{"id":"24b58496-48a9-4ab0-bdc9-337b0c8b455d","arxiv_id":"2501.07823","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Using wave-packets and a modified parton shower, the authors show that jets are transversely broad and derive a gluon-TMDPDF-based relation in which the jet transport coefficient qhat weakens with increasing parton virtuality.","lead":"This paper calculates the quantum uncertainty size of splitting partons and finds that jets spread much wider in the transverse plane than the classical antenna picture predicts. It then derives a connection between the coefficient that measures how strongly a jet is quenched by the medium and the gluon content of the medium, showing that this coefficient weakens as the parton's virtuality grows.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (49) defines qhat as a matching ratio, so the steep drop in f(mu^2) may reflect the fixed kinematics y=1/2, q^-=200*sqrt(2) GeV and the non-evolved TMD model rather than a universal medium property.","rationale":"The reader's weakest-assumption analysis correctly identifies the fragile premise: Eq. (49) is constructed by equating the full induced-gluon kernel with its second-order Taylor-expanded form, so the resulting qhat is a process- and model-dependent effective coefficient rather than an independently established medium transport coefficient. My stress-test agrees and sharpens this into a concrete check: because xL depends on y and q^-, qhat as defined in Eq. (49) can vary with the hard splitting kinematics even at fixed virtuality mu^2, which would undermine the universality needed for the 'modified coherence' interpretation. The paper is transparent about several limitations in Sec. VI (no Collins-Soper evolution, simple TMD model, limited scale range), and the authors frame the numerical result as a demonstration of the mechanics rather than a definitive extraction. Therefore the concern does not invalidate the paper's illustrative value, but it does mean the central claim should be read as conditional: the scale dependence shown in Fig. 10 is a property of the specific matching prescription and input model, not yet shown to be a universal medium property. This matches the reader's CONDITIONAL verdict, so no verdict adjustment is needed.","tokens_in":25505,"tokens_out":7930,"duration_ms":74819,"concrete_test":"Recompute f(mu^2) from Eq. (49) at fixed mu = 4 GeV and 7 GeV while varying the momentum fraction y from 0.2 to 0.8 (and separately varying q^- by a factor of 2), keeping the TMD model and all other inputs unchanged. If f changes by more than ~20% at fixed mu, qhat is not a universal function of the medium scale. As a second check, replace h in the numerator and denominator of Eq. (49) with the full next-to-leading-twist kernel of Ref. [30]; if the rapid drop in Fig. 10 weakens or reverses, the modified-coherence conclusion is an artifact of the approximate hard function.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the claim that qhat(xL, l_perp^2) in Eq. (49) is a genuine medium transport coefficient. Eq. (49) is derived by equating the full induced-gluon kernel Eq. (46) with its second-order collinear expansion Eq. (48), so qhat is defined as the ratio of the full l_perp-dependent integral to a fixed hard factor. The paper states this relation is 'true for any choice of h', but that is precisely the problem: the resulting qhat necessarily inherits the dependence of h on y, q^-, and l_perp through xL = l_perp^2/[2q^-P^+y(1-y)]. The numerical drop in f(mu^2) (Fig. 10) is computed at fixed y=1/2 and q^-=200*sqrt(2) GeV with a non-evolved BLNY/MSTW gluon TMD (Eqs. 51-53). If qhat depends on the hard splitting kinematics rather than only on the medium and the scale, the 'modified coherence' interpretation does not follow; the result could simply be a property of the chosen matching point. The paper does not demonstrate that Eq. (49) gives a qhat independent of y and q^- at fixed mu^2, nor that f is stable under replacing h with the full next-to-leading-twist kernel of Ref. [30].","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper has two main parts. In Secs. II–III the authors re-derive the single-gluon emission cross section in deep-inelastic scattering using incoming wave-packets, extract the transverse quantum-uncertainty size of the splitting quark, δz⊥ ~ 1/ℓ⊥, and implement this size in the MATTER Monte-Carlo generator to compute the transverse radius of 100 GeV quark showers at t = 5 fm/c. They find that the quantum-uncertainty size is larger than the classical antenna size and that the total shower size is not tightly correlated