{"id":"6beacd20-7bc4-4d8e-b4f6-b778d1f3c7ab","arxiv_id":"2505.01340","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The paper proposes a universal relation between the leading logarithmic coefficient and the mass-factorization pole for jet-associated production of any massive colourless particle.","lead":"This physics paper argues that certain next-order logarithmic corrections for making a heavy particle (W, Z, or Higgs) together with a jet follow one universal formula. If correct, it would let theorists compute these corrections more easily for LHC processes, though the proof for the W and Z cases is deferred.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed universality rests on Eq. (18), which is asserted without showing the angular integration, and on spin-1 W/Z results that the paper explicitly defers; neither the integration lemma nor the W/Z calculation is supplied.","rationale":"The reader's weakest-assumption identification is correct: Eq. (18) is the load-bearing step, and the paper does not show the angular integration that is claimed to yield it. I agree that the W/Z extension is also not demonstrated, since the paper itself defers those calculations. The previous H+jet results in refs. [92,96] and Eqs. (19)-(20) provide some evidence that the formalism works for spin-0, but they do not supply the proof of the general relation nor the spin-1 check. The paper's conclusion overstates the result as a demonstration when the core derivation is an unshown lemma and the main new application is deferred. A future version with the explicit angular integrals, a clear derivation of Eq. (15)'s convolution reduction, or an actual W/Z calculation could change this assessment, but as it stands the REJECT verdict is reasonable.","tokens_in":12047,"tokens_out":14210,"duration_ms":164071,"concrete_test":"Perform the angular integrations in Eq. (13) symbolically for the six term types (1/s_i5 and s_i5/(s_{i+1}5 s_{i+2}5)) with generic coefficients obtained from the soft-gluon theorem (Eq. (2)) and the soft-quark operators (Eq. (4)), and verify term-by-term that the coefficient of log(s45/\\bar\\mu^2) equals minus the residue of the 1/epsilon pole. Then substitute the H+jet coefficients and check that Eqs. (19)-(20) are reproduced. If any term violates the residue-log relation, or if the H+jet check fails, Eq. (18) is disproved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central pivot is Eq. (18), C_LL = -C_-1. The text in Section IV says that the Eikonal structure produces six term types and that 'upon performing the angular integration of these terms ... it follows straightforwardly' that the relation holds, but the angular integrals over theta1 and theta2 in Eq. (13) are not shown. For the claim to be valid, the coefficient of log(s45/\\bar\\mu^2) must equal minus the residue of the 1/epsilon pole for every term type, and the 1/epsilon pole itself must be fully accounted for by the initial-state mass-factorization expression in Eq. (15). Neither is demonstrated. In particular, Eq. (15) defines C_-1 through convolutions over x1 and x2 with the Born cross-section, yet the paper does not show how these convolutions reduce to a local coefficient multiplying (A)^2 in Eq. (14). If additional finite pieces from the angular integrals contribute to the log, or if final-state collinear or soft-virtual contributions contribute to C_-1, the relation fails. Furthermore, the W/Z results in Eqs. (21)-(22) are introduced as 'anticipated' and 'expected', and the paper explicitly states that a complete calculation for W and Z production is beyond its scope. Thus the abstract's claim that the paper demonstrates universality for arbitrary massive colourless particles exceeds what is actually derived.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes that the next-to-leading-power (NLP) leading logarithms for the production of an arbitrary massive colourless particle in association with a jet have a universal analytic form. The authors argue that the coefficient of the NLP leading logarithm, C_LL, is equal to minus the mass-factorization pole coefficient C_{-1}, so that the NLP logarithms can be obtained from helicity-dependent Altarelli-Parisi splitting functions alone. They illustrate this with explicit Higgs+jet results from their previous work and then give 'anticipated' formulas for W+jet production, while explicitly stating that a complete W/Z calculation is beyond the scope of the paper.","tokens_in":12361,"tokens_out":5299,"duration_ms":58016,"significance":"If the central relation C_LL = -C_{-1} is correct, the result would be practically valuable: it would reduce the computation of NLP leading logarithms for jet-associated