{"id":"4505a7f0-f77a-4112-a07f-fd8a99d39c53","arxiv_id":"2505.13183","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Subleading-color corrections in soft gluon evolution alter the differential shape of inter-jet radiation, and these shape effects can cancel only after integrating over large angular regions.","lead":"This paper calculates the exact color structure of extra gluon radiation in jet-producing collisions, going beyond the usual large-color approximation. It shows the corrections change where radiation is emitted, which matters for precise predictions at future colliders and for color reconnection models.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Coulomb/Glauber exchanges are switched off, and Appendix A shows a 10% cutoff-sensitive effect at rho=0.1, so the claimed differential shape distortions may not survive in full QCD.","rationale":"The reader identified Coulomb/Glauber exchange as the weakest assumption, and the manuscript itself flags the omission in Section 2 and Appendix A. My read agrees with that choice. The central claim is that subleading colour changes differential shapes, not just normalization. For that claim to hold in QCD, the omitted Coulomb sector must not materially alter the angular pattern of the highest-energy inter-jet gluon. Appendix A gives direct evidence that Coulomb exchanges can shift integrated results by about 10% at rho = 0.1 in the same q qbar -> q qbar process, with collinear-cutoff sensitivity. Since the paper's headline residuals range from roughly 5% to 40%, the omitted contribution is of the same order as the effects being interpreted. A precise differential rerun with Coulomb exchanges included for two collinear cutoffs would settle whether the shape conclusions survive. I do not see an internal inconsistency in the evolution framework; the event-generator versus dedicated-mode check in Fig. 1 is a meaningful validation and the fixed-order/colour-flow arguments are coherent. The issue is therefore a condition on the physical completeness of the result, which supports the reader's CONDITIONAL verdict rather than a rejection. No change to the verdict is needed.","tokens_in":11984,"tokens_out":2730,"duration_ms":29036,"concrete_test":"Use CVolver to recompute the q qbar to q qbar back-to-back, boosted, and recoiling dSigma/d(cos theta) and dSigma/dphi at r = 0.3 with Coulomb exchanges enabled for two collinear cutoffs, e.g. lambda = 0.001 and lambda = 0.0005, exactly as in Appendix A but differential. Then compare the full-vs-leading-colour residuals to those in Figs. 5, 7, 8, 9, 11 and 12. If including Coulomb exchanges shifts any residual by more than the claimed shape effect, or shows strong lambda-dependence at r = 0.3, the headline conclusion is not robust. If the Coulomb-induced changes are at the few-percent level and cutoff-independent at r = 0.3, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim—that subleading colour changes the shape of differential inter-jet radiation and that leading-colour evolution can fail for s- and t-channel exchange—is obtained with Coulomb (Glauber) exchanges deliberately switched off (Section 2). This is not a harmless technicality: without hard-collinear physics, Coulomb exchanges produce super-leading logarithms regulated by the collinear cutoff, and Appendix A shows that including them changes the q qbar to q qbar jet-veto cross section by about 10% at rho = 0.1 (Fig. 14), with residual collinear-cutoff dependence. The main differential results are presented at r = 0.3 with no uncertainty bands and no comparison against a calculation that includes Coulomb exchanges. Since Coulomb exchanges act on colour-density matrices and can swap colour flows, an omitted contribution of this size could flatten, steepen, or partially cancel the claimed 5-10% (|01><01|), 10% (s-channel dSigma/dphi), and 40% (s-channel dSigma/dcos theta) shape residuals. The statement in Section 4.2 that s-channel gluon exchange 'completely fails to be described by leading colour evolution' is therefore not yet established for full QCD. The concern is about completeness of the physical input, not internal inconsistency; the event-generator/dedicated-mode agreement in Fig. 1 is a genuine check but does not cover Coulomb effects.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses the CVolver amplitude-level evolution code in event-generator mode to compute fully differential soft-gluon observables for several 2-to-2 QCD processes and a four-parton e+e- final state. It compares full-colour and leading-colour evolution for the differential cross section of the highest-energy gluon emitted outside the jet/veto region, presenting dSigma/dOmega, dSigma/dcos(theta), dSigma/dphi and residual ratios. The main claims are that subleading colour corrections can change the shape of these distributions, that the s-channel gluon-exchange contribution is poorly described by leading-colour evolution, and that t-channel gluon exchange, which is well described in back-to-back and boosted configurations after cancellations, fails in the recoiling configuration. Coulomb/Glauber exchanges are deliberately omitted, and Appendix A quantifies their effect on the integrated jet-veto cross section at about 10% in one configuration.","tokens_in":12414,"tokens_out":8341,"duration_ms":75346,"significance":"If the results are correct, they provide a qualitative challenge to the common assumption that leading-colour evolution describes inter-jet radiation patterns up to an overall normalization, and they identify