{"id":"c62393ba-0e64-4d67-aaeb-a104deeed4f0","arxiv_id":"2502.02346","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"DDVCS beam and target spin asymmetries at JLab and EIC are predicted to discriminate between GPD models, with dominant sensitivity to GPD H and H~.","lead":"This paper predicts how sensitive the spin asymmetries of Double Deeply Virtual Compton Scattering are to the internal quark structure of the proton, using several competing models. It concludes these asymmetries could be measured at Jefferson Lab and the future Electron-Ion Collider, mainly probing the GPD H and its polarized counterpart.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The ξ≠ξ′ EKM ansatz is a toy-model truncation (linear-y DD) and drives the model-discrimination and sign-change predictions; if it distorts GPDs away from the DVCS line, the quantitative sensitivity claims are not robust.","rationale":"I read the paper as a feasibility/phenomenology study whose central contribution is that DDVCS asymmetries map GPDs at independent (ξ′,ξ) and that existing models produce distinguishable predictions in JLab/EIC kinematics. The imaginary-part relation is a standard CFF result, and the detector simulation chain (GEMC for µCLAS, acceptance maps for SoLIDµ, EpIC for EIC) is concrete, which supports the formal and experimental-feasibility parts of the paper. I agree with the reader that the weakest load-bearing point is the ξ≠ξ′ extension of the EKM model: it is an analytic-tractability truncation rather than a physics-constrained model, and the paper itself flags the unknown behavior in this region. I do not find an internal inconsistency in the main formalism, but the model-sensitivity conclusions are only as strong as this ansatz. The proposed numerical test would settle whether the truncation changes the qualitative predictions. The reader's conditional verdict should stand; the condition is that the EKM-based model-discrimination claims be checked against the untruncated DD or an independent ξ≠ξ′ model.","tokens_in":19937,"tokens_out":11564,"duration_ms":133072,"concrete_test":"Numerically evaluate the unexpanded DD integral (Eqs. A1-A3 with Eq. A2) at the representative points of Fig. 6 (ξ=0.5, t=-0.2 GeV², 0.05≤ξ′≤0.5) and in the bins of Figs. 11-14, and compare the resulting Im[H(ξ′,ξ,t)] and asymmetry amplitudes with the truncated closed form Eq. A10. If the sign changes, relative model ordering, or amplitudes differ qualitatively, the model-discrimination and feasibility claims are artifacts of the linear-y truncation. An independent algebraic re-derivation of Eq. A10 from Eq. A2 should accompany the check to expose any hidden assumptions in the linearization.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section III.C and Appendix A extend the EKM model to ξ≠ξ′ by truncating the double distribution to linear terms in y to keep the integration analytic (Eqs. A2-A10). This extension is not constrained by data; the paper's Section V concedes that the ξ≠ξ′ behavior of GPDs is unknown and that the Mellin-Barnes/D-term generalization is not established. Yet the quantitative demonstrations—the Im[H] sign changes and relative magnitudes in Fig. 6, the EKM-vs-GK differences in the BSA/TSA/DSA/BCA projections of Figs. 11-14 and 18, and the feasibility-amplitude estimates—are driven by this toy ansatz. If the linear-y truncation distorts the GPD away from the DVCS line, the claimed model-discrimination power is an artifact. The formal statement that Im CFF accesses F+(ξ′,ξ,t) is standard and would survive, but the paper's sensitivity conclusions rest on the ansatz.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies Double Deeply Virtual Compton Scattering (DDVCS) as a channel for accessing Generalized Parton Distributions (GPDs) at independent values of the two skewness parameters ξ and ξ′, going beyond the DVCS (ξ=ξ′) and TCS (ξ=−ξ′) lines. Using the standard LO twist-2 Compton form factor (CFF) formalism, the authors construct beam spin, target spin, double spin, and beam charge asymmetries for polarized electron/positron beams on a polarized proton target. They implement several GPD models (VGG, GK, and a new extension of the KM/EKM model to ξ≠ξ′) and compute DDVCS cross-sections with the EpIC generator, including detector acceptance and efficiency effects for the JLab CLAS12/µCLAS and SoLIDµ setups and for the EIC. The main quantitative results are model predictions for the asymmetry amplitudes in (ξ′,ξ) bins and statistical-error projections for the proposed measurements, with emphasis on sign changes of Im[H] around ξ′=0 and on the dominance of H and H̃ in different observables.","tokens_in":20223,"tokens_out":3905,"duration_ms":44755,"significance":"If the main claims hold, the paper provides a useful step toward establishing DDVCS as a complementary probe of GPDs in the ξ≠ξ′ region, which is currently poorly constrained. The use of well-established public