{"id":"5d8cd93a-c3b7-40b4-b8dc-2d812ac74d3e","arxiv_id":"2508.11895","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Direct T-matrix calculation without partial wave expansion reveals that partial wave sums need many more terms than expected to converge in QGP heavy quark scattering, and detects several orbital bound states simultaneously.","lead":"This paper computes heavy quark-antiquark scattering amplitudes in quark-gluon plasma without using the usual partial wave expansion, and compares the results to the standard approach. It finds that 10 to 20 partial wave terms can be needed for a precise match under moderate conditions, and that bound states of different angular momenta show up in a single energy scan.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Direct-method numerical accuracy is the load-bearing uncertainty; without an independent validation against an exact reference, the reported 10-20 partial-wave requirement is not yet established.","rationale":"This stress-test focuses on the abstract's central numerical claim: the partial wave expansion needs 10-20 terms to match the direct T-matrix. Since the full text was unavailable, I cannot assess the specific discretization or error control. The most critical assumption, highlighted by the reader, is that the direct method's amplitude is exact enough to be the reference. If the direct solver is not fully converged, the observed need for many partial waves could stem from numerical noise or from the presence of a singular potential tail that is not properly integrated. No evidence of convergence checks appears in the abstract, so this is a genuine open question rather than a manufactured doubt. I also note that the abstract says 'satisfactory matching' without defining the tolerance; the number 10-20 depends on it. The proposed test addresses both issues: an independent validation against an analytically solvable potential, and a direct check that the partial-wave convergence behavior at the claimed lmax is stable. The verdict remains UNCHANGED (unverified) because the concern is unconfirmed but cannot be dismissed from the abstract alone. The agreement with the reader is partial: the numerical exactness is the key, but I add the matching-criterion dependence.","tokens_in":716,"tokens_out":4157,"duration_ms":52565,"concrete_test":"Validate the direct no-partial-wave solver against an exactly solvable rank-1 separable potential (e.g., a Yamaguchi potential) on the same momentum grid and energy range, requiring agreement to at least 10^-6 relative error. Then, for a Cornell potential at one representative screening mass and center-of-mass energy, compute the partial wave expansion of the direct amplitude and plot the L2 difference versus lmax; check that the difference drops sharply at the reported 10-20 partial waves. If the solver's accuracy is not established, or if the partial-wave convergence is sensitive to the grid cutoff, the claim is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that 10-20 partial waves are needed to match the direct no-partial-wave T-matrix presumes that the direct 3D Lippmann-Schwinger solution is numerically converged and serves as a reliable reference. The abstract gives no evidence for this: no grid resolution study, no momentum cutoff dependence, no comparison with an analytic limit. If the direct solver has small numerical errors—from angular quadrature, principal-value integration across the potential singularity, or the treatment of the Coulomb tail—these errors could themselves require many partial waves to reproduce, making the count an artifact rather than a physical result. In particular, the screened Cornell potential has a 1/r singularity whose momentum-space representation decays slowly; how the direct method handles this is not described. Without a concrete definition of 'satisfactory matching' (e.g., relative error tolerance) and evidence that the direct amplitude is accurate to that tolerance, the magnitude of 10-20 cannot be interpreted. A second, related concern is that the partial wave expansion comparison may use a different truncation or regularization than the direct method, leading to a mismatch. Both points converge on the same load-bearing assumption: the reference amplitude must be independently verified.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a direct numerical solution of the Lippmann-Schwinger equation for the in-medium heavy quark-antiquark T-matrix with the screened Cornell potential, avoiding a partial-wave expansion. It compares this direct result with conventional partial-wave sums over a range of screening masses and center-of-mass energies. The central claim is that, for moderate screening masses (one to two times the crossover temperature), 10-20 partial waves are required to match the direct amplitude, substantially more than expected from the magnitudes of the first few partial-wave amplitudes. The abstract also reports bound states of different orbital angular momentum in a single sub-threshold energy scan.","tokens_in":979,"tokens_out":1819,"duration_ms":23150,"significance":"If the direct method is numerically reliable, the paper makes a useful methodological contribution: it offers an alternative to partial-wave expansions for heavy-quark T-matrices in QGP and provides a concrete warning about the number of partial waves needed for precision. The claim that naive low-l truncation is insufficient is phenomenologically relevant for T-matrix approaches to quarkonium spectral functions. However, the significance rests entirely on the numerical accuracy of the direct three-dimensional solver, which the abstract does not document. The paper also extends the method below threshold, which could be valuable for bound-state studies, but again the evidence is not presented.","major_comments":[{"comment":"The central quantitative claim—that 10-20 partial waves are required to match the direct result—presumes that the direct no-partial-wave solver is numerically converged to the tolerance used for 'satisfactory matching'. The abstract gives no convergence evidence: no grid resolution study, no momentum-cutoff dependence, no test of the angular quadrature, and no treatment of the 1/r Coulomb singularity in momentum space. If the direct solver has uncontrolled errors, the required partial-wave count could be an artifact rather than a physical statement. The