{"id":"ec05006c-0002-45cd-90f0-19fe502aed2b","arxiv_id":"hep-ph/9402335","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":8.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Exact quark and gluon propagators in the random color field of a large nucleus yield a sea quark distribution proportional to mu^2 alpha_s^2 ln(1/alpha_s) that saturates for quark masses below mu.","lead":"At near light speed a large nucleus looks like a thin sheet of random color charge, and the gluon field it produces has resisted first-principles treatment at small momentum fraction. This paper solves for how quarks and gluons propagate through that field and extracts a sea quark distribution that stops depending on quark mass below the nuclear charge scale.","discovery_kind":"unclear","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The finite sea-quark result of Eqs. (61)/(64) is extracted from the divergent integrals of Eq. (57) by an asserted cancellation of the k+′→k+ singular pieces; that unproven step is what makes the distribution well-defined.","rationale":"The central claim, Eq. (64), is a leading-log statement: the log(1/α_s) comes entirely from integrating p_t between α_sμ and μ with γ(p_t) ∝ μ²/p_t⁴. Two consequences follow. First, the reader's weakest_assumption — that the Gaussian measure of Eq. (2) fixes the normalization — is weaker than stated. In the window p_t >> α_sμ that dominates the log, γ(p_t) is the two-gluon-exchange tail, which depends only on the second moment ⟨ρρ⟩ = μ²; a non-Gaussian connected four-point function would enter at relative order α_s²μ²/p_t² and shift the constant under the log, not its coefficient. The coefficient of Eq. (64) is therefore fixed by the variance alone, and the Gaussian ansatz is not the load-bearing input. Second, the paper is candid about the limits that do matter: k_t << μ for classical sources, the unresolved region k_t ~ α_sμ where the log is cut off, missing α_s ln(k_t/μ) corrections, and the appendix's boundary condition. Those are acknowledged and should not be re-counted as new findings. What remains is the one unproven algebraic step, Eq. (57)→(58). It is load-bearing because it is the only place where a finite distribution is extracted from a divergent expression, and because the two integrals being combined run over disjoint k−′ ranges yet are assigned a common cutoff. If the cancellation is exact, the paper stands as written; if not, Eq. (61) is a subtraction artifact. My reading is that the cancellation is almost certainly correct — the final answer has the right 1/x scaling, the right α_s/π ratio to glue, and has been reproduced many times since — but the manuscript does not show it, and a reader cannot check it from the text. That is a presentational gap in an otherwise sound derivation, not a threat to the result, so the verdict stays CONDITIONAL. I also note the k+² versus 1/k+ mismatch between Eqs. (58)–(59) and Eq. (61), which is probably a transcription slip but should be resolved because it sits in the same chain.","tokens_in":25866,"tokens_out":44355,"duration_ms":851541,"concrete_test":"Repeat the k−′ integrations in Eq. (57) with k+′−k+ kept finite, expand the result in (k+′−k+), and verify that the coefficient of 1/(k+′−k++iε) vanishes identically and that the finite part reproduces Eq. (58) with a single common cutoff. If a residual pole survives, Eq. (61) is regulator-dependent and the sea-quark result is not well-defined as written. In the same pass, check the k+ power of Eqs. (58)–(59) against Eq. (61); they differ by k+², so one of the two must be corrected before the chain can be read as a derivation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The chain from Eq. (47) to Eq. (64) is short, and where I can check it independently it is correct: the inner integral of Eq. (62), ∫d²k_t ln[((k_t+p_t)²+M²)/(k_t²+M²)], does equal πp_t², and combining that with Eq. (63) reproduces the coefficient 2(N_c²−1)/π² of Eq. (64) exactly, as well as the α_s/π ratio to glue quoted in the text. The one step I cannot verify from the manuscript is Eq. (57)→(58). Eq. (55) defines the distribution through a k+′ integral that must be taken to k+′→k+ only after the k−′ integration, because δD carries a 1/(k+′−k++iε) singularity (Eq. 47). In Eq. (57) the limit is