colour-singlet processes to mass factorization and helicity-dependent splitting kernels, avoiding the difficult phase-space integrals that have prevented complete V+jet NLP calculations. The paper also makes concrete, checkable predictions in Eqs. (19)-(22) and draws on the authors' earlier Higgs+jet calculations. However, the generalization to arbitrary massive colourless particles is not derived: the W/Z formulas are stated as expectations, and the key angular-integration step behind Eq. (18) is asserted rather than shown. As it stands, the manuscript is better described as a research proposal than as a demonstration of universality.","major_comments":[{"comment":"The central relation C_LL = -C_{-1} is stated to follow 'straightforwardly' from the angular integration of the Eikonal-structured squared amplitudes, but the integration over theta1 and theta2 in Eq. (13) is not shown. No integrals for the six term types are displayed, and no argument is given that finite pieces from the angular integrals cannot contribute to the coefficient of log(s45/bar_mu^2). Because Eq. (18) is the load-bearing step for the claimed universality, this omission is substantive rather than a presentation issue.","section":"Section IV, Eq. (18)"},{"comment":"Mass factorization defines C_{-1} through convolutions over x1 and x2 of Gamma with the Born cross-section, but Eq. (14) assumes that the result is a local coefficient multiplying (A^{h1h2h3h4})^2. The reduction of the convolutions to this local form is not demonstrated, and the treatment of final-state collinear or soft-virtual contributions to C_{-1} is not discussed. Without this step, the equality C_LL = -C_{-1} cannot be verified from the mass-factorization expression alone.","section":"Section IV, Eq. (15)"},{"comment":"The W/Z coefficients are introduced as 'expected' and 'anticipated', and the text explicitly states that 'a complete and explicit calculation of the NLP contributions for W^+- and Z-boson production in association with a jet is beyond the scope of this article'. The abstract nonetheless claims demonstration of universality for arbitrary massive colourless particles. This exceeds what is actually derived; the authors should either provide the explicit spin-1 derivation or substantially weaken the universality claim to a conjecture supported by the Higgs+jet case.","section":"Section IV, Eqs. (21)-(22)"}],"minor_comments":[{"comment":"The text contains a typo: 'Altareli-Parisi' should be 'Altarelli-Parisi'.","section":"Section IV"},{"comment":"The notation 'C45 1/(s45)+' is not defined; if this is a plus distribution, it should be written explicitly, and the relation of this term to the log term should be clarified.","section":"Section III, Eq. (14)"},{"comment":"The captions say that F and |A|^2 are excluded, and the vertical axis is labelled as CLL rather than the barred quantity mentioned in the text; please make this notation consistent.","section":"Figures 1 and 2"},{"comment":"The paper says earlier vector-boson-plus-jet studies did not provide complete NLP logarithms, but it does not explain why the results of those references are insufficient or how the present proposal differs from them; a brief comparison would help the reader.","section":"Introduction, references [90,91]"}],"recommendation":"reject","confidential_remarks":"The central equation of the paper, Eq. (18), is not derived, and the spin-1 generalization is explicitly left to future work. The claims in the title and abstract go beyond the demonstrated content. I would not recommend considering this for publication in its present form; the authors would need to either supply the missing derivations or reframe the paper as a conjecture."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Pal and Seth have a clean idea: use mass factorization with helicity-dependent splitting functions to determine the NLP threshold logarithms in any colourless-plus-jet process, and claim a universal relation C_LL = -C_-1. If true, this would be a practical shortcut for a class of LHC processes that have so far resisted explicit calculation. The paper does a good job of laying out the structural argument, connecting it to the authors' previous Higgs+jet results, and giving explicit expected forms for W/Z in eqs. (21)-(22). The use of colour-ordered amplitudes and the two operators for soft quarks is coherent and internally consistent. That is the good part.