manuscript must include explicit convergence checks and, ideally, a benchmark against an independent analytic limit or a completely different discretization.","section":"Abstract"},{"comment":"The phrase 'satisfactory matching' is undefined. Without a quantitative matching criterion (for example, a relative error tolerance on the T-matrix elements, pointwise or in a norm), the number 10-20 cannot be audited. The authors should state the exact error measure and the tolerance used, and show that the direct solution itself satisfies that tolerance in the tested regime.","section":"Abstract"},{"comment":"The direct method and the partial-wave expansion may use different regularizations of the screened Cornell potential or different treatments of the singular long-range part. The abstract does not describe whether the same potential and same subtraction procedure are used in both approaches. If the direct method and the partial-wave sums are not solving exactly the same scattering problem, the comparison is not meaningful. The manuscript must specify the common input and any regularizations.","section":"Abstract"},{"comment":"The sub-threshold bound-state claim ('bound states of different orbital quantum numbers simultaneously in a single energy scan') is stated without supporting details. It is unclear how bound states are identified, what the energy resolution is, and whether the direct method is verified in the negative-energy regime where the Green's function has poles. This claim needs at least a description of the extraction procedure and a convergence test near threshold.","section":"Abstract"}],"minor_comments":[{"comment":"The abstract contains no numerical values for the screening masses, center-of-mass energies, or temperatures except 'one to two times the crossover transition temperature'. Quantitative axes would help the reader assess the regime of the claim.","section":"Abstract"},{"comment":"The phrase 'crossover transition temperature' should be defined or referenced; in QCD this is usually T_c ~ 155 MeV, but the paper should state the convention.","section":"Abstract"},{"comment":"No figures or references are included in the abstract; the reader cannot see the comparison. The full paper should show representative 'direct vs. partial-wave' curves with error bands.","section":"Abstract"},{"comment":"The abstract says 'comprehensive survey' but gives no range or number of parameter points. A sentence listing the ranges of screening mass and center-of-mass energy would be helpful.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":"This review is based only on the abstract and the accompanying reader's report, because the full text was not available. The load-bearing issue is the numerical verification of the direct solver; without it, the 10-20 partial-wave result cannot be interpreted. I recommend that the editor obtain the full manuscript for a complete review. No concerns about citation patterns or scope are apparent from the abstract."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe abstract makes one claim worth taking seriously: that a direct 3D solution of the Lippmann-Schwinger equation for the screened Cornell potential needs 10-20 partial waves to be matched by the conventional partial-wave sum at moderate screening masses. If that holds, it's a real practical result for heavy-quark T-matrix calculations in QGP.\n\nWhat's new is not the technique itself — solving scattering without partial waves is standard — but the application to the in-medium Q\\bar{Q} problem and the systematic survey across screening mass and energy. The below-threshold observation of simultaneous bound states with different orbital quantum numbers in a single energy scan is also a nice numerical byproduct.\n\nThe paper's own evidence, however, is missing from the abstract. The phrase \"precisely match\" is doing a lot of work. No tolerance is defined, no grid or quadrature checks are reported, and no comparison with an analytic limit is given. The stress-test note is right: the direct method is the reference, so its own convergence is load-bearing. If the direct solver has small errors — from the 1/r singularity, principal-value integration, or the Coulomb tail — those errors could inflate the partial-wave count. An independent validation would settle it.\n\nI can't audit any of this because the full text isn't in front of me. The reader at least is honest about that: low confidence, unverdictable from the abstract alone. My own prior is that the claim is plausible — a screened Cornell potential has a long tail, and partial-wave convergence for bound-state poles can be slow — but plausible isn't established.\n\nWho's this for? Anyone doing heavy-quark T-matrix phenomenology. If the 10-20 result replicates, it argues for direct solvers in regions where partial-wave truncation is a real source of error. The paper deserves a serious referee, not a desk rejection, because the question matters and the authors are likely competent. But the referee should ask for explicit convergence data and a well-defined matching criterion before signing off.\n\nI'd bring it to reading group once the full text is available, but I wouldn't cite it yet.\n\nBest.","headline":"Plausible and potentially useful numerical study, but the central claim about partial-wave counts rests entirely on the direct solver being accurate, and the abstract doesn't demonstrate that.","tokens_in":1412,"tokens_out":1900,"would_cite":false,"duration_ms":22175,"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 claims that computing the heavy quark-antiquark T-matrix in the quark-gluon plasma without the usual partial wave expansion reveals that a surprisingly large number of partial waves, 10 to 20, are needed to match the full scatteri","keywords":["heavy quark-antiquark T-matrix","quark-gluon plasma","screened Cornell potential","partial wave expansion","Lippmann-Schwinger equation","bound states","in-medium scattering amplitude"],"falsifier":"Recompute the same T-matrix with an independent high-order partial wave expansion (e.g., $\\ell$ up to 40) on a fine grid for the same screening masses and center-of-mass energies. If the summed amplitude converges to the direct method's amplitude with only a few partial waves (say 3 to 5) in the regime where the paper claims 10 to 20 are needed, the central claim fails. A second check: run the direct solver with different quadrature and grid resolutions; if the result drifts with resolution, the reference itself is not converged.","tokens_in":1324,"feed_emoji":"⚛️","tokens_out":1642,"duration_ms":92423,"temperature":0.7,"pith_summary":"This paper tries to establish that the standard way of computing the T-matrix for heavy quark-antiquark scattering in the quark-gluon plasma, by expanding in partial waves and keeping only the first few terms, can miss a substantial part of the true scattering amplitude. The authors solve the full three-dimensional Lippmann-Schwinger equation directly, without any partial wave expansion, and use that as the exact reference. For screening masses corresponding to one to two times the crossover temperature, matching this reference requires on the order of 10 to 20 partial waves, much more than one would expect from the sizes of the first few partial wave amplitudes. This matters because the T-matrix feeds into quarkonium dissociation and heavy quark transport observables, where truncating partial waves could bias the results. The method also resolves bound states of different orbital quantum numbers simultaneously in a single energy scan below the quark-antiquark mass threshold.","feed_headline":"10-20 partial waves needed to match quark-gluon plasma scattering","feed_subtitle":"Partial waves are the angular pieces of a scattering amplitude; matching the full result takes 10-20 of them.","key_machinery":"The load-bearing object is the numerical solution of the full three-dimensional Lippmann-Schwinger equation for the in-medium T-matrix, with the screened Cornell potential as the interaction, obtained without any partial wave expansion. It serves as the exact reference amplitude against which partial wave sums are judged, and it is also the tool that exposes below-threshold bound states of different orbital quantum numbers in one energy scan.","core_discovery":"The central claim is that the partial wave expansion, when truncated at low angular momentum values whose amplitudes look significant, underestimates the number of partial waves needed to reproduce the in-medium scattering amplitude for a screened Cornell potential. Solving the full three-dimensional Lippmann-Schwinger equation without any partial wave expansion provides the exact reference T-matrix, and matching it requires 10 to 20 partial waves in the moderate screening and energy regime, i.e., screening masses of one to two times the crossover temperature. In addition, computing the T-matrix below the quark-antiquark mass threshold reveals bound states of several orbital quantum numbers","pith_inferences":["A natural test that goes beyond the paper: recompute a known heavy quark observable, such as a transport coefficient or quarkonium dissociation width, with the direct method versus a low-order partial wave truncation; if the 10 to 20 partial wave requirement is real, the observable should shift with truncation order up to that number.","The same direct approach could plausibly be extended to complex-valued in-medium potentials, where the imaginary part represents thermal dissociation, to see whether the high partial wave demand persists in that setting.","If bound states of different orbital quantum numbers are resolved in a single scan, their energy positions could map to the screening mass, potentially turning the T-matrix calculation into a way to read off the in-medium potential from spectral data."],"forward_implications":["T-matrix based observables for heavy quarks in the quark-gluon plasma, such as quarkonium dissociation rates and transport coefficients, can be computed from the full amplitude and are freed from partial wave truncation error.","Truncation criteria based on the magnitude of the first few partial wave amplitudes are unreliable; the needed number of partial waves is set by the combined force range and incident momentum, not by those magnitudes.","A single energy scan below threshold can expose bound states of different orbital angular momenta simultaneously, offering a more direct spectral view of the in-medium potential.","The direct method supplies the full scattering amplitude without the cost of carrying many partial wave terms, making it efficient for further phenomenological applications."],"supporting_citations":[],"fun_headline_variants":["No partial wave shortcut: 10-20 terms needed in QGP scattering","Heavy quark T-matrix without partial waves finds hidden bound states","Exact QGP scattering method reveals 10-20 partial wave requirement","Beyond partial waves: new approach to quark-gluon plasma T-matrix","Partial wave count surprises in heavy quark scattering in QGP"],"cache_read_input_tokens":3328,"weakest_assumption_plain":"The direct method must solve the full three-dimensional Lippmann-Schwinger equation to numerical accuracy, meaning its output is the true reference amplitude and any mismatch with partial wave sums is entirely on the partial wave side.","fun_headline_variants_meta":{"raw":{"variants":["No partial wave shortcut: 10-20 terms needed in QGP scattering","Heavy quark T-matrix without partial waves finds hidden bound states","Exact QGP scattering method reveals 10-20 partial wave requirement","Beyond partial waves: new approach to quark-gluon plasma T-matrix","Partial wave count surprises in heavy quark scattering in QGP"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000113,"raw_usage":{"total_tokens":903,"prompt_tokens":750,"completion_tokens":153,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":494,"completion_tokens_details":{"reasoning_tokens":59}},"tokens_in":494,"tokens_out":153,"duration_ms":2719,"temperature":1.0,"reasoning_tokens":59,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T19:41:38.686225+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the same T-matrix with an independent high-order partial wave expansion (e.g., $\\ell$ up to 40) on a fine grid for the same screening masses and center-of-mass energies. If the summed amplitude converges to the direct method's amplitude with only a few partial waves (say 3 to 5) in the regime where the paper claims 10 to 20 are needed, the central claim fails. A second check: run the direct solver with different quadrature and grid resolutions; if the result drifts with resolution, the reference itself is not converged.","supporting_citations":[],"review_version":1}