tools (PARTONS, Gepard, EpIC, GEMC, acceptance maps) and the detailed detector studies are genuine strengths, as is the identification of specific asymmetries that isolate H and H̃. However, the quantitative sensitivity conclusions rest in part on an unvalidated toy-model extension of the EKM GPDs, and the feasibility projections are statistical-only. The central formal statement that the imaginary part of the CFF accesses F+(ξ′,ξ,t) is standard and would survive, but the claimed model-discrimination power is not yet robust.","major_comments":[{"comment":"The EKM extension to ξ≠ξ′ is an ad hoc ansatz: the double distribution is truncated to linear terms in y to make the integral analytic, and the only external benchmark is the DVCS limit ϑ=1. The paper itself concedes in Section V that the behavior of GPDs in the ξ≠ξ′ region is unknown and that no generalization of the D-term is established. Since the sign changes in Im[H] (Fig. 6), the TSA sign change, the BSA sign-change predictions of Figs. 11-14, and the EIC BSA amplitudes of Fig. 18 are driven by this ansatz, the claimed model-discrimination power is not robust. The authors should either restrict the model-comparison claims to the constrained GK and VGG models or add a robustness study (e.g., varying the profile parameter b, retaining quadratic terms, or testing alternative DDs) and clearly mark the EKM extension as illustrative.","section":"Section III.C and Appendix A, Eqs. (A2)-(A10)"},{"comment":"The statement that \"the number of bins was chosen so that the error bars of the asymmetry projections show feasible measurements\" introduces a selection bias: the reported statistical errors are computed on bins that were selected after inspecting the model predictions. In addition, the projections include only statistical errors and a few polarization/efficiency rescaling factors; they do not include systematic uncertainties from the detector calibration, background subtraction, radiative corrections, or the model dependence of the acceptance. The word \"feasible\" is therefore too strong. The paper should present the binning strategy independently of the projections and also give a systematic-error envelope, or at least state clearly that the projections are idealized statistical-error-only estimates.","section":"Section IV.A, binning paragraph and Figs. 10-14"},{"comment":"The conclusion that target-polarized and beam-charge asymmetries are not accessible at the EIC relies heavily on model support limitations. Table I shows that the EKM models have no Mellin-Barnes support for H̃ and Ẽ, and the text states that the null target-polarized EKM predictions come from the absence of the sea contribution to those GPDs. This is a property of the model implementation, not a physics statement. The statement that \"H̃ extraction is not foreseen unless the target-polarized asymmetries are at least in the 5-10% range\" should be accompanied by a calculation using a model with a nonzero sea contribution to H̃, or it should be explicitly labeled as a model-dependent bound.","section":"Section IV.B, EIC configuration and Table I"},{"comment":"The abstract and end of Section II state that DDVCS allows \"unrestricted GPD extraction\" because the imaginary part of the CFF isolates F+(ξ′,ξ,t). This is too strong: even at LO twist-2, the imaginary part gives the GPD only at the specific point x=ξ′, while the real part is a convolution over x. The paper should temper the wording to \"access to independent values of ξ′ and ξ\" rather than \"unrestricted extraction,\" and should note explicitly that the full x-dependence still requires a deconvolution or model input.","section":"Section II, Eqs. (2)-(3) and the claim of 'unrestricted GPD extraction'"}],"minor_comments":[{"comment":"The symbol ϑ is used with two different meanings: ϑ=ξ′/ξ in Eq. (28) and ϑ=x/ξ in Eqs. (32)-(33). This notation conflict makes the derivation confusing; a different symbol should be used for the GPD variable in the ξ≠ξ′ formulas.","section":"Section III.C, Eqs. (28) and (32)"},{"comment":"The notation F+ is used both for the GPD combination F+(x,ξ,t) and for the CFF F(ξ′,ξ,t), with the sign convention stated only in the text. Introducing a separate symbol for the CFF (e.g., F(ξ′,ξ)) would improve readability.","section":"Section II, Eq. (1)"},{"comment":"There is a typographical duplication: \"the error bars of the asymmetry projections show feasible measurements. .\" has an extra period and the sentence is incomplete in style; it should be rewritten as a complete sentence.","section":"Section IV.A, after Fig. 10"},{"comment":"The legend entry \"MRST02 NNLO@CTEQ18\" is confusing because it suggests a single PDF set; the text explains that two PDF choices are used for the VGG model, so the caption should explicitly say \"VGG with MRST02 and with CTEQ18.