{"id":"7c183b18-2343-4cf8-86be-7cce7b8e8ecb","arxiv_id":"2507.16250","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":13,"one_line_summary":"Pionless effective field theory with non-perturbative Coulomb at NLO predicts pd, dd, and p3He scattering lengths and effective ranges that agree with experimental phase-shift analyses.","lead":"A pionless effective field theory with explicit Coulomb interactions was used to compute low-energy scattering of charged nuclear clusters at next-to-leading order. The calculated pd, dd, and p3He scattering lengths and effective ranges match recent experimental phase-shift analyses, supporting the theory's predictive power for few-nucleon reactions.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Section III C names spin-singlet LECs (C1^(1), C4^(1)) for the all-triplet dd S=2 channel, contradicting Eqs. (3) and (5); the dd NLO prediction 6.262(42) fm is not reproducible as written.","rationale":"The reader's weakest assumption concerned the composite-cluster validity of Eq. (10), and that is a legitimate secondary caveat: the trap quantization condition is derived for two point charges, and no benchmark against an independent Coulomb-scattering method is shown. I do not build the verdict on that caveat, because the formula is plausibly valid for any short-range residual interaction and the paper states the needed separation of scales. The harder, manuscript-internal problem is the dd LEC inconsistency. In the S=2 channel the spin wavefunction is totally symmetric, so every two-nucleon pair is in a spin-triplet state; spin-singlet projectors annihilate the state. The NLO LECs named in Section III C are exactly such singlet projectors. This is not a matter of EFT convention or scale; it is a logical contradiction between the stated selection rule and the cited equations. Unless a typo is confirmed, the dd prediction is unsupported. Because the paper provides no code or data, the natural remedy is a conditional acceptance requiring the authors to state the correct LEC set and, ideally, to release or benchmark the dd computation. If the typo is confirmed and the recomputation matches the printed values, I would accept the dd result as part of the paper's claim. I therefore recommend CONDITIONAL rather than REJECT: the overall framework is coherent, the pd and p3He predictions are independently testable, and the issue is localized and resolvable.","tokens_in":19584,"tokens_out":22114,"duration_ms":256742,"concrete_test":"Recompute the NLO dd S=2 ERE parameters at a fixed cutoff (e.g., Lambda=6 fm^-1) with three two-body NLO choices: (a) the printed pair {C1^(1), C4^(1)}, (b) the spin-triplet pair {C2^(1), C3^(1)}, and (c) no NLO two-body terms; then apply the Eq. (13) extrapolation. The reported a_dd^2=6.262(42) fm should be reproduced only by choice (b). If it is reproduced by choice (a), the dd result is wrong rather than mislabeled.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"In Section III C the authors state that for dd S=2, 'all nucleon pairs must couple to S=1, consequently, only the terms with C1^(0), C1^(1) and C4^(1) LECs contribute.' The first of these is a spin-triplet isoscalar LEC and is consistent. The two NLO LECs named are not: in Eq. (3), C1^(1) multiplies the spin-singlet isovector projector P^(0,1), and in Eq. (5), C4^(1) multiplies the pp spin-singlet projector P^(0,1;pp). Both projectors vanish when every pair has S=1. The NLO spin-triplet LECs in the potential are C2^(1) (momentum-independent) and C3^(1) (momentum-dependent), neither of which is mentioned in the dd section. If the sentence reflects the actual computation, the dd NLO result a_dd^2=6.262(42) fm, r_dd^2=1.41(7) fm is invalid. If it is only a typo, the paper still gives an inconsistent specification of the calculation, and since no code or data files accompany the paper, the quoted dd numbers cannot be independently verified from the manuscript. This is load-bearing because dd S=2 is one of the three headline predictions and is the only result with no direct experimental scattering-length analysis to anchor it.