with the initial parton virtuality. In Secs. IV–V the authors reconsider the medium-modified emission kernel at next-to-leading twist, retain the k⊥ and xL dependence of the gluon TMDPDF, and, by comparing the full kernel with its collinear expansion, obtain Eq. (49) relating the jet transport coefficient q̂ to the gluon TMDPDF. Using a non-evolved BLNY/MSTW Gaussian TMDPDF at fixed y = 1/2 and q− = 200√2 GeV, they compute a scale-dependent factor f(μ²) that drops steeply from μ = 3.1 GeV to 9 GeV, a continuous weakening that the paper calls “modified coherence.”","tokens_in":25806,"tokens_out":8072,"duration_ms":81461,"significance":"If Eq. (49) were a robust q̂–TMDPDF relation and if the numerical drop in f(μ²) reflected a genuine medium property, the paper would be a valuable contribution: it would connect q̂ to the gluon TMDPDF in a way that can be improved with standard TMD evolution, and it would offer an alternative to the threshold-like coherence picture of jet quenching. The wave-packet derivation of the uncertainty size and the explicit Monte-Carlo implementation are also useful, and the authors are transparent that the final numerical model is simplified for reproducibility. The main strength is that Eq. (49) is stated in a form that can be tested with different hard kernels and different TMDPDF inputs; the main weakness is that the manuscript does not yet perform those tests, so the central claim currently rests on a matching definition and a single non-evolved input model.","major_comments":[{"comment":"The derivation of the q̂–TMDPDF relation is a matching construction rather than an independent derivation. The full kernel in Eq. (46) and its second-order Taylor expansion in Eq. (48) are set equal and solved for q̂; consequently Eq. (49) is true by construction for any h and any G. The statement in Sec. IV.C that the relation is “true for any choice of h” therefore does not by itself establish that the object in Eq. (49) is a universal transport coefficient. Since xL = ℓ⊥²/[2q−P+y(1−y)] enters G(xL, k⊥, ℓ⊥²), and h depends on y and q−, q̂ in Eq. (49) manifestly depends on the hard-splitting kinematics. The paper fixes y = 1/2 and q− = 200√2 GeV in Sec. V and provides no check that q̂ at fixed μ² is independent of y, q−, or of the infrared cutoff ΛQCD = 0.2 GeV used in the k⊥ integral. Without such a check, the computed f(μ²) cannot be interpreted as a scale-dependent property of the medium rather than a property of the chosen matching point.","section":"Sec. IV.C, Eq. (49)"},{"comment":"The numerical evidence for the central “modified coherence” claim rests on an un-evolved Gaussian TMDPDF whose x-dependence and width dominate the result. The drop in f(μ²) for μ ≳ 6 GeV is driven by xL = ℓ⊥²/100 rising toward the steeply falling large-x region of the MSTW input F(xL), while the width w(xL, μ²) is fixed by the BLNY ansatz with no Collins–Soper evolution. The authors assert that evolution would produce “a quantitative, but not a qualitative, shift,” but no calculation or argument is supplied; for μ² between roughly 10 and 80 GeV², TMD evolution is not negligible. The conclusion that the weakening is a universal medium effect would require repeating the calculation with an evolved TMDPDF, with alternative PDF inputs, and with the kinematics varied so that the result can be examined at fixed xL rather than at fixed y = 1/2.","section":"Sec. V, Eqs. (51)–(53) and Fig. 10"},{"comment":"The denominator of Eq. (49) is evaluated with the approximate result Eq. (50), which follows from the phase-derivative-neglecting collinear expansion of Ref. [24], while the numerator uses the full h from the second line of Eq. (41). The manuscript cites Ref. [30] to argue that the method of Ref. [24] is close to the complete next-to-leading-twist result at τ = 2τf, but it does not demonstrate that Eq. (49) is stable when the full kernel of Ref. [30] is used consistently in both numerator and denominator. Because Eq. (49) is a ratio of a k⊥-integral of hG to ∇²h|_{k⊥=0}, a partial use of an approximate h could bias the scale dependence of q̂.","section":"Sec. IV.C, Eq. (50)"},{"comment":"The Monte-Carlo claim that quantum uncertainty makes jets several femtometers wide depends on assigning the single-split uncertainty δr⊥ to every parton at the observation time, including partons that have not split and on-shell daughters after the split. Equation (31) is derived for the parent quark at the moment of a split, not as a time-dependent size of arbitrary partons. The measure in Eq. (33) also combines this uncertainty with classical antenna positions, so the statement