\"","section":"Figs. 11 and 13 captions"},{"comment":"The sentence that the MB representation \"diverges as ξ′→0\" should be clarified: it is a growth of the model prediction in the Mellin-Barnes evaluation, not a physical divergence of the CFF, and the location of the maximum depends on evolution inputs.","section":"Section III.C, Fig. 6 discussion"},{"comment":"The conclusion states that the 11 and 22 GeV configurations \"would allow the observation of the asymmetries sign-change,\" but the sign change is shown mainly for the EKM-based predictions; the GK and VGG models do not all exhibit the same sign-change pattern in the displayed bins. The sentence should be phrased as model-dependent.","section":"Section V, first paragraph"}],"recommendation":"major_revision","confidential_remarks":"The paper is a valuable feasibility study and the central formalism is standard, so rejection would be too harsh. The main issue is that the most striking quantitative claims (sign changes and model discrimination) are driven by an unvalidated toy-model extension, while the feasibility projections are statistical-only and binning is chosen after the fact. I would recommend major revision with a request either to add robustness checks for the EKM ansatz or to downgrade the claims that depend on it, and to add a systematic-error discussion. The manuscript is otherwise suitable for a specialized nuclear/particle physics journal."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe paper is a solid, honest feasibility study of DDVCS as a GPD probe, and the formal core holds up: at LO twist-2 the imaginary part of the DDVCS CFF does give direct access to the singlet GPD combination F+ at independent x=xi' and xi, beyond the DVCS/TCS on-shell lines. The new content is the first detector-specific comparison of four GPD models (VGG, GK, EKM variants) for the BSA/TSA/DSA/BCA asymmetries at muCLAS, SoLIDmu, and the EIC, plus the toy-model extension of EKM to xi != xi' in Appendix A. The event generation with EpIC and GEMC, including acceptance maps and reconstruction efficiencies, is a serious effort, and the conclusions are appropriately cautious: they frame the measurements as exploratory and explicitly say the xi != xi' behavior of GPDs is unknown without data.\n\nThe main soft spot is exactly where the stress-test lands. The EKM xi != xi' extension is a linear-y truncation of the double distribution, kept linear to make the integral analytic, and the paper itself concedes there is no generalization of the D-term or conformal moments. The sign changes and model differences in Figs. 6, 11-14 and 18 are driven by this ansatz. If the truncation distorts the GPD away from the DVCS line, the model-discrimination claims are not robust. That said, the paper labels it a toy model, benchmarks it against the DVCS limit (theta=1), and does not present the discrimination as a measurement; it calls for further phenomenological work. So the formal claim survives, but the quantitative sensitivity statements are conditional. I would not call this a load-bearing flaw; it is a caveat that a referee should ask to be sharpened.\n\nThe projections are also statistical-error-only, with binning chosen to keep the error bars feasible, and no systematic uncertainties. That is standard for a first feasibility study, but worth flagging. Not releasing the Gepard extension code is a minor inconvenience for reproducibility.\n\nWho is this for: GPD phenomenologists and experimentalists planning JLab 12 GeV or EIC programs. It deserves a serious referee. My recommendation: send it to review; the referee should push for a clear statement of the toy-ansatz limitations and ideally a validation of the xi != xi' extension against some external constraint beyond the DVCS limit.","headline":"A solid, honest DDVCS feasibility study whose formal core holds, but whose quantitative model-sensitivity claims rest on an explicit toy-model extension that the paper itself flags as unvalidated.","tokens_in":20774,"tokens_out":3321,"would_cite":true,"duration_ms":30469,"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":"DDVCS observables can read the singlet GPD combination directly at any x=ξ′, freeing GPD extraction from the on-shell diagonal of DVCS/TCS, and the projected measurements at fixed-target and collider luminosities could make that access…","keywords":["double deeply virtual Compton scattering","generalized parton distributions","Compton form factors","beam spin asymmetry","target spin asymmetry","double spin asymmetry","beam charge asymmetry","electron-ion collider"],"falsifier":"A single fixed-target run that measures the beam-spin asymmetry as a function of ξ′ at fixed ξ (e.g., one bin of Fig. 11a) would test the ansatz: if the measured amplitude is consistent with zero where the models predict a few percent, or shows the opposite sign of the expected ξ′ → 0 crossing, the extended double-distribution ansatz for the off-diagonal region is ruled out. The same measurement, interpreted through Eq. (1), would also directly