gives no title or journal, only the arXiv number; please supply the full citation.","section":"Ref. [19]"}],"recommendation":"major_revision","confidential_remarks":"The paper's qualitative mechanism is plausible and the analytic mapping is useful, but the central numerical support currently conflates the multiple-emission effect with the intrinsic-kT parametrization and the choice q0=1 GeV. I recommend asking for a matched-input numerical experiment and a sensitivity scan; if those confirm the conclusions, the paper would be suitable for publication. I do not see grounds for rejection at this stage."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a useful, honest paper from the PB TMD group, but the headline phenomenological claim is more fragile than it first appears. What is actually new: the explicit transverse-momentum-space form of the PB branching equations, with the subtraction term for x below 1 - q0/mu0 (Sec. 3.2). That is clean, and it gives the paper a solid formal core. The analytic comparison with KMRW and CMW in Sec. 4 is also well organized, and the numerical comparison is set up fairly: both PB and MRW-CT10nlo start from CT10nlo, and the paper states plainly that only central values are shown.\n\nThe soft spot is the attribution of the numerical differences. The stress-test note has it right: PB uses a Gaussian intrinsic-kT with width k0/√2, k0 = 0.5 GeV, while MRW-CT10nlo from TMDlib uses a flat intrinsic kT below 1 GeV. So the low-kT kink in MRW and its absence in PB, which the text calls a consequence of single versus multiple emission, is at least partly a difference in nonperturbative input shapes. The paper does not separate those effects. Related, the analytic comparison in Sec. 4 sets q0 ≈ mu0 to match KMRW's phase space, but the numerics use q0 = 1 GeV, so the analytic identification is not exactly what the figures are showing. With no uncertainty bands and no scan over q0 and k0, the agreement with ATLAS data is not an independent validation, and the claim that pT below 5–10 GeV can quantitatively probe dynamical resolution scales is not pinned down.\n\nNone of this sinks the paper. The multiple-versus-single-emission distinction is physically well motivated and the formal results stand. But the empirical punchline needs more work: a sensitivity scan over q0 and k0, plus some estimate of the intrinsic-kT shape dependence, before the ATLAS comparison can carry the weight assigned to it.\n\nSend this to peer review. The formal material is worth referee time, and the concerns above are addressable in revision.","headline":"Clean new equations for PB TMDs with dynamical resolution scale, but the paper overreads its low-pT comparison by mixing q0, intrinsic-kT shape, and emission multiplicity.","tokens_in":12347,"tokens_out":3094,"would_cite":true,"duration_ms":29119,"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 claims that initial-state transverse momentum in QCD is built from many angular-ordered emissions rather than a single last emission, and that this is why the low- and high-$p_T$ regions of the $Z$-boson spectrum discriminate…","keywords":["transverse momentum distributions","parton branching","soft-gluon resolution scale","TMD evolution","Drell-Yan Z production","angular ordering","Sudakov form factor","LHC"],"falsifier":"A decisive test would be to recompute the PB prediction with the same inputs but with $q_\\perp$ given by the alternative angular-ordering choice $q_\\perp = z(1-z)\\mu'$, or with $q_0$ varied between 0.5 and 2 GeV, and compare the resulting $Z$ $p_T$ slopes below 10 GeV against finely binned LHC data; if the data no longer prefer the dynamical-resolution-scale shape, the central claim is refuted.","tokens_in":11312,"feed_emoji":"🎯","tokens_out":8949,"duration_ms":87503,"temperature":0.7,"pith_summary":"The paper tries to show that an apparently technical detail of QCD evolution — how finely soft gluons are separated from resolvable radiation — changes the physics of transverse-momentum-dependent (TMD) distributions at hadron colliders. It argues that a parton-branching (PB) picture, where the initial-state transverse momentum accumulates through many angular-ordered emissions, differs sharply from the widely used one-step KMRW picture, where it comes from one last emission. The numerical differences are concentrated at very low and very high transverse momentum, and are small in the middle region. Applied to $Z$-boson production at the LHC, the PB calculation describes the measured transverse-momentum spectrum, while the KMRW-based calculation does not; the low-$p_T$ region is the most sensitive test. The paper concludes that finely binned measurements of the $Z$ $p_T$ spectrum below about 5–10 GeV can quantitatively probe the dynamical resolution scale.","feed_headline":"Many emissions fit the Z spectrum; one emission does not","feed_subtitle":"Parton branching with many emissions reproduces the measured Z-boson spectrum; the one-emission version fails at low and high pT.","key_machinery":"The load-bearing object is the dynamical soft-gluon resolution scale $z_M(\\mu') = 1 - q_0/\\mu'$, which separates resolvable branchings ($z < z_M$) from non-resolvable ones. It is derived from the requirement that an emitted parton have transverse momentum $q_\\perp = (1-z)\\mu'$ above the minimum resolvable value $q_0 \\sim 1$ GeV. Because $z_M$ depends on the branching scale $\\mu'$, both the real-emission kernel and the Sudakov form factor in the PB evolution equation acquire a scale-dependent phase-space boundary. This is the mechanism that puts multiple emissions into the transverse momentum and generates the differences with the single-emission KMRW approach.","core_discovery":"In the parton branching method, the soft-gluon resolution scale is a function of the branching scale, $z_M(\\mu') = 1 - q_0/\\mu'$, with the angular-ordering relation $q_\\perp = (1-z)\\mu'$ fixing the transverse momentum of the emitted parton. With this dynamical scale, the PB equation for integrated distributions coincides with the coherent-branching (CMW) equation, but the PB and KMRW descriptions of how $k_\\perp$ is built up are different: PB sums the recoils of all resolvable branchings, KMRW keeps only the last emission. The paper shows analytically and numerically that this structural difference makes the two TMDs disagree strongly for $k_\\perp \\ll \\mu$ and $k_\\perp \\gg \\mu$, while they nearly coincide for $k_\\perp \\sim \\mu$. For $Z$-boson production, the multiple-emission PB prediction matches the measured LHC $p_T$ spectrum, and the slope at low $p_T$ is sensitive to the dynamical resolution scale, so measurements with fine bins in the region $p_T \\lesssim 5$–10 GeV could test the effect.","pith_inferences":["If the dynamical resolution scale is the right description, the same multiple-emission logic should also leave visible signatures in other Drell-Yan observables, such as the $W$ boson transverse momentum or low-mass dilepton spectra; the paper does not compute these predictions.","A way to isolate the single-versus-multiple-emission difference from phase-space choices would be to compare PB with a version of KMRW whose Sudakov form factor satisfies the no-branching probability product rule given in Eq. (19).","The paper's PB-last-step variant is an internal control: a quantitative match between PB-last-step and KMRW would confirm that the single-emission picture, not the PDF set or intrinsic-$k_\\perp$ smearing, drives the KMRW discrepancy.","Future high-luminosity data with small $p_T$ bins could turn the fitted value of $q_0$ into a measurable nonperturbative parameter, effectively pinning down the minimum transverse momentum at which a gluon is resolvable."],"forward_implications":["The $Z$-boson transverse momentum spectrum at the LHC, measured with fine binning in the region $p_T \\lesssim 5$–10 GeV, can act as a direct probe of soft-gluon angular ordering and of whether the resolution scale is dynamical.","PB and CMW agree at the level of integrated distributions, so the multiple-emission picture is consistent with established coherent-branching results; KMRW is the outlier among the three.","The largest differences between PB and KMRW TMDs lie at $k_\\perp \\ll \\mu$ and $k_\\perp \\gg \\mu$, with only mild differences near $k_\\perp \\sim \\mu$.","Because the integrated KMRW TMDs do not reduce to the collinear input PDF at all $k_\\perp$, the choice of resolution scale also affects how much of the distribution sits in the high-transverse-momentum tail."],"supporting_citations":[{"why":"Defines the parton branching TMD formalism and its iterative solution, which this paper extends with a dynamical resolution scale.","marker":"[3,4]"},{"why":"The CMW coherent-branching equations that PB is shown to reproduce at integrated level; supplies the angular-ordering input.","marker":"[9,10]"},{"why":"Provides the Monte Carlo solution method used to obtain the numerical PB TMDs and spectra.","marker":"[12]"},{"why":"Defines the KMRW single-emission TMD construction that PB is compared against.","marker":"[13–16]"},{"why":"Establishes the Drell-Yan application method and the fixed-resolution PB set used as a baseline in the Z pT comparison.","marker":"[18]"},{"why":"Supplies the KMRW TMD set used for the numerical comparison.","marker":"[27]"},{"why":"Provides the common starting collinear PDF for both PB and KMRW calculations.","marker":"[28]"},{"why":"The LHC Z-boson pT measurement against which the PB and KMRW predictions are compared.","marker":"[31]"}],"fun_headline_variants":["Many emissions fit Z spectrum; single emission fails at LHC","Dynamical resolution scale alters TMD evolution and Z pT","PB with recoils matches Z pT; KMRW last-emission does not","Low pT slope in Z production probes resolution scale","One emission fails low and high pT; many emissions succeed"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole low-$p_T$ conclusion hangs on two calibration choices: that a branching's transverse momentum is exactly $(1-z)$ times its scale, and that a gluon becomes resolvable only above 1 GeV; with different choices, the difference between the multiple-emission and single-emission results could vanish.","fun_headline_variants_meta":{"raw":{"variants":["Many emissions fit Z spectrum; single emission fails at LHC","Dynamical resolution scale alters TMD evolution and Z pT","PB with recoils matches Z pT; KMRW last-emission does not","Low pT slope in Z production probes resolution scale","One emission fails low and high pT; many emissions succeed"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000313,"raw_usage":{"total_tokens":1765,"prompt_tokens":915,"completion_tokens":850,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":531,"completion_tokens_details":{"reasoning_tokens":760}},"tokens_in":531,"tokens_out":850,"duration_ms":9202,"temperature":1.0,"reasoning_tokens":760,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:37:42.195013+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive test would be to recompute the PB prediction with the same inputs but with $q_\\perp$ given by the alternative angular-ordering choice $q_\\perp = z(1-z)\\mu'$, or with $q_0$ varied between 0.5 and 2 GeV, and compare the resulting $Z$ $p_T$ slopes below 10 GeV against finely binned LHC data; if the data no longer prefer the dynamical-resolution-scale shape, the central claim is refuted.","supporting_citations":[{"cited_title":"Calculations with off-shell matrix elements, TMD parton densities and TMD parton showers","cited_arxiv_id":"1712.05932","evidence_quote":"Supplies the KMRW TMD set used for the numerical comparison."}],"review_version":1}