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper formulates a pionless EFT with a non-perturbative Coulomb interaction at leading order and perturbative NLO corrections, using local regulators and two-, three-, and four-body contact interactions. The authors solve the few-body Schrödinger equation with the stochastic variational method in a harmonic-oscillator trap corrected for Coulomb long-range effects, and extract s-wave phase shifts for pd, dd, and p3He scattering. Low-energy constants are fitted to two-nucleon scattering data and the binding energies of 3H, 3He, and 4He, so the reported scattering parameters are genuine predictions. The headline NLO results are a_pd^{3/2}=12.76(29) fm, r_pd^{3/2}=1.17(7) fm; a_dd^{2}=6.26(3) fm, r_dd^{2}=1.41(7) fm; and a_p3He^0=11.26(4) fm, r_p3He^0=1.65(26) fm, a_p3He^1=9.06(4) fm, r_p3He^1=1.36(25) fm. These are compared with experimental phase-shift analyses and potential-model calculations and are found to agree well, supporting the predictive power of the framework.","tokens_in":20077,"tokens_out":13632,"duration_ms":167521,"significance":"If the stated results hold, this is a significant methodological advance: it extends potential-formulation pionless EFT with non-perturbative Coulomb interactions to four-nucleon charged scattering, provides a concrete demonstration that the NLO ppn three-body force is necessary for renormalization, and delivers scattering-length predictions that do not enter the LEC fits. The cutoff-dependence analysis with explicit 1/Λ and 1/Λ^2 extrapolations, the careful specification of fitting targets, and the comparison with experimental phase-shift analyses are notable strengths. The paper is generally careful about error estimation and clearly identifies where calculations without mandated counterterms fail to converge. However, the internal inconsistency in the dd channel specification prevents acceptance in the present form, and the applicability of the point-charge trap quantization condition to composite clusters needs a quantitative justification.","major_comments":[{"comment":"The text states that for dd S=2 scattering only the C1^(0), C1^(1), and C4^(1) LECs contribute, because all nucleon pairs couple to S=1. This is internally inconsistent with the definitions in Eqs. (3) and (5): C1^(1) multiplies the spin-singlet isovector projector P^(0,1), and C4^(1) multiplies the pp spin-singlet projector P^(0,1;pp). Both projectors vanish when every pair is in a triplet state. The NLO spin-triplet operators in Eq. (3) are the C2^(1) and C3^(1) terms, which are not named in Section III C. If the quoted sentence reflects the actual computation, the dd NLO results a_dd^2=6.262(42) fm and r_dd^2=1.41(7) fm are invalid; if it is only a typographical error, the manuscript still gives an unreproducible account of the calculation. Because dd S=2 is one of the three headline predictions and has no direct experimental scattering-length anchor, the authors must correct this specification and confirm the quoted dd numbers with the corrected set of contributing LECs.","section":"III C, Eq. (3), Eq. (5)"},{"comment":"The phase-shift extraction uses Eq. (10), a Coulomb-corrected harmonic-oscillator quantization condition derived for two point charges, and applies it to composite clusters such as d and 3He. In the A-body calculation the Coulomb interaction acts between individual protons, so the asymptotic cluster-cluster potential contains finite-size, multipole, and polarization contributions beyond the point-charge q1 q2 e^2/r term. Equation (10) subtracts only the point-Coulomb Green's functions; if these additional long-range tails are not negligible at the quoted precision, particularly for the dd scattering length quoted to 0.03 fm, the extracted ERE parameters carry a systematic error not included in the reported uncertainties. The authors should justify that these contributions are beyond NLO in their power counting and provide a numerical estimate of their effect, or otherwise demonstrate that the point-charge subtraction is exact for their cluster wavefunctions.","section":"II C, Eq. (10)"}],"minor_comments":[{"comment":"The pd spin-quartet values differ between the abstract and the main text: the abstract gives a_pd^{3/2}=12.76(29) fm and r_pd^{3/2}=1.17(7) fm, while Section III B gives a_pd^{3/2}=12.76(26) fm and r_pd^{3/2}=1.16(8) fm; the final values and uncertainties should be harmonized.","section":"Abstract and III B"},{"comment":"References [21] and [52] appear to be the same paper (Marcucci et al., Frontiers in Physics 8, 69 (2020)) and should be consolidated or differentiated.","section":"References"},{"comment":"The modified effective range expansion for the spin-doublet channel is written with a sign in the denominator that is only described in words; stating the sign convention explicitly before Eq. (14) would improve reproducibility.","section":"Eq. (14)"},{"comment":"The four-body LEC E0^(1) shows strongly non-monotonic cutoff dependence, including a sign change around Λ=6 fm^-1; a brief comment on this running behavior would be helpful.","section":"Table IV"}],"recommendation":"major_revision","confidential_remarks":"The central blocker is the Section III C LEC inconsistency. If the authors can confirm that the dd calculation actually used the spin-triplet NLO LECs C2^(1) and C3^(1) and reproduce the same numbers, the paper is close to acceptable after a clear correction and a quantitative justification of the trap method for composite clusters. The absence of code or data files makes the contradiction harder to resolve, so I would encourage the editor to request a clear reproducibility statement or the relevant numerical data."