moved outside the k−′ integrals, and the text then states in a single sentence that “the pieces singular in the limit k+′→k+ either vanish or cancel out,” and that the sum of the two remaining integrals equals ½(ln[(k_t+p_t)²+M²] − ln Z)k+². No demonstration is given. This is load-bearing because the two integrals being combined run over disjoint ranges (k−′<0 and k−′>0) yet are assigned a common cutoff Z; if the singular pieces do not cancel identically, the “distribution” is regulator-dependent and Eq. (61) is an artifact of the subtraction rather than a property of the background field. The Z piece itself is removed cleanly by the sum rule Eq. (60), so the concern is specifically the 1/(k+′−k+) pieces, not the logarithmic divergence. A secondary check in the same chain: Eqs. (58)–(59) carry k+² while Eq. (61) carries 1/k+, a mismatch of k+²; if that is not a transcription slip, one of the two equations is wrong.","agreement_with_reader":"partial"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"The manuscript computes the Green's functions for scalars, fermions, and gluons propagating in the classical color field generated by the valence quarks of a large nucleus in the infinite-momentum frame. The valence charges are treated as static light-cone sources with a Gaussian weight of variance µ² per unit transverse area (Eq. 2), and the resulting field is a pure gauge for x⁻<0 and x⁻>0 separately, with a step at x⁻=0 (Eqs. 5–9). Matching free solutions across that discontinuity yields the scalar propagator (Eq. 40), its Fourier-space form (Eq. 47), and the corresponding fermion and gluon propagators (Eqs. 49, 52, 54). Averaging over color orientations reduces the result to a single scalar correlator Γ(x_t), or γ(p_t) in momentum space (Eqs. 42–45). Using the fermion–scalar relation of Eq. (49), the authors then extract the sea quark distribution, Eq. (61), and, inserting the leading small-p_t form of γ from Eq. (63), obtain the central result Eq. (64): (1/πR²)dN_sea/dy = 2(N_c²−1)µ²α_s²ln(1/α_s)/π², independent of the sea quark mass for m_quark << µ and suppressed relative to the glue result Eq. (65) by α_s/π. An appendix treats the constrained field A₋.","tokens_in":13278,"tokens_out":10593,"duration_ms":142239,"significance":"If the result holds, this is a foundational computation: it gives, for the first time within this framework, an explicit and parameter-free-in-form expression for the intrinsic sea quark content of the small-x nuclear wavefunction, and it makes the sharp, falsifiable statement that this content saturates and is mass-independent for m_quark << µ. The paper is also candid about its kinematic window (α_s²µ² << k_t² << µ²) and about where the method fails (m_quark ≳ µ, k_t ≳ µ). I give explicit credit for the parts of the chain I could check independently: the inner integral of Eq. (62), ∫d²k_t ln[((k_t+p_t)²+M²)/(k_t²+M²)], does equal πp_t², and combining that with Eq. (63) reproduces the coefficient 2(N_c²−1)/π² of Eq. (64) and the α_s/π ratio to Eq. (65) exactly. The continuity check at x⁻=0 in Eq. (36) also closes, since ∫d²q_t/(2π)² e^{iq_t·x_t}U(x_t)V†(q_t) = U(x_t)U†(x_t) = 1.","major_comments":[{"comment":"The step from Eq. (57) to Eq. (58) is asserted rather than shown, and it is load-bearing for the well-definedness of Eq. (61). Eq. (55) defines the distribution through a k₊′ integral that must be taken to k₊′→k₊ only after the k₋′ integration, precisely because δD carries a 1/(k₊′−k₊+iε) singularity (Eq. 47). In Eq. (57) the limit is moved outside the k₋′ integrals, and the text then states in one sentence that “the pieces singular in the limit k₊′→k₊ either vanish or cancel out.” No demonstration is given. This matters because the two integrals being combined run over disjoint ranges (k₋′<0 and k₋′>0) yet are assigned a common cutoff Z; if the singular pieces do not cancel identically, the extracted distribution is regulator-dependent and Eq. (61) is an artifact of the subtraction rather than a property of the background field. Please show the cancellation explicitly, or state the subtraction prescription that makes it hold.","section":"§5, Eqs. (55)–(58)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The printed equations are not mutually consistent in their power of k₊. Eq. (58) gives ½(ln[(k_t+p_t)²+M²] − ln Z)k₊², and Eq. (59) carries the prefactor 4N_c/((2k₊)(2π)⁴), so the combination scales as k₊; Eq. (61) instead carries 4N_c/((2π)⁴k₊). Since dN/d³k must scale as 1/k₊ at fixed dN/dy, Eq. (61) is presumably the correct one and Eqs. (58)–(59) contain a transcription error. As printed, a reader cannot verify the normalization of the central result Eq. (64) from the preceding equations. Please correct the k₊ powers and check the overall factor.","section":"§5, Eqs. (58)–(61)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The key input γ(p_t) ∝ α_s²µ²/p_t⁴ in Eq. (63) is quoted from Ref. [2], which is listed as “to appear in Phys. Rev. D” and is therefore not available to the reader; the same is true of the framework result of Ref. [1] on which §1 rests. A short derivation of Eq. (63), or at least a statement of the approximations under which it holds, would make the paper self-contained. Relatedly, Eq. (63) is only the leading term in the range α_s²µ² << p_t² << µ² and by itself does not saturate the sum rule Eq. (45); the coefficient of Eq. (64) therefore inherits the uncertainty of the matching at p_t ~ α_sµ. The authors acknowledge this in §6, but the leading-log qualification should be stated at Eq. (64) itself, where the reader will first meet the result.","section":"§5, Eq. (63) and Refs. [1], [2]","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The entire normalization of Eq. (64) traces to the Gaussian model for the valence color charge, Eq. (2), which assigns a single variance µ² and no higher cumulants. Nothing in the paper derives this form from QCD; it is a modeling assumption about the small-x nuclear wavefunction. A non-Gaussian charge distribution with the same µ² would leave the propagator algebra of §§3–4 intact but change the coefficient of Eq. (64). The paper should say so explicitly at Eq. (64), and comment on whether higher cumulants are expected to be organized as a 1/ρ or 1/N_c² correction at large A.","section":"§1, Eq. (2); §5, Eq. (64)","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The numerical coefficient in µ² = 1.1 A^{1/3} fm⁻² is not derived or referenced; a one-line explanation of its origin would help.","section":"§1, Eq. (1)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The line reads “Aa− = = 0”, with a doubled equals sign; presumably one of these should be Aa+ = 0.","section":"§3, Eq. (28)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The factorization of the two-point function of the adjoint operators into the color structure times a single scalar function Γ(x_t−y_t) is an assumption (it holds in the Gaussian approximation) and should be stated as such.","section":"§4, Eq. (53)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The bracket structure in the second line of Eq. (70) is unbalanced and the expression cannot be parsed as printed; also the text says “To obtain an expression for A₊, we integrate both sides of Eq. (67)” but Eq. (67) is the equation for A₋, and the boundary condition A₋(x⁻=0)=0 is imposed on a different field than the one being solved for. Please reconcile the labels.","section":"Appendix A, Eq. (70)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The statement that the solution is defined only up to a term Bx⁻, and the infrared singularities in p₊, are acknowledged as deferred; a forward pointer to the intended regularization scheme would be useful.","section":"Appendix A","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"No numerical estimate is given. A sample value of µ² and of (1/πR²)dN_sea/dy for a heavy nucleus would let the reader judge whether the effect is phenomenologically relevant.","section":"§5, Eq. (64)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The renormalization scale at which α_s in Eqs. (63)–(65) is evaluated is not specified; presumably α_s(µ), but this should be stated.","section":"§1 and §5","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Typographical: “explictly” (abstract and §1), “Wiezsäcker–Williams” for Weizsäcker–Williams (§1 and §5), “bremstrahlung” for bremsstrahlung (§1), “atleast” (§1), “degees” (§2), and “explictly” again in the abstract.","section":"Throughout","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"The physics is very likely right and the final coefficient checks out numerically, so the required revision is local: supply the missing cancellation argument in §5, fix the k₊ powers in Eqs. (58)–(59), and add the caveats at Eq. (64). The dependence on the two companion papers listed as “to appear” is the main obstacle to a self-contained assessment and is worth pressing on."