that there is no clear relation between virtuality and transverse size is tied to this particular prescription. The authors should state more carefully what fraction of the width in Figs. 4–7 comes from the added δr⊥ term and what fraction comes from the antenna coordinates.","section":"Sec. III, Eq. (33) and Figs. 4–7"}],"minor_comments":[{"comment":"The text contains several typos (“spilts,” “preceeding,” “naïve,” “vanishies”) and Ref. [49] duplicates Ref. [29]; these should be corrected in a revision.","section":"General"},{"comment":"The infrared regulator ε appears as log(1/ε) in Eqs. (27)–(30) and is said to have no significance, but the final relation Eq. (31) is obtained by cancelling these logarithms; a sentence explaining the cancellation would improve clarity.","section":"Sec. II, Eqs. (27)–(31)"},{"comment":"The caption of Fig. 5 should state whether the plotted distributions are normalized to unit area; without this information it is difficult to compare the widths across virtuality bins.","section":"Fig. 5 caption"},{"comment":"The assumption that the parent quark transverse momentum distribution is much narrower than the radiated gluon’s is stated in the text, but it is a strong approximation; the derivation of the uncertainty size should note where this assumption breaks down at small ℓ⊥.","section":"Sec. II, text below Eq. (22)"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a timely topic and contains a transparent derivation, but the central claim currently rests on a matching definition of q̂ in Eq. (49) and on a single non-evolved TMD input. I would ask the authors to add tests of Eq. (49) at several values of y and q−, and to repeat the numerical calculation with an evolved TMDPDF and an alternative PDF input. If the steep drop in f(μ²) survives those tests, the paper would be a solid contribution; without them, the “modified coherence” interpretation is not yet supported."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The short version: this paper deserves a serious referee, but the headline claim needs to be read at the level of what is actually derived. Eq. (49) is the ratio that makes the full induced-gluon kernel equal to its second-order collinear expansion. It is a matching definition, not an independent first-principles relation, and the statement that it is 'true for any choice of h' is true only in the sense that any ratio can be formed. The resulting qhat inherits the y, q^-, and l⊥ dependence of h through xL, so the scale-dependent f(mu^2) in Fig. 10 has not been shown to be a universal medium property. The authors are candid about the limitations—no Collins-Soper evolution, fixed kinematics, a limited scale window—and they frame this as a simple reproducible case. That is honest, but it means the 'modified coherence' conclusion is currently an illustration of a mechanism, not a demonstrated general result.\n\nWhat is genuinely new and good: the wave-packet derivation of the quantum uncertainty size in Sec. II, the first Monte-Carlo estimate of jet transverse size including that uncertainty (Sec. III, Figs. 4-7), and the explicit matching relation Eq. (49) with the numerical f(mu^2). The uncertainty-size formula itself is a textbook Heisenberg-scale estimate, but the DIS derivation and the shower-size application are new. The result that showers are wide objects—around 2 fm at 5 fm/c—and that the size does not cleanly track initial virtuality is a useful challenge to coherence-based intuition and will matter for medium-response studies.\n\nSoft spots beyond Eq. (49): the numerical input is a non-evolved Gaussian TMDPDF with externally fitted BLNY/MSTW parameters at scales 3–9 GeV; the authors say evolution will be a quantitative shift, not qualitative, but that is an assertion, not a demonstration. The Monte-Carlo code is not released, so the shower-size numbers are not independently reproducible from the paper alone, though the procedure is described in enough detail to re-implement. None of this makes the paper incoherent; it just moves the claim from 'derived' to 'proposed with evidence.'