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read it. The genuinely new piece is the first potential-formulation pionless EFT with non-perturbative Coulomb at NLO, applied to pd, dd, and p3He s-wave scattering. The LECs are fit to two-body scattering data and the 3H, 3He, and 4He binding energies, and every scattering parameter they quote comes out as a prediction, not a fit input. That is a real step beyond the dibaryon-formalism calculations.\n\nThe pd quartet and p3He results are the strong part. They agree with the existing phase-shift analyses and potential models, and the cutoff dependence is quantified with the expected 1/Lambda and 1/Lambda^2 extrapolations. The demonstration that the NLO ppn three-body force is necessary — they show the calculation diverges without it — is convincing and matches the earlier analytical dibaryon result. The LEC tables in the appendix are useful.\n\nNow the soft spots. Section III C states that in the dd S=2 channel only C1^(0), C1^(1), and C4^(1) contribute. That is inconsistent with Eqs. (3) and (5): both C1^(1) and C4^(1) multiply spin-singlet projectors, which vanish when every pair is in a triplet. The NLO spin-triplet terms are C2^(1) and C3^(1). If the sentence is a typo, the dd calculation is still not reproducible from the text, and since no code or data files accompany the paper, a_dd^2 = 6.262(42) fm has to be taken on faith. If the computation really used C1^(1) and C4^(1), the NLO shift would be zero, which is not what they report, so I suspect a typo — but it is a headline result and has to be corrected.\n\nThe second concern is the trap quantization condition, Eq. (10), borrowed from a two-point-charge derivation and applied to composite clusters. Representing d and 3He as point charges and absorbing finite-size Coulomb effects into short-range contacts may be fine in the EFT power counting, but it is an assumption that deserves a benchmark against a potential-model calculation with the same Coulomb subtraction, not just a statement.\n\nBottom line: this deserves a serious referee. The pd and p3He predictions alone justify the review. I would send it back for revision, asking for a corrected dd operator specification and ideally a reproducibility statement or data release.","headline":"Solid NLO pionless-EFT calculation of charged few-nucleon scattering, with a fixable but real operator error in the dd section.","tokens_in":20704,"tokens_out":3530,"would_cite":true,"duration_ms":34434,"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":"A renormalizable pionless EFT with non-perturbative Coulomb reproduces low-energy charged few-nucleon scattering at next-to-leading order.","keywords":["pionless effective field theory","Coulomb interaction","few-nucleon scattering","scattering length","effective range expansion","harmonic oscillator trap","proton-deuteron scattering","proton-helium-3 scattering"],"falsifier":"Extract the same EFT phase shifts with an independent Coulomb-handling scheme—for example, screening-and-renormalization of the Coulomb potential in the continuum—and check whether the effective-range parameters reproduce $12.76(29)$, $6.26(3)$, $11.26(4)$, and $9.06(4)\\,\\mathrm{fm}$ within their quoted errors; a systematic shift beyond those bands would falsify the point-charge trap assumption. Alternatively, a future precision measurement of the pd quartet scattering length with error below $0.3\\,\\mathrm{fm}$ that disagrees with $12.76(29)\\,\\mathrm{fm}$ would directly test the central prediction.","tokens_in":19331,"feed_emoji":"⚛️","tokens_out":7928,"duration_ms":74659,"temperature":0.7,"pith_summary":"The paper aims to show that pionless effective field theory—a theory built only from nucleon contact interactions, with no pions—can describe low-energy scattering of charged nuclei once the Coulomb force is treated non-perturbatively. Working at next-to-leading order, the authors extract phase shifts and effective-range parameters for proton-deuteron, deuteron-deuteron, and proton-helium-3 scattering from a harmonic-oscillator trap. Their central numerical predictions are a pd spin-quartet