{"id":"e6b7e179-fc6d-4128-a807-ae671527ff95","arxiv_id":"2608.08894","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The authors extend the GLV momentum broadening formalism with finite path length and improved kinematics corrections, reporting that the combined effect can change the transport coefficient qhat by tens of percent at high transverse momentum.","lead":"This paper adds two corrections to the standard theory of how fast-moving quarks and gluons get knocked sideways as they travel through the quark-gluon plasma created in heavy-ion collisions. These corrections matter mostly for small collision systems like oxygen collisions, where the usual approximations break down.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper's central claim rests on two correction factors (Table 1 and Eq. 13) whose derivations are not shown; without them the reported phenomenology is unsupported.","rationale":"The reader identified exactly the same load-bearing weakness: the correction factors are stated without derivation and deferred to the authors' Ref. [14]. I agree that this is the main issue. In addition, the numerical figure parameters are unspecified, but that is secondary; if the factors are correct, the analytic claim stands and the figure is just an illustration. My proposed test is the direct analytic check of the two factors, which would settle the concern. The verdict CONDITIONAL is appropriate: the claim is potentially correct but currently unverifiable from the manuscript alone. I did not identify an independent internal flaw or a disagreement-with-consensus objection, so I would not escalate to REJECT. I also note that the paper gives no algebraic derivation of the e^{-mu_perp Delta z} dependence, and that Eq. (12) changes P^+ by q_z/sqrt(2) without showing how q_z is fixed by the amplitude; this is precisely the kind of step that needs to be checked by an independent re-derivation.","tokens_in":5195,"tokens_out":1490,"duration_ms":12762,"concrete_test":"Recompute the first-order GLV amplitude with the Regge-limit momenta of Eq. (11) replaced by the sub-Regge momenta of Eq. (12), and separately with the exact e^{-mu_perp Delta z} dependence retained, and verify whether Eq. (13) and the APL factor in Table 1 emerge. If the factors do not follow exactly, the paper's central corrections are unsupported; if they do, the concern is resolved and the underlying formulas should be written out in the paper or its appendix.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that APL and sub-Regge corrections substantially modify the GLV broadening distribution and qhat. The entire quantitative content is carried by two multiplicative factors: (1 - 1/2 e^{-mu_perp Delta z})^2 in Table 1 and gamma = sqrt(1 - 2 q_perp^2 / P^{+2}) in Eq. 13. These factors are stated without derivation and are the only mechanism producing the effects shown in Fig. 2. The manuscript explicitly defers the derivation to the authors' own prior work, Ref. [14], which is not accessible to the reader. Treating this unpublished reference as the sole support makes the central claim unverifiable in this paper. If either factor is wrong (e.g., the 1/2 coefficient or the 2 inside the square root), the sign, magnitude, and momentum dependence of the corrections change, and the claimed qualitative behavior in Fig. 2 is not established. The paper itself flags its internal incompleteness by saying 'The derivation presented here closely follows [14], to which we refer the reader for further details' (Section 2), without reproducing or even outlining the key steps that produce Eqs. (13) and Table 1. The retained exponential is stated to follow from keeping e^{-mu_D Delta z} terms, but no amplitude-level expression is shown; the sub-Regge momentum replacement in Eq. (12) is presented, but the route from that replacement to the specific gamma factor is not given. This is not a disagreement with consensus; it is a missing derivation at the core of the claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript extends the first-order Gyulassy-Levai-Vitev (GLV) opacity expansion for transverse momentum broadening to include all-path-length (APL) corrections, which relax the large separation distance approximation, and improved sub-Regge kinematics, which go beyond the strict Regge limit. The paper states analytic expressions for the first-order broadening distribution for four approximation schemes in Table 1, defines the corresponding transport coefficient qhat, and illustrates in Fig. 2 that these corrections can be sizable for short path lengths and large transverse momentum. The central formulas are presented as results, but their derivation is largely deferred to an unpublished self-citation, Ref. [14], and the route from the stated kinematic modifications to the specific correction factors is not shown in this manuscript.","tokens_in":5642,"tokens_out":5496,"duration_ms":52583,"significance":"If the formulas in Table 1 are correct, the paper addresses a timely question: how momentum broadening in the QGP is modified when the medium length is not asymptotically large and when the exchanged transverse momentum is not far below the projectile longitudinal momentum. The observation that APL suppression is partially compensated by sub-Regge enhancement is a potentially useful contribution, and