differential observables for which subleading colour matters. The event-generator versus dedicated-mode check in Fig. 1 is a strong internal consistency test, and the study is genuinely exploratory: no parameter is fitted to produce the claimed shapes, and the work is a step toward full-colour Monte Carlo event generation. The significance is, however, tempered by the omission of Coulomb/Glauber exchanges and by the absence of statistical uncertainties in the differential plots, both of which bear directly on the quantitative statements.","major_comments":[{"comment":"The central claims are presented as full-colour results, but the evolution is computed with Coulomb (Glauber) exchanges switched off. Section 2 states that this is necessary because, without hard-collinear physics, Coulomb exchanges generate super-leading logarithms regulated by the collinear cutoff. Appendix A then shows that including Coulomb exchanges changes the q qbar to q qbar jet-veto cross section by about 10% at rho=0.1 (Fig. 14) and that this residual is collinear-cutoff independent at high rho. Because Coulomb exchanges act on the colour-density matrix and can swap colour flows, they can in principle modify the differential shape residuals on which the paper's claims rest, e.g. the 40% s-channel effect in Section 4.1 and the claimed failure of leading colour for t-channel exchange in Section 4.3. As written, the Abstract and Conclusions assert without qualification that 'subleading colour does affect the shapes of distributions' and that the approximations 'fail'; these statements are established only in the no-Coulomb approximation. The authors should either include Coulomb exchanges in the differential analysis, estimate their differential impact, or explicitly and consistently qualify all central claims as conditional on neglecting Coulomb/Glauber contributions.","section":"Section 2 and Appendix A"},{"comment":"None of the differential plots carry uncertainty bands or error bars, and the text repeatedly refers to 'fluctuations' without quantifying them (Sections 4.1 and 4.2). The quantitative claims—5-10% shape residuals in the |01><01| contribution, ~10% in the s-channel dSigma/dphi, 40% between the edges and middle of the veto region, and ~10% enhancement in the recoiling configuration—require a statement of the statistical precision of the event-generator mode, especially because the residuals are ratios of full-colour to leading-colour results. The authors should provide confidence bands or at least per-bin uncertainties for the residual panels so that the reader can distinguish genuine shape distortions from Monte Carlo noise.","section":"Figures 5-12"},{"comment":"The paper chooses r=0.3 throughout to avoid missing contributions from >=7 gluon emissions, which are visible at large rho in Fig. 1. However, no convergence test is shown for the differential observables at r=0.3: the figures break down the results by multiplicity, but they do not compare a five-emission-truncated result with the six-emission result to demonstrate that the sixth emission is negligible in each kinematic configuration and colour channel. This matters because the strongest claims, such as the failure of leading colour for s-channel exchange in Section 4.2, are made for the full six-emission evolution. The authors should add a convergence check, e.g. the relative difference between truncation at n and n-1 emissions for the integrated and differential quantities, or explicitly quantify the residual truncation uncertainty.","section":"Section 2 and Fig. 1"}],"minor_comments":[{"comment":"The numerical values of the collinear cutoff lambda are not given for the main results; the text says it is 'sufficiently small' and refers to [1]. For reproducibility, please state the value or values used for each figure.","section":"Section 2"},{"comment":"The notation dSigma/dOmega used throughout the paper suppresses the r-dependence of d^2Sigma(r)/dOmega defined in Eq. (2.2). Please make the r-dependence explicit or state once that r=0.3 for all results.","section":"Section 2, Eq. (2.2)"},{"comment":"The sentence 'In both cases we consider the back-to-back kinematic configuration considered in the main text' is confusing, since Z->q qbar is not analysed in the main text; please clarify the geometry used for this process.","section":"Appendix A"},{"comment":"The abbreviation L1, LCH is used without definition in this paper. Since the comparison depends on this leading-colour choice, please define it or give a precise reference to the partner paper [1].","section":"Sections 4.1 and 4.2"}],"recommendation":"major_revision","confidential_remarks":"The paper is transparent about the Coulomb omission, but the abstract and conclusions overgeneralize. The referee's main concern is the combination of omitted Coulomb exchanges and absent error bars, which makes the quantitative shape claims difficult to evaluate. The underlying methodology and the event-generator check in Fig. 1 are sound, and I would support a revised version that adds uncertainties, a convergence check, and either Coulomb estimates or appropriately conditional wording."