\n\nThe soft spot is the central pivot. Eq. (18) is the whole ballgame, and it is not derived in the paper. The six eikonal terms are said to yield C_LL = -C_-1 'straightforwardly' after angular integration, but the integrals are not shown, and the convolution in eq. (15) is not shown to reduce to a local coefficient. That is a load-bearing gap: a referee cannot check the main claim without either redoing the calculation or trusting the authors' prior work. The authors may well be right, but the paper as written asks the reader to accept the step on faith. Then there is the spin-1 issue: eqs. (21)-(22) are explicitly 'anticipated' and 'expected', and the paper states that a complete W/Z calculation is beyond its scope. The abstract's 'we demonstrate' overstates this. A conjecture is fine, but label it as such.\n\nThe reliance on the authors' own formalism (refs [92,96]) is not a flaw; the caution about helicity configurations, however, is a caveat that could shrink the universality claim. The paper is honest about the limitation, but that limits its reach.\n\nWho is this for? Specialists in threshold resummation and NLP corrections, especially for jet-associated production. It works as a research note that frames a tractable target for explicit calculation. I would not cite it as a proof, but I would cite it as a conjecture worth checking.\n\nFor peer review: send it out. A good referee could either verify the angular integration or ask for the W/Z computation as a condition for publication. The idea is important enough to merit a referee's time, and the paper is coherent enough to be salvageable. But as it stands, it does not support the full claim in the abstract.","headline":"The universal relation C_LL = -C_-1 is a clean, plausible conjecture, but the paper asserts the key angular integration rather than showing it, and the spin-1 W/Z results are explicitly deferred; the abstract overstates what is demonstrated.","tokens_in":12848,"tokens_out":3048,"would_cite":false,"duration_ms":30798,"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":"For any colourless particle produced with a jet, the leading logarithmic corrections at next-to-leading power have a universal coefficient set by mass factorization.","keywords":["next-to-leading power","threshold logarithms","universality","jet-associated production","mass factorization","helicity amplitudes","soft quark operators","QCD resummation"],"falsifier":"Compute the full NLP leading-logarithmic coefficient for $W^+$+jet (or $Z$+jet) by explicit phase-space integration of the colour-ordered helicity amplitudes for a fixed helicity configuration, and compare the coefficient of $\\log(s_{45}/\\bar\\mu^2)$ with $-C_{-1}$ obtained from the mass-factorization expression in eq. (15) using helicity-dependent splitting functions. Any mismatch would falsify the universal relation.","tokens_in":11800,"feed_emoji":"⚛️","tokens_out":7520,"duration_ms":73730,"temperature":0.7,"pith_summary":"This paper tries to establish that the leading logarithmic corrections at next-to-leading power (NLP) for producing a colourless particle together with a jet are universal: their coefficient is fixed by mass factorization through helicity-dependent Altarelli-Parisi splitting functions, and is simply the negative of the infrared-divergence coefficient. The key identity is $C_{LL} = -C_{-1}$. If true, this removes the need for process-specific phase-space integrations when extracting these corrections, and applies to Higgs, $W$, $Z$, and photon plus jet production. It also unifies the two physically distinct sources of these logarithms, next-to-soft gluon radiation and soft quark radiation, under one formula.","feed_headline":"Jet-associated production logs obey one universal formula","feed_subtitle":"The leading next-to-leading-power logarithms equal minus the mass-factorization pole, for any colourless particle plus a jet.","key_machinery":"The central object is the identity $C_{LL} = -C_{-1}$ (eq. (18)), with $C_{-1}$ fixed by mass factorization through eq. (15) and the helicity-dependent Altarelli-Parisi splitting kernels. What makes the argument run is the colour-ordered helicity-amplitude formalism: next-to-soft gluon emission is handled by the subleading soft theorem, while soft quark emission is handled by operators that merge the soft quark with the adjacent hard coloured particle. Because the Eikonal factor multiplies the squared NLP amplitudes, the angular integrals reduce to terms of the form $1/s_{i5}$ and $s_{i5}/(s_{i+1,5}s_{i+2,5})$ with coefficients independent of $s_{i5}$; the paper states that performing those angular integrals and multiplying by the phase-space factor yields the relation.","core_discovery":"The central claim is that for production of an arbitrary colourless particle in association with a jet, the coefficient $C_{LL}$ of the leading logarithm at NLP equals $-C_{-1}$, where $C_{-1}$ is the coefficient of the $1/\\epsilon$ pole that mass factorization must