the concise tabulation of the four approximation schemes is convenient. However, the significance is presently conditional: the two multiplicative factors that carry the entire effect, the APL factor (1 - 1/2 e^{-mu_perp Delta z})^2 and the sub-Regge factor 4/(1+gamma)^2 with gamma from Eq. (13), are stated without derivation, and gamma becomes imaginary in an important kinematic region. The paper cannot be fully evaluated until these points are resolved.","major_comments":[{"comment":"The central results of the paper, the APL factor (1 - 1/2 e^{-mu_perp Delta z})^2 in Table 1 and the sub-Regge factor 4/(1+gamma)^2 with gamma from Eq. (13), are stated without derivation. The text only says that the derivation \"closely follows [14]\" (Section 2) and that retaining subleading contributions \"gives rise to\" gamma (Section 3.2). Since Ref. [14] is an unpublished self-citation with a nearly identical title, the present manuscript is not self-contained and the central claim cannot be verified by the reader. Please provide the amplitude-level derivation, or at least the key intermediate steps, showing how these factors arise from the first-order GLV amplitude and the kinematics of Eqs. (11)-(12).","section":"Section 2 / Table 1"},{"comment":"The gamma factor becomes imaginary for q_perp > P^+/sqrt(2), so the integrals in Table 1 are not defined over the full q_perp plane unless a kinematic cutoff or analytic continuation is specified. This is not a peripheral issue because the paper emphasizes corrections for q_perp ~ P^+; the domain of validity of Eq. (13) and of the final expressions must be stated explicitly.","section":"Section 3.2, Eq. (13)"},{"comment":"With qhat defined in Eq. (7) as a single number <p_perp^2>/L, the ordinate of Fig. 2b as a function of p_perp is undefined. Please specify the accumulated or differential observable being plotted and the integration limits; otherwise the quantitative statement that qhat is enhanced or suppressed cannot be evaluated.","section":"Section 4, Fig. 2b"},{"comment":"In all four rows of Table 1 the integrand contains 1/mu_perp^4 and no explicit q_perp dependence, whereas the interaction in Eq. (3) has a momentum-dependent potential 4 pi alpha_s / (q^2 + mu_D^2). Please clarify how the potential has been processed (for example, whether part of the q_perp integral has already been carried out) and whether mu_perp in the table is the same as mu_D; as written, the connection to Eq. (3) is not transparent.","section":"Table 1"}],"minor_comments":[{"comment":"The quantity dT in the denominator is not defined; please define it when it is first used (for example, as the dimension of the representation).","section":"Eq. (4)"},{"comment":"The text uses mu_D in the exponential e^{-mu_D Delta z}, while Table 1 uses mu_perp; please use a single symbol or define the relation between them.","section":"Section 3.1 / Table 1"},{"comment":"The source J(p) is referred to but not explicitly defined; since Table 1 uses |J(p-q)|^2 - |J(p)|^2, please specify J or state that it represents a sharply peaked initial distribution.","section":"Eq. (5)"},{"comment":"The caption says \"at leading order in the opacity\" but should read \"in the opacity expansion\" for consistency with the text.","section":"Fig. 1 caption"},{"comment":"The word \"dissapear\" should be \"disappear\" in the sentence about the corrections disappearing in the appropriate limits.","section":"Section 4"},{"comment":"The final sentence connects the combined correction to the negative energy loss of Ref. [15] in a speculative way; consider labeling this explicitly as a future direction rather than a conclusion of this paper.","section":"Section 4"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is built on a self-citation, Ref. [14], which is not accessible to the reader and appears to contain the actual derivation of the central formulas. In a journal context this is problematic: either the derivation should be included in the present paper (for example, in an appendix) or the paper should be deferred until the companion paper is published. The imaginary-gamma issue in Eq. (13) is another concrete point that must be fixed. If these points are addressed, the paper could be a useful contribution to small-system jet phenomenology."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the paper addresses a legitimate problem in an important direction, but in its current form it is a results memo that leans entirely on the authors' own unpublished Ref [14] for the two factors that do all the work. If you want to evaluate the actual physics, you need that other paper in hand; the manuscript itself does not stand alone.\n\nWhat is genuinely useful: the motivation is timely. With the LHC now running O-O and p-O/Ne-Ne, the assumptions that formation and coherence scales are small relative to the medium are worth questioning, and the GLV broadening setup is the right place to ask. The paper also does a good job of laying out the four approximation schemes in Table 1, so the reader can see exactly where each correction enters. The qualitative finding—APL suppresses, sub-Regge enhances, and the two partially cancel—is plausible and connects to an existing puzzle (negative energy loss in Ref [15]). That is a reasonable physics story.