scattering length of $a_{pd}^{3/2}=12.76(29)\\,\\mathrm{fm}$, a dd spin-quintet scattering length of $a_{dd}^{2}=6.26(3)\\,\\mathrm{fm}$, and p-3He scattering lengths of $a_{p^3\\mathrm{He}}^0=11.26(4)\\,\\mathrm{fm}$ and $a_{p^3\\mathrm{He}}^1=9.06(4)\\,\\mathrm{fm}$, with effective ranges near $1.2$–$1.7\\,\\mathrm{fm}$. The results show mild cutoff dependence and agree with existing experimental phase-shift analyses and potential-model calculations, which would establish that this minimal EFT has predictive power for charged few-nucleon systems.","feed_headline":"Pionless EFT predicts charged-nucleus scattering lengths","feed_subtitle":"At next-to-leading order, minimal nuclear forces match measured phase shifts in three charged-scattering channels.","key_machinery":"The load-bearing objects are the local regulator-dependent contact potentials of pionless EFT. The two-body spin-singlet proton-proton channel is split off and treated as Coulomb plus its own LO and NLO contact terms; a ppn three-body contact force is added at NLO to renormalize channels containing two protons and a neutron. Scattering information is extracted by placing the clusters in a harmonic-oscillator trap and using the Coulomb-corrected trap quantization condition (Eq. 10), which relates bound-state energies in the trap to Coulomb-subtracted phase shifts through Coulomb Green's functions; the stochastic variational method with correlated Gaussians solves the many-body Schrödinger equation, and observables are extrapolated to the contact limit from cutoff dependence.","core_discovery":"The paper's central discovery is that a renormalizable pionless EFT with the Coulomb interaction summed to all orders, and only next-to-leading-order short-range corrections treated perturbatively, reproduces low-energy charged few-nucleon scattering. The key structural finding is that, at NLO, a new isospin-symmetry-breaking ppn three-body contact force is required to cancel logarithmic cutoff divergences in the 3He channel and in pd spin-doublet scattering; without it, binding energies and phase shifts fail to converge as the cutoff grows. With that force plus the mandatory four-body force, the extrapolated effective-range parameters for pd, dd, and p3He scattering land close to experimental values and are renormalization-group invariant, implying the theory, though simple, is predictive rather than merely descriptive.","pith_inferences":["A direct test of the point-charge trap assumption would be to recompute the same EFT potentials with a screened-Coulomb or finite-charge-distribution trap condition and compare the effective-range parameters; disagreement outside the quoted errors would indicate that the uncertainties omit a systematic effect.","The almost flat cutoff dependence of $a_{p^3\\mathrm{He}}^1$ suggests that a next-to-next-to-leading-order calculation in this channel could sharpen the prediction below the current $0.04\\,\\mathrm{fm}$ uncertainty, a testable next step.","The ppn three-body force's role could be probed experimentally through spin observables or polarization-dependent pd scattering, where doublet and quartet channels contribute differently.","The trap-based phase-shift extraction, combined with the EFT's cutoff-based error estimates, offers a path to computing low-energy charged fusion rates without solving the full continuum scattering problem."],"forward_implications":["The NLO pd spin-quartet scattering length, $a_{pd}^{3/2}=12.76(29)\\,\\mathrm{fm}$, moves from the LO value $9.9(1.1)\\,\\mathrm{fm}$ into the region of the most recent experimental extraction and potential-model predictions, so the NLO correction is the one that brings the theory into agreement.","The p3He spin-triplet scattering length has almost flat cutoff dependence at NLO, suggesting that this channel is already well converged at next-to-leading order.","No three-body force is needed in the pd spin-quartet or dd spin-quintet channels up to NLO, because all nucleon pairs couple to spin-triplet/isospin-singlet configurations; those calculations test only two-body input.","The failure of NLO 3He and 4He binding energies to converge when the ppn three-body force or the four-body force is omitted confirms that these forces are mandatory for renormalization, not optional refinements.","The same interaction can be applied to reactions of astrophysical interest, such as dd fusion, for which the elastic dd channel is already computed here."],"supporting_citations":[{"why":"Establishes the non-perturbative Coulomb treatment and the additional pp LEC that the paper's power counting builds on.","marker":"[7]"},{"why":"Shows analytically