cancel. In the paper's setup, $C_{-1}$ is computed from the helicity-dependent Altarelli-Parisi splitting kernels $\\Gamma_{i\\to jk}$. The relation is claimed to hold for both diagonal ($q\\bar q$, $gg$) and off-diagonal ($qg$, $\\bar q g$) partonic channels, for next-to-soft gluon emission and soft quark emission alike, and for colourless particles of arbitrary spin, provided the helicity configurations are handled correctly: soft quarks are clubbed with the neighbouring hard parton in colour-ordered amplitudes, and sums over gluon helicities and massive-particle polarisations are taken.","pith_inferences":["Read as a general statement, the paper's colourless set includes the massless photon, so the same $C_{LL}=-C_{-1}$ formula should also apply to prompt-photon-plus-jet production; this extension is not demonstrated explicitly.","The identity at leading logarithm raises the question of whether the same mass-factorization relation also determines the next-to-leading logarithms at NLP; the paper does not claim this.","An independent calculation of the $W$+jet or $Z$+jet NLP coefficients, for instance through a subtraction scheme, would provide a direct test of the universal formula."],"forward_implications":["The NLP leading-logarithmic coefficients for $W$+jet and $Z$+jet can be obtained directly from mass factorization and helicity-dependent splitting functions, without performing the full NLP phase-space integrals.","The same universal structure covers diagonal $q\\bar q$ and $gg$ channels as well as off-diagonal $qg$ channels, so no separate resummation machinery is needed for each partonic channel.","Because the identity holds for both next-to-soft gluon and soft quark radiation, the two sources can be combined into a single NLP formula for each helicity configuration.","This sets a practical foundation for resumming NLP leading logarithms in jet-associated colour-singlet production at the LHC."],"supporting_citations":[{"why":"Supplies the colour-ordered helicity-amplitude formalism for computing NLP corrections from next-to-soft gluon radiation.","marker":"[92]"},{"why":"Defines the soft quark operators used to treat soft quark emission at NLP.","marker":"[96]"},{"why":"Provides the subleading soft theorems of gauge theory that convert next-to-soft gluon emission into shifts of the hard amplitude.","marker":"[93–95]"},{"why":"Established universality of NLP threshold effects for colourless final states; the present work extends this to jet-associated production.","marker":"[45]"},{"why":"Earlier investigation of NLP logarithms for prompt photon plus jet that the present universal formula would subsume.","marker":"[46]"},{"why":"Earlier attempt at next-to-leading power corrections for vector-boson-plus-jet production, which the paper cites as incomplete.","marker":"[51]"}],"fun_headline_variants":["One NLP log formula for all jet-associated production","Universal NLP logs for jet plus any colourless particle","NLP logs tie to mass-factorization pole universally","Jet+colourless NLP logs: same universal formula","All jet+colourless share one NLP leading-log formula"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing step is the claim that the angular integration of the Eikonal-structured squared amplitudes produces exactly $C_{LL} = -C_{-1}$ with no extra finite terms; if that integration were to generate additional leading-logarithmic contributions, the universality formula would not hold.","fun_headline_variants_meta":{"raw":{"variants":["One NLP log formula for all jet-associated production","Universal NLP logs for jet plus any colourless particle","NLP logs tie to mass-factorization pole universally","Jet+colourless NLP logs: same universal formula","All jet+colourless share one NLP leading-log formula"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.0005,"raw_usage":{"total_tokens":2358,"prompt_tokens":768,"completion_tokens":1590,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":384,"completion_tokens_details":{"reasoning_tokens":1514}},"tokens_in":384,"tokens_out":1590,"duration_ms":10470,"temperature":1.0,"reasoning_tokens":1514,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T04:20:17.371929+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the full NLP leading-logarithmic coefficient for $W^+$+jet (or $Z$+jet) by explicit phase-space integration of the colour-ordered helicity amplitudes for a fixed helicity configuration, and compare the coefficient of $\\log(s_{45}/\\bar\\mu^2)$ with $-C_{-1}$ obtained from the mass-factorization expression in eq. (15) using helicity-dependent splitting functions. Any mismatch would falsify the universal relation.","supporting_citations":[],"review_version":1}