},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"Third paper in the McLerran–Venugopalan series, and the one that makes the model usable: explicit background-field Green's functions for scalars, fermions and gluons, plus a closed-form sea quark distribution. If you work on small-x nuclear partons, this is the reference for the propagators themselves, not just the source picture of the earlier papers (abstract:s3). What is new: Sections 3 and 4 do the matching across x⁻ = 0 carefully — the field is pure gauge on either side, only the step function matters — and the results (Eqs. 40, 47, 52, 54) are simple enough to check by hand. The fermion case reduces to the scalar one by a 2k⁺ factor, which is right. Section 5 then gets Eq. (61), and with γ(p_t) from the companion paper, Eq. (64): dN_sea/dy ∝ μ² α_s² ln(1/α_s), independent of quark mass for m << μ (abstract:s4). I checked the inner k_t integral of Eq. (62) — it is πp_t² — and the coefficient of Eq. (64) comes out exactly, as does the α_s/π suppression relative to glue. Soft spots, in order of how much they matter. The step from Eq. (57) to Eq. (58) is one sentence: 'It can also be shown that the pieces singular in the limit k⁺′→k⁺ either vanish or cancel out.' That is load-bearing. The whole point of Eq. (55) is that the k⁺′→k⁺ limit must be taken after the k⁻′ integral because of the 1/(k⁺′−k⁺+iε) pole, and the two surviving integrals run over disjoint k⁻′ ranges yet are assigned a common cutoff Z. If the singular pieces do not cancel identically, Eq. (61) is regulator-dependent and the distribution is an artifact of the subtraction. I would want that shown. Related: Eqs. (58)–(59) carry k⁺² while Eq. (61) carries 1/k⁺, a k⁺² mismatch that is either a transcription slip or an error in one of the two. Second, the normalization of Eq. (64) traces entirely to the Gaussian weight Eq. (2) and to γ(p_t) ∝ μ²/p_t⁴ in Eq. (63), which is quoted from Ref. [2] — listed there as 'to appear.' A reader cannot check Eq. (63) from this manuscript. The Gaussian ansatz is stated, not derived; a non-Gaussian charge distribution with the same μ² would leave the propagators intact and change the coefficient. The authors are otherwise candid about the limits: k_t << μ for the classical treatment, α_s ln(k_t/μ) corrections uncomputed, m ≥ μ dominated by k_t >> μ, and the appendix flags its own boundary-condition and light-cone IR problems. Who should read it: anyone doing small-x nuclear QCD or building on the MV model. It deserves referees — the propagator sections are solid and the sea quark result should be checked once and then cited for a long time.","headline":"The paper that makes the McLerran–Venugopalan model usable — explicit background-field propagators and a closed-form sea quark distribution — with one load-bearing step in Section 5 asserted rather than shown.","tokens_in":14022,"tokens_out":2520,"would_cite":true,"duration_ms":36787,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["12.38.-t","13.60.Hb","24.85.+p"],"model":"selfhosted/deepseek-v4.1-flash","headline":"Inside the color field of a large nucleus, the sea quark distribution saturates at a value set by the nuclear color charge density alone, a factor $/alpha_s//pi$ below the glue.","keywords":["small-x nuclear wavefunction","classical color source","Gaussian color charge weight","sea quark distribution","light-cone propagator","background gauge field","two-dimensional Euclidean correlator","parton saturation"],"falsifier":"Recompute the sea quark distribution with a non-Gaussian valence charge weight that holds $/mu^2$ fixed but adds a fourth cumulant: if the coefficient of $/mu^2/alpha_s^2/ln(1//alpha_s)$ moves, Eq. (64) is a statement about the Gaussian model rather than about QCD. On the data side, the ratio of intrinsic sea quarks to glue in a large nucleus at $x //ll A^{-1/3}$ and $/alpha_s^2/mu^2 //ll k_t^2 //ll /mu^2$ is predicted to be $/alpha_s//pi$; a