\n\nThe soft spots are real, and they are load-bearing, not cosmetic. The two central factors—(1 − 1/2 e^{−µ⊥ ∆z})^2 in Table 1 and γ = sqrt(1 − 2q⊥²/P^{+2}) in Eq. (13)—are introduced without derivation. The text says 'retaining the leading subleading contributions' and 'this yields', but no amplitude-level expression or expansion is shown. The paper itself points to Ref [14] for further details, and that reference has nearly the same title as this manuscript; it is a self-citation that carries the core of the derivation. That is not acceptable in a standalone result. If [14] is available, the authors should either reproduce the derivation in an appendix or give equation-level pointers; otherwise the central claim is unverifiable from this paper alone.\n\nThe numerics are also not reproducible: Fig. 2 has no α_s, µ_D, medium density profile, or even a statement of whether the medium is static or Bjorken-expanding. Those parameters are essential because the size of the corrections depends on them. This is minor in the sense that it can be fixed by stating inputs, but it should be fixed.\n\nNet: I would not desk-reject this; the topic is relevant and the corrections, if correct, matter for small-system jet tomography. But I would send it back with a strong request for the derivation or a precise mapping to [14], plus full numerical inputs. With those, this could be a useful contribution to the jet quenching literature.","headline":"Timely idea, but the two correction factors are imported from the authors' own unpublished Ref [14] and the numerics lack inputs—send back for derivation and reproducibility, not desk reject.","tokens_in":6046,"tokens_out":2768,"would_cite":false,"duration_ms":25749,"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":"The paper extends the GLV formalism with all-path-length and improved sub-Regge corrections and shows these can substantially change the momentum broadening distribution and the jet transport coefficient in small collision systems.","keywords":["quark-gluon plasma","transverse momentum broadening","jet quenching","GLV opacity expansion","all-path-length corrections","sub-Regge kinematics","jet transport coefficient","small collision systems"],"falsifier":"Evaluate the first-order GLV broadening amplitude numerically with the full kinematic replacement of Eq. (12), without expanding in $1/P^+$, and check whether the ratio to the standard GLV integrand is exactly $4/(1+\\gamma)^2$ with $\\gamma = \\sqrt{1 - 2q_\\perp^2/P^{+2}}$; repeat for the full $\\Delta z$ dependence and check whether the coefficient of $e^{-\\mu_\\perp\\Delta z}$ is exactly $1/2$. If either factor differs, the correction is not what the paper claims.","tokens_in":4995,"feed_emoji":"⚛️","tokens_out":8107,"duration_ms":73451,"temperature":0.7,"pith_summary":"The paper extends the standard Gyulassy-Levai-Vitev (GLV) description of how a high-energy parton gains transverse momentum while crossing a quark-gluon plasma. It relaxes two approximations of that formalism: the assumption that the first scattering happens far from the production point and the assumption that the exchanged momentum is tiny compared with the parton's longitudinal momentum. The paper derives analytic first-order expressions for the broadening distribution and the transport coefficient qhat with these relaxations. These corrections matter because in small collision systems the relevant length and coherence scales are comparable, so the standard approximations may fail. The paper finds that the all-path-length correction suppresses broadening while the improved sub-Regge kinematics enhance it, and that the two partially cancel when combined.","feed_headline":"Jet broadening in small QGP systems gets two opposing corrections","feed_subtitle":"Analytic corrections show the jet transport coefficient is lower at short paths and higher at large momentum exchange.","key_machinery":"The central object is the first-order GLV opacity expansion for transverse momentum broadening, truncated at one hard scattering with the medium. The argument is carried by two multiplicative correction factors that modify the standard GLV integrand: the all-path-length factor $(1 - \\frac{1}{2} e^{-\\mu_\\perp \\Delta z})^2$ from relaxing the large-separation-distance approximation, and the improved sub-Regge factor $4/(1+\\gamma)^2$ with $\\gamma = \\sqrt{1 - 2q_\\perp^2/P^{+2}}$ from retaining subleading contributions in the $1/P^+$ expansion. These factors show how finite path length and finite exchanged momentum alter the broadening distribution and $\\hat{q}$, and they reduce to the conventional GLV results in the appropriate limits.","core_discovery":"The paper's central claim is that, to first order in the opacity expansion, the standard GLV momentum broadening distribution is changed by two independent factors. Relaxing the large-separation-distance approximation produces the all-path-length factor $(1 - \\frac{1}{2} e^{-\\mu_\\perp \\Delta z})^2$, which suppresses both the distribution and the transport coefficient $\\hat{q}$ at short path lengths. Retaining subleading terms in the $1/P^+$ expansion replaces the strict Regge kinematics by the sub-Regge factor $4/(1+\\gamma)^2$ with $\\gamma = \\sqrt{1 - 2q_\\perp^2/P^{+2}}$, which enhances both observables when the exchanged momentum is a sizable fraction of the parton's longitudinal momentum. The