\n\nWho this is for: anyone working on jet quenching or TMD phenomenology. It is a serious, well-written contribution with a new observable and a concrete matching formula. It deserves peer review, with referees asked to check whether the qhat–TMDPDF ratio is stable under changes of kinematics and under using the full next-to-leading-twist kernel.","headline":"A useful, clearly written first pass at a qhat–TMDPDF matching, with a new coordinate-space shower-size estimate, but the central relation is a matching definition and the numerical weakening is illustrative rather than established.","tokens_in":26390,"tokens_out":4373,"would_cite":true,"duration_ms":42542,"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":"The paper claims that the effective jet-medium coupling weakens continuously with parton virtuality because the medium's gluon transverse-momentum distribution cannot keep up with the shrinking radiating antenna.","keywords":["jet quenching","jet transport coefficient","transverse momentum dependent PDF","modified coherence","higher-twist formalism","parton shower transverse size","quantum uncertainty","deep inelastic scattering"],"falsifier":"Compute Eq. (49) with a fully QCD-evolved gluon TMDPDF and the complete next-to-leading-twist hard kernel; if the resulting $f(\\mu^2)$ no longer falls steeply between 3.1 and 9 GeV, or if it depends strongly on the chosen form of the hard function $h$, the modified-coherence interpretation fails.","tokens_in":25224,"feed_emoji":"⚛️","tokens_out":8882,"duration_ms":82496,"temperature":0.7,"pith_summary":"This paper tries to establish that the apparent suppression of high-virtuality jet interactions with a medium is not an all-or-nothing coherence threshold but a continuous, calculable weakening. It derives the quantum uncertainty size of a splitting parton, shows that full jet showers are wider than classical antenna estimates, and links the jet transport coefficient to a gluon transverse-momentum-dependent parton distribution function (TMDPDF). Solving that link with a simple Gaussian TMDPDF model yields a transport coefficient that drops steeply as the splitting scale rises from about 3 to 9 GeV. The authors name this gradual scale-dependent suppression \"modified coherence.\"","feed_headline":"Jet-medium coupling sinks as parton virtuality climbs","feed_subtitle":"Derived from gluon distributions, the drop replaces sharp coherence thresholds with a continuous 'modified coherence'.","key_machinery":"The load-bearing identity is Eq. (49), a quotient: in the numerator the hard emission factor $h(\\vec{k}_\\perp, q^-, y, \\vec{\\ell}_\\perp)$ from the higher-twist kernel is integrated against the medium's gluon TMDPDF $G(x_L, \\vec{k}_\\perp, \\mu^2)$, while the denominator is $\\vec{\\nabla}^2_{k_\\perp} h$ evaluated at $k_\\perp = 0$. This equation converts the TMDPDF into a scale-dependent $\\hat{q}$, and solving it produces the falling $f(\\mu^2)$. A second piece of machinery is the wave-packet re-derivation of single-gluon emission, which extracts the uncertainty width $\\delta z_\\perp \\sim 1/\\ell_\\perp$ at the split point; that width is inserted into a Monte-Carlo shower to obtain the transverse-size distributions. The final piece is the Gaussian ansatz for the gluon TMDPDF with a momentum-fraction-dependent width, which supplies the numerical input that makes the drop quantitative.","core_discovery":"On its own terms, the paper's central discovery is Eq. (49): the jet transport coefficient $\\hat{q}(x_L, \\ell_\\perp^2)$ equals the full induced-gluon kernel, integrated against the gluon TMDPDF $G$, divided by the second derivative of the hard factor $h$ at zero exchanged momentum $k_\\perp$. Equating the complete kernel with its Taylor-expanded form defines $\\hat{q}$ as a scale- and momentum-fraction-dependent quantity rather than a constant medium parameter. Solving this relation with a Gaussian gluon TMDPDF and a leading-order gluon PDF gives a scaling function $f(\\mu^2)$ that drops steeply as the splitting scale rises from 3.1 to 9 GeV. The accompanying wave-packet calculation gives the quantum uncertainty size $\\delta z_\\perp \\sim 1/\\ell_\\perp$ for a splitting parton, and a Monte-Carlo shower carrying that size produces transverse shower radii around 2 fm at 5 fm/c, with no clean relation between the full shower width and the originating parton's virtuality.","pith_inferences":["If Eq. (49) survives more realistic input, the same relation can be run in reverse: the measured scale dependence of $\\hat{q}$ in a quark-gluon plasma becomes a probe of that plasma's effective gluon transverse-momentum distribution, which has no direct definition today.","The Monte-Carlo result that jets are several fm wide at 5 fm/c suggests that the soft periphery of a jet deposits energy into a much larger volume of the medium than antenna-based simulations assume, so jet wakes and medium response should be correspondingly broader.","A discriminating test, not performed in the paper, is to solve Eq. (49) with a fully QCD-evolved gluon TMDPDF: if the steep drop in $f(\\mu^2)$ persists, modified coherence is a robust kinematic