that a ppn three-body force must appear at NLO; the paper verifies this finding numerically.","marker":"[9]"},{"why":"Provides the preceding non-Coulomb NLO pionless EFT potential and cutoff-extrapolation scheme used here.","marker":"[13]"},{"why":"Supplies the harmonic-oscillator trap phase-shift extraction and SVM few-body framework extended to Coulomb.","marker":"[14]"},{"why":"Derives the Coulomb-corrected trap quantization condition, Eq. (10), from which all phase shifts in this paper are extracted.","marker":"[26]"},{"why":"Gives the earlier N2LO quartet pd scattering length whose discrepancy with potential models motivated the Coulomb-subtraction scheme used here.","marker":"[17]"},{"why":"Provides the experimental p3He phase-shift analysis and effective-range parameters the paper's NLO results are compared against.","marker":"[58]"},{"why":"Supplies the low-energy pd phase-shift data used to benchmark the calculated quartet and doublet phase shifts.","marker":"[47]"}],"fun_headline_variants":["Pionless EFT predicts pd, dd, and p3He scattering","Renormalizable pionless EFT matches charged-scattering data","Coulomb-aware EFT reproduces charged few-nucleon scattering","Next-to-leading-order pionless EFT predicts charged scattering"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the trap quantization condition for two point charges (Eq. 10) remains valid for composite charged clusters such as the deuteron and 3He, with all finite-size Coulomb effects absorbed into the short-range contact terms; if that subtraction fails, the quoted scattering lengths and effective ranges carry a systematic error not included in their uncertainties.","fun_headline_variants_meta":{"raw":{"variants":["Pionless EFT predicts pd, dd, and p3He scattering","Renormalizable pionless EFT matches charged-scattering data","Coulomb-aware EFT reproduces charged few-nucleon scattering","Next-to-leading-order pionless EFT predicts charged scattering"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000748,"raw_usage":{"total_tokens":3394,"prompt_tokens":1067,"completion_tokens":2327,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":683,"completion_tokens_details":{"reasoning_tokens":2253}},"tokens_in":683,"tokens_out":2327,"duration_ms":18785,"temperature":1.0,"reasoning_tokens":2253,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T15:17:06.004769+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Extract the same EFT phase shifts with an independent Coulomb-handling scheme—for example, screening-and-renormalization of the Coulomb potential in the continuum—and check whether the effective-range parameters reproduce $12.76(29)$, $6.26(3)$, $11.26(4)$, and $9.06(4)\\,\\mathrm{fm}$ within their quoted errors; a systematic shift beyond those bands would falsify the point-charge trap assumption. Alternatively, a future precision measurement of the pd quartet scattering length with error below $0.3\\,\\mathrm{fm}$ that disagrees with $12.76(29)\\,\\mathrm{fm}$ would directly test the central prediction.","supporting_citations":[{"cited_title":"Kong and F","cited_arxiv_id":null,"evidence_quote":"Establishes the non-perturbative Coulomb treatment and the additional pp LEC that the paper's power counting builds on."},{"cited_title":"Vanasse, D","cited_arxiv_id":null,"evidence_quote":"Shows analytically that a ppn three-body force must appear at NLO; the paper verifies this finding numerically."},{"cited_title":"Sch¨ afer and B","cited_arxiv_id":null,"evidence_quote":"Provides the preceding non-Coulomb NLO pionless EFT potential and cutoff-extrapolation scheme used here."},{"cited_title":"Bagnarol, M","cited_arxiv_id":null,"evidence_quote":"Supplies the harmonic-oscillator trap phase-shift extraction and SVM few-body framework extended to Coulomb."},{"cited_title":"Guo, Coulomb corrections to two-particle interactions in artificial traps, Physical Review C 103, 064611 (2021)","cited_arxiv_id":null,"evidence_quote":"Derives the Coulomb-corrected trap quantization condition, Eq. (10), from which all phase shifts in this paper are extracted."},{"cited_title":"K¨ onig and H.-W","cited_arxiv_id":null,"evidence_quote":"Gives the earlier N2LO quartet pd scattering length whose discrepancy with potential models motivated the Coulomb-subtraction scheme used here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the experimental p3He phase-shift analysis and effective-range parameters the paper's NLO results are compared against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the low-energy pd phase-shift data used to benchmark the calculated quartet and doublet phase shifts."}],"review_version":1}