combined scheme interpolates between these limits, and the paper argues that this may alleviate the negative energy loss found when only APL corrections are included.","pith_inferences":["Because the correction factors are multiplicative and depend on $\\mu_\\perp\\Delta z$ and $q_\\perp^2/P^{+2}$, the predicted deviation of $\\hat{q}$ from GLV should vary in a specific way with jet energy and medium size; comparing proton-nucleus and light-nucleus collisions at different beam energies would probe that scaling.","The square root in $\\gamma$ implies a kinematic bound $q_\\perp \\leq P^+/\\sqrt{2}$; beyond it the eikonal parameterization becomes unphysical, so an extension dropping the eikonal approximation would be needed to describe the most extreme momentum transfers.","The same correction factors could be inserted into implementations of jet quenching beyond first order in opacity, offering a test of whether the short-path and sub-Regge effects remain as simple multiplicative factors when multiple scatterings are included."],"forward_implications":["In small systems where $\\Delta z$ is comparable to the inverse Debye mass, the all-path-length factor suppresses $\\hat{q}$ relative to the standard GLV value, so extractions of medium properties from such systems must account for it.","When the transverse momentum exchange is a non-negligible fraction of the parton's longitudinal momentum, the sub-Regge factor enhances the broadening distribution and $\\hat{q}$, an effect that grows with $p_\\perp/P^+$.","The combined correction lies between the APL-only and sub-Regge-only predictions, so the two effects partially cancel and the net deviation from GLV is smaller than either correction alone.","The analytic formulas provide a direct extension path to the full GLV radiative energy-loss framework, where the sub-Regge enhancement may offset the negative energy loss previously seen from short-path-length corrections."],"supporting_citations":[{"why":"Supplies the GLV opacity-expansion formalism that the paper extends.","marker":"[12]"},{"why":"Provides the reaction-operator treatment of multiple elastic scatterings underlying the GLV approach.","marker":"[13]"},{"why":"Gives the preceding derivation of momentum broadening in the opacity expansion that the present work modifies.","marker":"[14]"},{"why":"Supplies the short-path-length radiative energy-loss result that the combined correction is expected to modify.","marker":"[15]"}],"fun_headline_variants":["APL suppresses, sub-Regge enhances jet broadening","Short-path down, high-momentum up in QGP jets","Two opposing corrections reshape QGP jet broadening","QGP jet spread: two corrections, two directions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that the two analytic correction factors, the all-path-length factor $(1 - \\frac{1}{2} e^{-\\mu_\\perp \\Delta z})^2$ and the sub-Regge factor $\\gamma = \\sqrt{1 - 2q_\\perp^2/P^{+2}}$, are the correct consequences of relaxing the stated approximations; the paper does not derive these factors from the modified amplitudes, so an error in either coefficient would change the magnitude and possibly the sign of the reported corrections.","fun_headline_variants_meta":{"raw":{"variants":["APL suppresses, sub-Regge enhances jet broadening","Short-path down, high-momentum up in QGP jets","Two opposing corrections reshape QGP jet broadening","QGP jet spread: two corrections, two directions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001449,"raw_usage":{"total_tokens":5833,"prompt_tokens":937,"completion_tokens":4896,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":553,"completion_tokens_details":{"reasoning_tokens":4832}},"tokens_in":553,"tokens_out":4896,"duration_ms":36005,"temperature":1.0,"reasoning_tokens":4832,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:20:29.855546+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Evaluate the first-order GLV broadening amplitude numerically with the full kinematic replacement of Eq. (12), without expanding in $1/P^+$, and check whether the ratio to the standard GLV integrand is exactly $4/(1+\\gamma)^2$ with $\\gamma = \\sqrt{1 - 2q_\\perp^2/P^{+2}}$; repeat for the full $\\Delta z$ dependence and check whether the coefficient of $e^{-\\mu_\\perp\\Delta z}$ is exactly $1/2$. If either factor differs, the correction is not what the paper claims.","supporting_citations":[{"cited_title":"Jet quenching in thin quark gluon plasmas. 1. Formalism,","cited_arxiv_id":null,"evidence_quote":"Supplies the GLV opacity-expansion formalism that the paper extends."},{"cited_title":"Reaction operator approach to multiple elastic scatterings,","cited_arxiv_id":null,"evidence_quote":"Provides the reaction-operator treatment of multiple elastic scatterings underlying the GLV approach."},{"cited_title":"Momentum Broadening in the Opacity Expansion: All-Path-Length Correc- tions and Improved Regge Kinematics,","cited_arxiv_id":null,"evidence_quote":"Gives the preceding derivation of momentum broadening in the opacity expansion that the present work modifies."},{"cited_title":"Short path length corrections to Djordjevic-Gyulassy-Levai-Vitev energy loss,","cited_arxiv_id":null,"evidence_quote":"Supplies the short-path-length radiative energy-loss result that the combined correction is expected to modify."}],"review_version":1}