feature of the TMDPDF; if it mostly disappears, much of the advertised weakening is an artifact of the unevolved Gaussian model."],"forward_implications":["The effective $\\hat{q}$ used in jet-quenching simulations should inherit a falling $f(\\mu^2)$ from the gluon TMDPDF rather than being treated as a constant fit parameter.","Above roughly $\\mu \\sim 9$ GeV for the kinematics studied, the medium-induced emission rate is strongly suppressed, so the high-virtuality stage of a jet is nearly vacuum-like in a continuous way rather than because of a hard resolution threshold.","The radiating system's size $\\delta z_\\perp \\sim 1/\\ell_\\perp$ makes jets substantially wider objects than antenna estimates, so a larger portion of the medium is probed by the soft periphery of the jet.","Because shower width does not track initial virtuality in a simple way, observables that measure jet broadening cannot be inverted straightforwardly to infer the originating parton's virtuality.","Because Eq. (49) is presented as true for any choice of the hard function, the same method can be recycled with different emission kernels and different media to generate scale-dependent transport coefficients."],"supporting_citations":[{"why":"Provides the virtuality-ordered parton shower whose default antenna-size mode is the baseline for the Monte-Carlo transverse-size comparison.","marker":"[14]"},{"why":"Provides the wave-packet treatment of split locations and formation time that the paper extends to extract the transverse uncertainty size.","marker":"[15]"},{"why":"One origin of the higher-twist formalism for medium-modified gluon emission in deep inelastic scattering, from which the kernel in Eq. (39) descends.","marker":"[23]"},{"why":"Introduces the collinear Taylor expansion in $k_\\perp$ that defines the standard second-derivative form of the induced-gluon yield used in Eqs. (47)-(48).","marker":"[24]"},{"why":"Supplies the more complete next-to-leading-twist analysis cited to justify keeping only the second derivative of $h$ at $\\tau = 2\\tau_f$.","marker":"[30]"},{"why":"Formulates the color-coherence antenna picture that the paper's modified-coherence result is contrasted with.","marker":"[45]"},{"why":"Gives the decoherence and antenna-size argument that the present paper argues should be replaced by a continuous TMDPDF-driven weakening.","marker":"[46]"},{"why":"Supplies the Gaussian form and scale-dependent width for the gluon TMDPDF used in Eq. (51).","marker":"[60]"},{"why":"Provides the fitted Gaussian width parameters adopted in Eq. (52).","marker":"[63]"},{"why":"Provides the leading-order gluon PDF $F(x)$ used in Eq. (53) to evaluate the TMDPDF normalization.","marker":"[64]"}],"fun_headline_variants":["q-hat drops as splitting scale climbs in jet showers","Jet-medium coupling weakens with parton virtuality","Modified coherence: continuous drop replaces sharp jet thresholds","Shower size from wave-packets: jets wider than antenna picture","Gluon distributions expose virtuality-dependent jet coupling"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the quantity defined by Eq. (49) is a genuine, process-independent medium transport coefficient, not a ratio that merely absorbs whatever the chosen splitting kernel and Gaussian gluon model happen to put there.","fun_headline_variants_meta":{"raw":{"variants":["q-hat drops as splitting scale climbs in jet showers","Jet-medium coupling weakens with parton virtuality","Modified coherence: continuous drop replaces sharp jet thresholds","Shower size from wave-packets: jets wider than antenna picture","Gluon distributions expose virtuality-dependent jet coupling"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000785,"raw_usage":{"total_tokens":3473,"prompt_tokens":964,"completion_tokens":2509,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":580,"completion_tokens_details":{"reasoning_tokens":2431}},"tokens_in":580,"tokens_out":2509,"duration_ms":16768,"temperature":1.0,"reasoning_tokens":2431,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:36:25.153831+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute Eq. (49) with a fully QCD-evolved gluon TMDPDF and the complete next-to-leading-twist hard kernel; if the resulting $f(\\mu^2)$ no longer falls steeply between 3.1 and 9 GeV, or if it depends strongly on the chosen form of the hard function $h$, the modified-coherence interpretation fails.","supporting_citations":[{"cited_title":"Majumder, E","cited_arxiv_id":null,"evidence_quote":"Supplies the Gaussian form and scale-dependent width for the gluon TMDPDF used in Eq. (51)."}],"review_version":1}