{"id":"61ac19b8-b87c-4439-a10e-798b00e1e5ed","arxiv_id":"2412.08726","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A new FLUKA-based database and Python tool give the joint energy and angular distribution of gamma rays from proton-proton collisions between threshold and 100 GeV, with an approximate fit formula.","lead":"This paper computes how gamma rays from proton-proton collisions are spread in both energy and direction, not just energy alone, using FLUKA simulations from near the production threshold up to 100 GeV. The results come with public tables and a Python tool, which matters for interpreting Fermi-LAT observations of sources like the Sun and jets where emission is not collinear.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Angle-integrated validation against Kafexhiu et al. cannot certify the new angular dimension; FLUKA's d2N/dE dΩ is the central deliverable and its angular shape is never independently checked.","rationale":"The reader's weakest_assumption identifies the same load-bearing concern: FLUKA's angular predictions are the novel content, and they are tested only after integrating over angle. The argument structure is: (1) the angular distribution matters in off-axis and near-threshold regimes; (2) FLUKA provides that distribution; (3) angle-integrated spectra match Kafexhiu et al.; (4) tables and a Python tool are provided. Steps 1 and 3 are fine. Step 2 is the empirical premise, and step 3 does not test its angular content. The paper explicitly justifies FLUKA as 'well-calibrated to experimental data' (Sec. II.B), but no angular comparison is shown. A prior angular model, Karlsson & Kamae, is cited, making a quantitative comparison feasible; its omission is a concrete gap rather than a mere preference. I do not see a fatal internal inconsistency: the analytic fit is openly ad hoc, the θ > 90° restriction and ncut are disclosed, and the GitHub tables are a useful resource. The appropriate verdict is CONDITIONAL: accept the resource, but require angular validation—or at minimum explicit caveats about untested angular systematics—before the tables are used as precise astrophysical inputs. Because the reader already reaches CONDITIONAL, the verdict is unchanged. If an independent angular comparison later shows large discrepancies, the deliverable's central usefulness would be materially reduced, possibly to REJECT as a validated tool.","tokens_in":17404,"tokens_out":3975,"duration_ms":44318,"concrete_test":"Reproduce the FLUKA setup (same Ep grid, Δlog Eγ = 0.125, Δθ = 5°) with an independent hadronic generator that is also validated in this energy range, e.g., UrQMD or GEANT4's FTFP_BERT, and compute d2N/dE dΩ. Compare, for Eγ > 100 MeV and Ep = 1.33, 1.78, 2.37, 5.62, 10, and 56.2 GeV, the bin-wise yield ratio and the 75%/90% containment angles from Fig. 5. If the independent generator disagrees with the FLUKA tables by more than ~30% in yield-weighted bins or by more than 5° in the 90% containment angle at Ep ≤ 10 GeV, the angle-integrated agreement with Kafexhiu et al. is insufficient to validate the new angular dimension, and the tables' central claim would need qualification.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central deliverable is the double-differential gamma-ray yield d2Nγ/dE dΩ from FLUKA, advertised as reliable in the non-collinear regime. The only quantitative validation (Sec. III, Fig. 4) integrates over solid angle and compares with Kafexhiu et al., an angle-integrated model; agreement there constrains dN/dE only and cannot detect a compensating error in which the pion production angular distribution is too narrow or too broad while the total yield is preserved. FLUKA is cited as calibrated to hadronic data (Sec. II.B), but no angular distribution of pions or gamma rays is compared to experiment or to the existing angular model of Karlsson & Kamae [45]. Because the gamma-ray angle is set by π0 production angle and decay kinematics, this is precisely the quantity users need when collinearity fails (Secs. I, V). The tables also carry no quoted systematic uncertainties, so the size of the risk is not quantified. Thus the load-bearing assumption—that FLUKA's angular predictions are accurate at Ep = 1.33–100 GeV—is unsupported by the validation shown. This is a correctness-risk concern, not a statement that FLUKA is wrong; it is a statement that the paper's evidence does not yet establish the angular accuracy on which its primary product depends.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper calculates the double-differential gamma-ray yield d²Nγ/dE dΩ from inelastic proton-proton collisions for incident proton energies from 1.33 to 100 GeV, using FLUKA simulations for pion production and secondary decays. The authors present the results as public tables and a Python tool, validate the angle-integrated yields against Kafexhiu et al. and check the inclusive π0 cross section, provide an analytic fit over the first decade above threshold with quantified errors, and discuss applications to off-axis jets and solar gamma rays.","tokens_in":17662,"tokens_out":4063,"duration_ms":45273,"significance":"If the tabulated results are accurate, the paper fills a genuine gap: the commonly used models provide dNγ/dE only, while the earlier angular treatments either cover different energy