measured ratio that does not scale this way with $/mu^2$ would contradict it.","tokens_in":14189,"feed_emoji":"⚛️","tokens_out":4487,"duration_ms":48384,"temperature":0.7,"pith_summary":"The paper asks what the propagators for scalars, fermions and gluons look like inside the color field of a very large nucleus seen in the infinite momentum frame, where the valence quarks act as a thin sheet of color charge travelling at the speed of light. The authors solve the fluctuation equations in that background exactly, then average over the random color orientations of the sheet; the average collapses the problem onto a two-dimensional Euclidean, ultraviolet-finite field theory whose only input is one correlation function $/gamma(p_t)$. Feeding that propagator into the standard propagator-to-distribution relation gives the sea quark spectrum, and the answer is striking: for $m_{/rm quark} //ll /mu$ the sea quark distribution is the same as for massless quarks, so it saturates rather than falling with quark mass. The motivation is concrete: if the intrinsic strange and charm content of a nucleus is enhanced by the higher parton density, this is the calculation that would say by how much, and the answer is that it is fixed by $/mu^2 /sim A^{1/3}$ and suppressed relative to glue by $/alpha_s//pi$. The authors are explicit that the result holds only in the window $/alpha_s^2/mu^2 //ll k_t^2 //ll /mu^2$, and that for quarks with $m /gtrsim /mu$ the dominant contribution comes from $k_t //gg /mu$, outside the reach of the method.","feed_headline":"Sea quarks in a big nucleus saturate at a fixed value","feed_subtitle":"The intrinsic sea quark density depends on nuclear color charge, not on quark mass, and stays a fixed fraction of the glue.","key_machinery":"The load-bearing mechanism is the structure of the background field: it vanishes for $x^-<0$ and is a pure gauge transform $/alpha_i = -/frac{1}{ig} U /nabla_i U^/dagger$ for $x^->0$, so only the step function at $x^-=0$ prevents it from being entirely a gauge artifact. That lets the authors write down the scalar wavefunctions in each half-space and match them across the discontinuity, giving a closed-form Green's function (Eq. 40). Averaging over the random color orientations of the valence sheet replaces $/langle U(x_t)U^/dagger(y_t)/rangle$ by $/delta_{/alpha/beta}/Gamma(x_t-y_t)$, whose Fourier transform $/gamma(p_t)$ obeys the sum rule $/int d^2p_t/(2/pi)^2 /,/gamma(p_t) = 1$. The resulting correction to the propagator, Eq. (47), is the object everything else is built from; fermions follow by the relative factor $2p^+$ (Eq. 49) and gluons by the same algebra plus a Fierz identity in the adjoint representation. The sum rule is what kills the divergent constant in the sea quark integral and leaves a finite, cutoff-independent answer.","core_discovery":"The central claim is Eq. (64): the sea quark distribution per unit rapidity per unit transverse area is $$/frac{1}{/pi $R^{2}$}/frac{dN_{/rm sea}}{dy} = /frac{2($N_c^{2}$-1)}{/$pi^{2}$}/, /$mu^{2}$ /$alpha_s^{2}$ /ln(1//alpha_s),$$ and it does not depend on the sea quark mass as long as $m_{/rm quark} //ll /mu$. Compared with the gluon result of the same regime, $$/frac{1}{/pi $R^{2}$}/frac{dN_{/rm glue}}{dy} = /frac{2/alpha_s /ln(1//alpha_s)/$mu^{2}$ ($N_c^{2}$-1)}{/pi},$$ the intrinsic sea quark content of the nuclear wavefunction is suppressed by $/alpha_s//pi$. Both distributions carry the same $1/x$ scaling, so their ratio is flat in rapidity at this order. The authors present this as a leading-order statement in $/alpha_s$ but exact in $/alpha_s^2/mu^2$, valid where the classical-source treatment of the valence quarks is justified.","pith_inferences":["Because the final answer depends on $/gamma(p_t)$ only through its behaviour at small transverse momentum, the prediction is insensitive to the short-distance details of the charge distribution but sensitive to its cumulant structure; that asymmetry is a useful handle when comparing models of the nuclear wavefunction.","The mass independence suggests a practical test that needs no absolute normalization: the ratio of heavy to light sea quark yields in the same nucleus should approach one as $A$ grows, since $/mu /sim A^{1/6}$ rises with nuclear size.","The whole reduction hinges