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper extends CVolver from integrated jet-veto cross sections to fully differential distributions of the highest-energy inter-jet gluon, and it passes a genuine internal check: the new event-generator mode reproduces the dedicated-mode results for the |10><10| and interference contributions exactly, with different multiplicity structures. The main qualitative finding—subleading color can change the shape, not just the normalization, of radiation patterns—is plausible and consistently reproduced across back-to-back, boosted, and recoiling kinematics. The t-channel cancellation story, where the |01><01| enhancement is cancelled by interference and subleading |10><10| contributions, is a nice illustration of how integrated observables can hide differential effects.\n\nThe paper is honest about its limits. It states that Coulomb/Glauber exchanges are turned off because, absent hard-collinear physics, they generate super-leading logarithms regulated by the collinear cutoff. Appendix A shows that including Coulomb changes the qbar-q veto cross section by about 10% at rho=0.1, with some residual cutoff dependence. That means the headline claim—that s-channel exchange \"completely fails\" at leading color—is not yet established for full QCD. It could survive, but a 10% shift in the underlying cross section could easily alter 40% shape residuals. This is a completeness concern, not an internal inconsistency. The authors acknowledge they plan to return to Coulomb in a later study.\n\nOther soft spots are minor in comparison. The plots carry no uncertainty bands; the authors mention fluctuations but do not quantify them. The restriction to r=0.3 is explained by the six-emission cap, and is fine for a proof-of-concept. The event-generator code is not released, though the internal check partly compensates.\n\nThis is a solid paper for a specialized audience. It deserves a serious referee. A referee should ask for uncertainty estimates and a discussion of Coulomb effects on the differential shapes, but the core check and the new differential results justify publication after revision.","headline":"Genuine internal check, honest Coulomb caveat, and a shape-distortion claim that is provisional but worth refereeing.","tokens_in":12774,"tokens_out":3155,"would_cite":true,"duration_ms":30474,"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":"Subleading colour corrections change the shape of inter-jet soft gluon radiation, not just its overall rate.","keywords":["soft gluon evolution","subleading colour","colour flow","jet veto","non-global logarithms","amplitude-level resummation","inter-jet radiation","full colour QCD"],"falsifier":"Repeat the same full-colour evolution with the phase-type exchanges included (regulating the resulting super-leading logarithms with hard-collinear physics) and compare $\\mathrm{d}\\Sigma/\\mathrm{d}(\\cos\\theta)$ and $\\mathrm{d}\\Sigma/\\mathrm{d}\\phi$ for the $s$- and $t$-channel contributions; if the residuals against leading colour flatten to a constant normalisation, the claim that subleading colour changes shapes is overturned. A cheaper proxy is the $\\rho=0.1$ comparison in Appendix A, where the phase-type exchanges already shift the integrated cross section by about 10%.","tokens_in":11774,"feed_emoji":"⚛️","tokens_out":8349,"duration_ms":82163,"temperature":0.7,"pith_summary":"This paper asks whether the subleading-colour corrections that QCD resummation must include change only the overall size of inter-jet soft gluon radiation, or also its angular shape. By evolving soft gluon emissions at the amplitude level with all colour corrections, the authors compare full-colour differential distributions with the strictly leading-colour approximation for $q\\bar q\\to q\\bar q$ and for a colourless-initiated four-jet final state. They find that subleading colour does change shapes, not just normalisation: the $s$-channel gluon exchange contribution is badly described by leading colour, and the $t$-channel approximation fails when the jets recoil. This matters because inclusive observables such as gaps-between-jets can hide these effects after integrating over solid angle, so measurements and simulations that assume leading colour for differential radiation patterns can be wrong.","feed_headline":"Subleading colour reshapes inter-jet radiation, not just rates","feed_subtitle":"Full-colour resummation shows leading-colour approximations can fail for t-channel jets with a recoil.","key_machinery":"The machinery is amplitude-level soft gluon evolution in a colour-flow basis: real and virtual emissions act on a density matrix whose entries are colour-flow configurations, here $|01\\rangle$ and $|10\\rangle$ and their interference, so that virtual gluon exchange can change the colour configuration instead of only adding a phase to a fixed dipole. The observable that carries the argument is the triple-differential cross section $\\mathrm{d}^3\\sigma/\\mathrm{d}\\Omega\\,\\mathrm{d}\\rho$ for the highest-energy gluon emitted into the veto region, integrated into $\\mathrm{d}\\Sigma/\\mathrm{d}(\\cos\\theta)$ and $\\mathrm{d}\\Sigma/\\mathrm{d}\\phi$. This is what exposes subleading-colour shape effects that vanish in fully inclusive integrals.","core_discovery":"The central claim is that full-colour soft gluon evolution produces differential radiation patterns that leading-colour evolution cannot reproduce, and that the apparent success of leading colour in inclusive veto cross sections relies on cancellations across phase space. In the $q\\bar q\\to q\\bar q$ back-to-back configuration the $s$-channel contribution shows a roughly 40% shape difference between the edges and the middle of the veto region, while the $|01\\rangle\\langle01|$ contribution shows 5\\textendash 10% residual shape effects and the $t$-channel contribution appears flat once interference is included. In the