regimes or are less accessible. The public database and Python tool are a useful community resource for Fermi-LAT-era modeling, and the paper is explicit that the analytic formula is an ad-hoc fit with quantified errors rather than a prediction. The main risk is that the angular dimension itself, which is the central deliverable, is not independently validated against experiment or another angular model. The paper's angle-integrated agreement with Kafexhiu et al. is necessary but not sufficient to certify the off-axis and low-energy regime for which the tables are intended.","major_comments":[{"comment":"The only quantitative validation shown is the solid-angle-integrated yield compared with Kafexhiu et al.; this constrains dN/dE only. The abstract's deliverable is d²N/dE dΩ, and the angular shape of pion production is never checked against experiment, against the earlier model of Karlsson & Kamae [45], or against an alternative Monte Carlo. Because off-axis and low-energy users rely precisely on the angular shape, the paper should add a direct comparison of angular distributions (e.g., π0 or γ-ray yields at representative Ep) or otherwise provide a quantitative estimate of FLUKA's angular uncertainty. Without this, the central product is not yet supported.","section":"Sec. III, Fig. 4"},{"comment":"The primary tabular results carry no quoted statistical or systematic uncertainties per bin. The analytic fit errors are quantified in Sec. IV, but the tables themselves are presented without error bars, so the reader cannot assess the significance of discrepancies in the non-collinear regime. Please state the number of simulated events per energy and provide at least a global systematic uncertainty estimate, for example from FLUKA version dependence or from comparison with an alternative code.","section":"Sec. III (public tables and GitHub database)"},{"comment":"The analytic fit is restricted to 0°–90° and to the first decade above threshold, with maximum errors of roughly 40% and larger errors above ~13.3 GeV. This is clearly stated in the text, but the abstract's advertised range of 'the pion production threshold to 100 GeV' could mislead users into applying the formula outside its fitted domain. The text should state prominently that the analytic formula is only for the first decade and that the tables are the intended product for the full range.","section":"Sec. IV, Eqs. (15)-(16) and Fig. 7"}],"minor_comments":[{"comment":"In the sentence following Eq. (9), 'Fp,γ(Ep, Eγ, θ), defined similarly to Fp,γ(Ep, Eπ, θ)' should refer to Fp,π in the second occurrence; the pion index is lost.","section":"Sec. III, Eq. (9)"},{"comment":"The cutoff ncut depends on xmin = 100 MeV/Ep, which varies with primary energy; please state this dependence explicitly when defining ncut.","section":"Sec. III, Eq. (12)-(13)"},{"comment":"The caption notes that x ranges and colorbar ranges vary among panels, which makes quantitative cross-panel comparison difficult; consider adding a fixed reference scale or contour labels.","section":"Sec. III, Fig. 2"},{"comment":"The power-law integration in the jet example uses an arbitrary high-energy cutoff at 1000 GeV; please state in the text or caption that the displayed spectra may depend on this cutoff choice.","section":"Sec. V.A, Eq. (21)-(22) and Fig. 9"},{"comment":"The GitHub repository URL is given, but the text does not state the exact FLUKA version or release used to generate the tables; because FLUKA results can change between releases, this information should be included with the tables.","section":"Sec. III, simulation setup"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a useful phenomenological resource, not a physics breakthrough. What is actually new is a public FLUKA-based database and Python tool for d2Nγ/dE dΩ in pp collisions from threshold to 100 GeV, plus an honest 29-parameter analytic fit. The angle-integrated comparison to Kafexhiu et al. is the right sanity check and it passes. The paper also deserves credit for shipping tables and code, for the cone-containment plots that quantify the onset of collinearity, and for explicitly stating where the fit fails.\n\nThe stress-test note lands, though not fatally. The central new quantity is the angular shape from FLUKA, and that shape is never checked against an independent model or experimental data. Agreement after integrating over angle constrains only dN/dE; a too-narrow or too-wide pion angular distribution with compensated total yield would pass Figure 4. FLUKA's calibration to hadronic data is cited, but no pion angular distribution comparison is shown. Since the double-differential yield is the advertised product, this is a real gap. The tables also carry no quoted statistical or systematic uncertainties, so users cannot tell how much risk they are taking in the non-collinear regime. A quantitative comparison to Karlsson and Kamae would partially address this; the paper only discusses that prior model qualitatively. The fit itself is openly a fit, so there is no circularity problem, and the ncut choice is disclosed and reasonable.\n\nOne place the stress test is too harsh: this is not a load-bearing flaw in the sense that the whole enterprise is wrong. FLUKA's track record plus the angle-integrated agreement mean the tables are probably usable with caution. But the paper slightly overstates its own support when it leans on FLUKA's general calibration without testing the specific double-differential quantity being delivered.