on the source being infinitely thin in $x^-$; any correction that gives the sheet a finite thickness would break the pure-gauge matching argument, so the leading correction in $/alpha_s$ is the natural place to look for the breakdown.","An observed nuclear enhancement of intrinsic strangeness larger than the $/alpha_s//pi$ fraction of glue would point to the $k_t /gtrsim /mu$ region that this paper explicitly cannot reach, rather than to a failure of the classical-source picture itself."],"forward_implications":["The intrinsic sea quark density of a large nucleus is fixed by $/mu^2 /propto A^{1/3}$, so it grows with nuclear size while remaining a fixed fraction $/alpha_s//pi$ of the glue.","Strange and charm quarks contribute as much as massless quarks whenever their mass is below $/mu$, so heavy-quark enhancement in nuclei is a saturation statement rather than a mass-suppression story.","Sea quarks and gluons share the same $1/x$ behaviour in this regime, making their ratio rapidity-independent at leading order.","The propagators computed here are the ingredients needed for the first radiative corrections to the quark and gluon distributions, which is where a Lipatov-type enhancement would first appear."],"supporting_citations":[{"why":"Supplies the classical-source setup, the light-cone constraint equations and the identification of the valence quarks as static color sources that the whole propagator calculation is built on.","marker":"[1]"},{"why":"Supplies the averaging over color charge orientations and the explicit form of $/gamma(p_t)$ in the regime $/alpha_s^2/mu^2 //ll p_t^2 //ll /mu^2$, which sets the coefficient of the final sea quark result.","marker":"[2]"}],"fun_headline_variants":["Sea quarks saturate independent of mass in a large nucleus","Leading-order sea quark saturation holds only for classical valence sources","Sea quark density tracks color charge and stays flat in rapidity","Intrinsic sea quarks stay αs/π below glue at this order","Sea quark saturation requires quark mass well below color charge"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The entire normalization traces back to modelling the valence color charge as a Gaussian random variable with a single variance $/mu^2$ and no higher cumulants; nothing in the paper derives that Gaussian form from QCD, and a different charge distribution with the same $/mu^2$ would leave the propagator algebra intact but change the coefficient of Eq. (64).","fun_headline_variants_meta":{"raw":{"variants":["Sea quarks saturate independent of mass in a large nucleus","Leading-order sea quark saturation holds only for classical valence sources","Sea quark density tracks color charge and stays flat in rapidity","Intrinsic sea quarks stay αs/π below glue at this order","Sea quark saturation requires quark mass well below color charge"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":2117,"prompt_tokens":948,"completion_tokens":1169,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":1096}},"tokens_in":948,"tokens_out":1169,"duration_ms":11247,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":1096,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-29T19:41:12.125205+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"falsifier":"Recompute the sea quark distribution with a non-Gaussian valence charge weight that holds $/mu^2$ fixed but adds a fourth cumulant: if the coefficient of $/mu^2/alpha_s^2/ln(1//alpha_s)$ moves, Eq. (64) is a statement about the Gaussian model rather than about QCD. On the data side, the ratio of intrinsic sea quarks to glue in a large nucleus at $x //ll A^{-1/3}$ and $/alpha_s^2/mu^2 //ll k_t^2 //ll /mu^2$ is predicted to be $/alpha_s//pi$; a measured ratio that does not scale this way with $/mu^2$ would contradict it.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the classical-source setup, the light-cone constraint equations and the identification of the valence quarks as static color sources that the whole propagator calculation is built on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the averaging over color charge orientations and the explicit form of $/gamma(p_t)$ in the regime $/alpha_s^2/mu^2 //ll p_t^2 //ll /mu^2$, which sets the coefficient of the final sea quark result."}],"review_version":1}