recoiling configuration, which mimics vector-boson-fusion-like topologies, even the $t$-channel gluon exchange contribution fails to be described by the strictly leading-colour approximation, and the $|10\\rangle\\langle01|$ interference contribution radiates with a distinctly steeper pattern despite having no leading-colour dipoles.","pith_inferences":["I infer that observables integrating over a smaller solid-angle patch, such as azimuthal asymmetries or wedge jet shapes around a rapidity gap, will show larger subleading-colour distortions than the 5\\textendash 40% residuals reported for the full veto region.","The recoiling-configuration failure suggests vector-boson-fusion-like topologies at hadron colliders are the most promising place to look for subleading-colour shape effects experimentally, e.g. in the angular distribution of the third jet.","If the neglected non-Abelian phase (Coulomb-type) exchanges are included, the picture may change: the appendix's roughly 10% shift at $\\rho=0.1$ is a lower bound on the possible distortion of the differential patterns, and the true shape residuals could be larger once super-leading logarithms are regulated.","A natural next step would be to feed the same amplitude-level evolution into a parton shower for collinear-sensitive observables; that would test whether subleading-colour shape effects extend into jet substructure."],"forward_implications":["Inclusive jet-veto cross sections cannot certify leading-colour accuracy; shape effects that cancel in the angular integral will survive in more differential measurements.","Event generators and resummation tools that emit only from leading-colour dipoles will mispredict the angular distribution of the hardest inter-jet gluon for $s$-channel exchange and for $t$-channel processes with recoil.","The $|10\\rangle\\langle01|$ interference term, although $1/N_c^2$-suppressed and absent at leading colour, contributes a numerically visible and differently shaped radiation pattern.","Colour-reconnection studies using $ZZ\\to$ four jets at lepton colliders need the full-colour interference pattern as the reference, rather than a leading-colour or model-based guess."],"supporting_citations":[{"why":"Partner paper on exact colour evolution for jet observables; supplies the hard-scatter colour-flow density matrices and the dedicated-mode veto-cross-section results the generator mode must match.","marker":"[1]"},{"why":"Introduces the colour-flow evolution and tower summation method that the paper's full-colour numerical evolution is built on.","marker":"[2]"},{"why":"Earlier resummation and simulation of soft gluon effects beyond leading colour; provides the dedicated-mode baseline and the beyond-leading-colour framework extended here.","marker":"[3]"},{"why":"Sets out the amplitude-level soft gluon evolution and the treatment of non-global logarithms that underlies the differential cross section used.","marker":"[4]"},{"why":"Defines the colour evolution and infrared physics, including the collinear-anomalous-dimension reasoning that justifies omitting the phase-type exchanges in the present calculation.","marker":"[5]"},{"why":"Document the leading-colour approximation's success for t-channel gaps-between-jets observables, the claim this paper stress-tests and finds to fail in the recoiling configuration.","marker":"[10, 11]"}],"fun_headline_variants":["Full-colour resummation exposes hidden shape effects in QCD jets","Leading-colour fails: subleading corrections reshape jet radiation","Shapes of QCD jets shift under full colour, not just rates","Subleading colour twists jet shapes in ways leading colour misses","Soft gluon evolution at full colour: shape surprises for jets"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes the non-Abelian phase-type (Coulomb or Glauber) gluon exchange can be turned off, and Appendix A shows that including it changes the $q\\bar q\\to q\\bar q$ integrated cross section by about 10% at $\\rho=0.1$, so the differential patterns could shift once those exchanges and hard-collinear physics are added.","fun_headline_variants_meta":{"raw":{"variants":["Full-colour resummation exposes hidden shape effects in QCD jets","Leading-colour fails: subleading corrections reshape jet radiation","Shapes of QCD jets shift under full colour, not just rates","Subleading colour twists jet shapes in ways leading colour misses","Soft gluon evolution at full colour: shape surprises for jets"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001454,"raw_usage":{"total_tokens":5779,"prompt_tokens":797,"completion_tokens":4982,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":413,"completion_tokens_details":{"reasoning_tokens":4908}},"tokens_in":413,"tokens_out":4982,"duration_ms":36961,"temperature":1.0,"reasoning_tokens":4908,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:17:32.251529+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the same full-colour evolution with the phase-type exchanges included (regulating the resulting super-leading logarithms with hard-collinear physics) and compare $\\mathrm{d}\\Sigma/\\mathrm{d}(\\cos\\theta)$ and $\\mathrm{d}\\Sigma/\\mathrm{d}\\phi$ for the $s$- and $t$-channel contributions; if the residuals against leading colour flatten to a constant normalisation, the claim that subleading colour changes shapes is overturned. A cheaper proxy is the $\\rho=0.1$ comparison in Appendix A, where the phase-type exchanges already shift the integrated cross section by about 10%.","supporting_citations":[],"review_version":1}