verify whether Im F equals the model's F+(ξ′, ξ, t).","tokens_in":19725,"feed_emoji":"⚛️","tokens_out":11353,"duration_ms":102998,"temperature":0.7,"pith_summary":"Double Deeply Virtual Compton Scattering (DDVCS) removes the on-shell constraint that pins GPD experiments to the diagonal line x=±ξ, so the same process can probe a generalized parton distribution at two independent values, ξ′ and ξ. The paper argues that, at leading order and twist 2, the imaginary part of the DDVCS Compton form factor directly measures the singlet combination F+ at x=ξ′, making the off-diagonal GPD region experimentally accessible. Using polarized electron/positron beams and a polarized proton target, the authors construct four asymmetry observables that weight different GPD combinations and show that several current GPD models predict large, sometimes sign-changing, amplitudes in the (ξ′, ξ) plane. They then present realistic statistical projections for 11 and 22 GeV fixed-target runs and for a future electron-ion collider, concluding that the spin-dependent DDVCS observables are measurable and that the data would discriminate among the models, with H dominating most amplitudes and H̃ contributing in target-polarized cases.","feed_headline":"DDVCS maps quark distributions beyond the DVCS diagonal","feed_subtitle":"The imaginary part of a Compton amplitude reads the singlet GPD at x=ξ′, not just at the DVCS diagonal.","key_machinery":"The machinery is the leading-order, twist-2 Compton form factor F(ξ′, ξ, t) and its dispersion relation, Eq. (1), whose imaginary part selects the singlet GPD combination F+ at x=ξ′; the four asymmetry observables (BSA, TSA, DSA, BCA) with the projection identities of Eqs. (11)–(14) that map each asymmetry moment onto a specific combination of CFFs; and the t-dependent double-distribution ansatz of Appendix A that extends the KM/EKM model into the ξ≠ξ′ region by keeping only linear terms in the profile variable, rendering the integrals analytic in terms of Appell hypergeometric functions.","core_discovery":"The central claim is that the leading-order imaginary part of the DDVCS Compton form factor, Im F(ξ′, ξ, t) = −π F+(ξ′, ξ, t), gives a direct, model-independent reading of the singlet GPD combination at x=ξ′, while the two skewness parameters ξ′ and ξ remain independent. This lifts the DVCS/TCS limitation, where the on-shell conditions force x=±ξ and only the diagonal GPD can be reached. Building on this identity, the paper shows that the beam-spin, target-spin, double-spin, and beam-charge asymmetries of ep→epℓ+ℓ− select different chiral-even GPD combinations—typically dominated by H, with H̃ entering through target polarization—and that the amplitudes differ appreciably among established GPD models in the ξ≠±ξ′ region. Feasibility projections for high-luminosity fixed-target experiments and a future electron-ion collider indicate that the asymmetries could be measured with sufficient precision to see the predicted sign changes around ξ′=0 and to distinguish among the models.","pith_inferences":["If the imaginary-part identity is exact at leading twist, one could invert the BSA measurement directly to obtain Im[H] + ... at each (ξ′, ξ) point, turning DDVCS into a point-by-point GPD measurement rather than a fit of CFF convolutions; the paper demonstrates sensitivity but does not develop this direct-extraction algorithm.","The analytic extension of the KM/EKM model keeps only linear terms in the double-distribution profile; comparing the resulting GPDs with a nonlinear extension or with lattice QCD evaluations in the ξ≠ξ′ region would quantify the systematic bias in the claimed model-discrimination power.","The predicted TSA sign change between VGG-type and KM-like models appears where the H and H̃ contributions balance; a dedicated low-ξ′ TSA measurement would therefore be a direct discriminator between competing axial-vector GPD parametrizations, which is a sharper test than the H-dominated BSA."],"forward_implications":["DDVCS asymmetries can map quark GPDs off the diagonal x=±ξ, enabling a genuinely two-dimensional scan of the (ξ′, ξ) GPD plane.","The beam-spin and double-spin asymmetries are dominated by the unpolarized GPD H over most of the phase space, while the target-spin asymmetry gives access to the polarized GPD H̃, making the target-polarized observables the clean probe of H̃.","At 11 GeV, the fixed-target acceptance populates mainly the timelike (TCS-like) region; at 22 GeV the experiment reaches both timelike and spacelike regions, so the two energies together should reveal the predicted sign change of the asymmetries across ξ′=0.","With the assumed luminosities, BSA and DSA are measurable accurately, while TSA and BCA become feasible when their amplitudes exceed about 5%, which is enough to distinguish the tested GPD models in the cells with the largest model spread.","At a future electron-ion collider, the small-ξ, small-ξ′ kinematics