\n\nThe paper is for modelers working on off-axis jets, solar gamma rays, and lunar emission with Fermi-LAT; they will want this tool. It deserves a serious referee. The main revision requests should be uncertainty estimates on the tables and either an explicit angular validation or a clearly scoped caveat that the angular shapes inherit FLUKA's unquantified systematics. I would accept it with major revisions rather than desk-reject.","headline":"A genuinely useful public resource for gamma-ray modelers, held back by the fact that the new angular dimension is never independently validated.","tokens_in":18231,"tokens_out":1608,"would_cite":true,"duration_ms":18485,"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 provides the joint energy-angle yield of gamma rays from proton-proton collisions, from the pion threshold to 100 GeV, and shows that the gamma rays are measurably non-collinear at the low energies that dominate astrophysical…","keywords":["gamma-ray production","proton-proton collisions","angular distribution","cosmic rays","hadronic interactions","pion decay","astrophysical gamma rays","Monte Carlo simulations"],"falsifier":"Measure the gamma-ray yield per collision in a fixed energy-angle bin, for example near $E_p=5.6$ GeV, $E_\\gamma \\sim 200$ MeV, and $\\theta \\sim 60^\\circ$, using an independent hadronic simulation or a dedicated accelerator measurement; if the measured or independently computed yield disagrees with the tables beyond the estimated hadronic uncertainties, the angular component of the central claim fails.","tokens_in":17162,"feed_emoji":"📊","tokens_out":6242,"duration_ms":61099,"temperature":0.7,"pith_summary":"The paper's target is the joint energy-angle gamma-ray yield of a single proton-proton collision, $d^2N_\\gamma/dE\\,d\\Omega$, over proton kinetic energies from threshold to 100 GeV and photon energies above 100 MeV. Its central claim is that collinearity—the assumption that gamma rays follow the parent proton's direction—fails badly in exactly the regime where much of the astrophysical yield lives, so modellers need the correlated distribution rather than the angle-integrated spectrum alone. The authors provide that distribution as public tables with a software tool, validate their angle-integrated spectra against established results, and add an approximate analytic form. This matters because off-axis jets, the Sun, and the Moon all produce observable gamma rays whose interpretation depends on the off-axis contribution, which is largest at low proton energy and low photon energy where existing treatments are least reliable.","feed_headline":"Gamma-ray yield now mapped by angle in proton-proton collisions","feed_subtitle":"Off-axis sources need the joint energy-angle yield, not just the collinear spectrum.","key_machinery":"The carrying mechanism is a particle-transport Monte Carlo code calibrated to accelerator data, used to simulate inelastic proton-proton collisions and the subsequent decays of pions and other secondaries, with gamma-ray energy binned logarithmically ($\\Delta\\log E_\\gamma=0.125$) and angle in $5^\\circ$ bins. The paper's central objects are the per-interaction joint yield $F_{p,\\gamma}(E_p,E_\\gamma,\\theta)$ and its dimensionless form $x\\,d^2N_\\gamma/dx\\,d\\Omega$ with $x=E_\\gamma/E_p$, chosen to exploit approximate Feynman scaling. The ancillary analytic fit, $f(x,\\theta,E_p)=A(x,E_p)\\exp[-B(x,E_p)\\theta^{I(E_p)}]$, captures the exponential suppression with angle and resolves the peak position through the $e^{-A_1 x^2}-e^{-A_3 x}$ factor. The critical kinematic ingredient is that pion decay produces a flat-in-log photon spectrum centered near $E_\\gamma=E_\\pi/2$, so backward-emitted photons fall below the 100 MeV threshold and the forward beaming cone widens as energy drops.","core_discovery":"The core claim is that gamma-ray production in $pp$ collisions is measurably non-collinear up to primary energies of tens of GeV, and that the full double-differential yield per inelastic collision, expressed as $E_\\gamma F_{p,\\gamma}(E_p,E_\\gamma,\\theta)$, can be tabulated with enough accuracy to replace the collinear approximation. The paper shows that near threshold the yield extends beyond $90^\\circ$ with low-energy photons, that the spectral shape depends sharply on viewing angle, and that even at high $E_p$ a low-energy off-axis component persists. It further claims that by roughly 65 GeV a $10^\\circ$ cone contains 90% of the $\\geq100$ MeV gamma rays, establishing 100 GeV as the energy above which the old collinear formulas suffice. The compiled tables, the analytic fit, and the validation against angle-integrated spectra together constitute the deliverable.","pith_inferences":["If the tables are correct, lunar gamma rays are a clean test: the Moon lacks a magnetic field, so only gamma rays emitted at large angles can escape, making the observed limb profile a direct read-off of the off-axis yield.","A natural extension is to generate analogous tables for proton-helium and alpha-proton collisions rather than a simple nuclear enhancement factor, because intranuclear cascades could