simplify the CFF combinations, and the beam-spin asymmetry can still access H at xB down to ~10^-4, although target-polarized and beam-charge asymmetries are expected to be too small to measure."],"supporting_citations":[{"why":"Supplies the DDVCS cross-section decomposition and the integration over the muon-pair angles that suppresses the Bethe-Heitler squared amplitude, defining the 5-fold observables.","marker":"[12]"},{"why":"Establishes DDVCS as the generalization of DVCS and TCS with two independent skewness parameters, motivating the unrestricted GPD phase space.","marker":"[13]"},{"why":"Provides the DDVCS kinematics and cross-section estimates at small xB used for the electron-ion collider feasibility projections.","marker":"[14]"},{"why":"Series of papers defining the VGG double-distribution GPD model, used as one of the benchmark predictions for all four observables.","marker":"[39–42]"},{"why":"Define the GK GPD model fitted to high-energy vector-meson production data; the GK19 parameterization is the reference for the GPD-decomposition analysis.","marker":"[46, 47]"},{"why":"Defines the KM/Mellin-Barnes GPD model that the paper extends to the ξ≠ξ′ region.","marker":"[52]"},{"why":"Provides the Mellin-Barnes representation of sea-quark CFFs whose Wilson-coefficient Taylor expansion is restored to introduce the ξ′ dependence.","marker":"[53]"},{"why":"Supplies the event generator used for the experimental projections and statistical uncertainty estimates at both fixed-target and collider setups.","marker":"[57]"}],"fun_headline_variants":["DDVCS reads GPDs at x=ξ′, lifting the diagonal constraint","DDVCS asymmetries distinguish GPD models off the diagonal","Unrestricted DDVCS phase space reveals full GPD picture","Double deeply virtual Compton scattering probes off-diagonal GPDs","DDVCS offers model-independent access to off-diagonal GPDs"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The model-sensitivity and feasibility conclusions depend on an unvalidated ansatz for GPDs when ξ≠ξ′: the paper extends the KM/EKM model with a t-dependent double distribution (Appendix A) whose analytic integrability is bought by keeping only linear terms in the profile variable, and it concedes that 'the behavior of GPDs in the ξ ≠ ξ′ region is unknown in the absence of DDVCS experimental data'.","fun_headline_variants_meta":{"raw":{"variants":["DDVCS reads GPDs at x=ξ′, lifting the diagonal constraint","DDVCS asymmetries distinguish GPD models off the diagonal","Unrestricted DDVCS phase space reveals full GPD picture","Double deeply virtual Compton scattering probes off-diagonal GPDs","DDVCS offers model-independent access to off-diagonal GPDs"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000441,"raw_usage":{"total_tokens":2226,"prompt_tokens":926,"completion_tokens":1300,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":542,"completion_tokens_details":{"reasoning_tokens":1207}},"tokens_in":542,"tokens_out":1300,"duration_ms":11874,"temperature":1.0,"reasoning_tokens":1207,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T12:28:26.393741+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A single fixed-target run that measures the beam-spin asymmetry as a function of ξ′ at fixed ξ (e.g., one bin of Fig. 11a) would test the ansatz: if the measured amplitude is consistent with zero where the models predict a few percent, or shows the opposite sign of the expected ξ′ → 0 crossing, the extended double-distribution ansatz for the off-diagonal region is ruled out. The same measurement, interpreted through Eq. (1), would also directly verify whether Im F equals the model's F+(ξ′, ξ, t).","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the DDVCS cross-section decomposition and the integration over the muon-pair angles that suppresses the Bethe-Heitler squared amplitude, defining the 5-fold observables."},{"cited_title":"Guidal and M","cited_arxiv_id":null,"evidence_quote":"Establishes DDVCS as the generalization of DVCS and TCS with two independent skewness parameters, motivating the unrestricted GPD phase space."},{"cited_title":"Deja et al , Phys","cited_arxiv_id":null,"evidence_quote":"Provides the DDVCS kinematics and cross-section estimates at small xB used for the electron-ion collider feasibility projections."},{"cited_title":"Kumeriˇ cki and D","cited_arxiv_id":null,"evidence_quote":"Defines the KM/Mellin-Barnes GPD model that the paper extends to the ξ≠ξ′ region."},{"cited_title":"Investissements d’avenir","cited_arxiv_id":null,"evidence_quote":"Provides the Mellin-Barnes representation of sea-quark CFFs whose Wilson-coefficient Taylor expansion is restored to introduce the ξ′ dependence."},{"cited_title":"Kumeriˇ ckiet al ., Nucl","cited_arxiv_id":null,"evidence_quote":"Supplies the event generator used for the experimental projections and statistical uncertainty estimates at both fixed-target and collider setups."}],"review_version":1}