alter the angular spread at low energy.","The exponential form of the analytic fit suggests a compact universal scaling in $\\theta^{I(E_p)}x$ that could be tested across independent Monte Carlo codes; if it holds, the distribution reduces to a one-dimensional family of curves.","The analogy drawn to off-axis neutrino beams suggests the same tables could be applied to studies of beam-dump and collider neutrino fluxes where parent meson direction matters."],"forward_implications":["Above roughly 65 GeV, a $10^\\circ$ cone contains 90% of the $\\geq100$ MeV yield, so for higher-energy systems the collinear approximation remains valid and the new tables are not needed.","For a power-law cosmic-ray spectrum like $\\propto E_p^{-2.2}$, protons near threshold dominate, so a large fraction of the observed gamma rays are emitted at significant angles; jet-cloud models that assume collinearity will mispredict off-axis spectra.","The gamma-ray spectrum shape varies with viewing angle, so in principle a measured spectrum can be inverted to determine the direction of an unseen cosmic-ray beam.","Solar gamma rays from cosmic rays reflected by magnetic fields require the joint distribution to predict the disk-versus-annulus brightness pattern; the paper sketches how the brightness moves from a thin limb ring to a full disk as photon energy decreases.","The analytic fit keeps maximum error under about 40% over the first decade above threshold (away from sharp pion-multiplicity thresholds), making the distribution cheap enough for repeated use in astrophysical simulations."],"supporting_citations":[{"why":"Provides the high-energy angle-integrated spectra and the collinear analytic formulas that the paper's range connects to at the 100 GeV upper end.","marker":"[46]"},{"why":"The angle-integrated gamma-ray spectra used to validate the new results over the shared energy range.","marker":"[47]"},{"why":"Earlier angular-distribution calculation that this work extends and improves upon by using a different simulation basis.","marker":"[45]"},{"why":"Earlier analytic study of angular dependence at high energies, providing context for the regime where collinearity starts to break.","marker":"[49]"},{"why":"The simulation code and its validation record; the source of the double-differential yields.","marker":"[53–56]"},{"why":"The empirical gamma-ray production model underlying the earlier angular calculation in Ref. [45].","marker":"[44]"},{"why":"The companion data repository containing the tables and Python tool that are the paper's primary deliverable.","marker":"[83]"}],"fun_headline_variants":["New tables map gamma-ray angles from proton collisions","Off-axis gamma rays matter in proton-proton collisions","Gamma-ray direction now tabulated for pp collisions","Beyond collinear: gamma-ray angular yields from pp","Non-collinear gamma-ray emission from pp collisions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The angular shape of the simulated secondary production is trusted as accurate; the paper validates only the angle-averaged spectra against independent calculations, so a systematic error in the off-axis yield would invalidate the tables even if the total spectra match.","fun_headline_variants_meta":{"raw":{"variants":["New tables map gamma-ray angles from proton collisions","Off-axis gamma rays matter in proton-proton collisions","Gamma-ray direction now tabulated for pp collisions","Beyond collinear: gamma-ray angular yields from pp","Non-collinear gamma-ray emission from pp collisions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00062,"raw_usage":{"total_tokens":2847,"prompt_tokens":889,"completion_tokens":1958,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":505,"completion_tokens_details":{"reasoning_tokens":1895}},"tokens_in":505,"tokens_out":1958,"duration_ms":14572,"temperature":1.0,"reasoning_tokens":1895,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T17:38:15.459851+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the gamma-ray yield per collision in a fixed energy-angle bin, for example near $E_p=5.6$ GeV, $E_\\gamma \\sim 200$ MeV, and $\\theta \\sim 60^\\circ$, using an independent hadronic simulation or a dedicated accelerator measurement; if the measured or independently computed yield disagrees with the tables beyond the estimated hadronic uncertainties, the angular component of the central claim fails.","supporting_citations":[{"cited_title":"Parameterization of the Angular Distribution of Gamma Rays Produced by p-p Interaction in Astronomical Environment","cited_arxiv_id":"0709.0233","evidence_quote":"Earlier angular-distribution calculation that this work extends and improves upon by using a different simulation basis."},{"cited_title":"Parameterization of the energy and rapidity distributions of secondary pions and kaons produced in energetic proton-proton collisions","cited_arxiv_id":"hep-ph/0611219","evidence_quote":"Earlier analytic study of angular dependence at high energies, providing context for the regime where collinearity starts to break."},{"cited_title":"Angular distribution of gamma rays pro- duced in proton-proton collisions,","cited_arxiv_id":null,"evidence_quote":"The companion data repository containing the tables and Python tool that are the paper's primary deliverable."}],"review_version":1}