{"id":"750c72a7-bdc2-44b8-bfd1-8e0c24cca0d3","arxiv_id":"2502.08725","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"In the double Coy dark matter model, full phase-space Boltzmann evolution with conversions changes relic abundances by up to an order of magnitude per component and by more than 100% for the total in some parameter regions.","lead":"A two-component dark matter model, doubling the Coy DM scenario, is studied with full phase-space Boltzmann equations that include conversion processes between the two dark states. The solution shows that kinetic decoupling effects can change the total relic abundance by more than 100% in some regions, and substantially shift predicted Galactic Centre gamma-ray fluxes.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Fokker-Planck treatment of subdominant elastic channels may bias the reported fBE-nBE abundance deviations; a full-collision-term rerun is needed to confirm.","rationale":"The reader identified the FP approximation as the weakest assumption; I agree. The paper's own Appendix A demonstrates the failure modes (mass ratio near 1, t-dependent amplitude) that are present in this model. The mitigation—using the full term for the largest γX—is plausible but unquantified for the remaining channels. Because the central claim is explicitly quantitative (ranges of -20% to 50%, >100%, per-component up to 10×), even a small systematic shift in the kinetic decoupling rate can amplify into the reported deviations. The proposed test directly isolates the FP contribution by replacing it with the exact treatment; it is computationally feasible (the full term is already implemented for some channels) and would settle whether the headline numbers are robust. I keep the reader's CONDITIONAL verdict (encoded as UNCHANGED) because the paper is otherwise careful and the test is a clear validation step; if the test reveals large shifts, the verdict should move toward REJECT.","tokens_in":24889,"tokens_out":8303,"duration_ms":78639,"concrete_test":"Rerun the benchmark point of Sec. 3 (M_χ1=44 GeV, M_χ2=38 GeV, M_s=80 GeV, λ1=0.0226, λ2=0.39, λy=0.3) and the c-scan of Sec. 5.4 with the full elastic collision term (eq. 23) used for every scattering partner X (all SM fermions and s), instead of the mixed FP/full scheme. Compare the resulting fBE abundances and fBE−nBE deviations (total and per-component) against the published values. If the total deviation changes by more than ~10 percentage points, or if the >100% region and the χ²=62 (fBE) GCE-fit result move qualitatively, the FP treatment is load-bearing; if changes remain within the stated few-% numerical accuracy, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim—departure from kinetic equilibrium altering total abundance by >100% in some regions and -20% to 50% elsewhere—rests on the accuracy of the elastic scattering rates that set the time of kinetic decoupling. In Sec. 4.2 the authors use the full t-channel collision term only for the scattering partners with the largest momentum-transfer rates γX, and the Fokker-Planck (FP) approximation (eq. 17) for the remainder. Appendix A itself shows FP fails when the scattering partner mass is comparable to (or larger than) the DM mass and when the amplitude depends strongly on t, exactly the situation for scattering off the pseudoscalar s (M_s = 75–84 GeV vs M_χ = 30–44 GeV) and for the t^2/(t-M_s^2)^2 amplitudes in eq. (2). The selection by γX does not guarantee that the sum of the remaining channels' contributions is negligible: a channel with small γX can still transfer large momentum per event, and FP errors of order unity in that channel could translate into non-negligible changes in the kinetic decoupling epoch. Since early kinetic decoupling drives the reported fBE deviations, the headline numbers (including the GCE-fit reversal in Sec. 5.4) could shift quantitatively if the FP-treated channels contribute at the ≥10% level to the total momentum transfer. This is not merely a formal concern: the paper uses FP for 'remaining particles' without reporting which channels those are or their fractional contribution to γ_total, so the reader cannot assess the induced error.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper extends the DRAKE framework to solve the full phase-space Boltzmann equations (fBE) for a two-component dark sector consisting of two stable fermions and a pseudoscalar mediator, including annihilation, elastic scattering, and 2-to-2 conversion processes. The model is the \"double Coy DM\" extension of the Coy DM model, and the authors scan parts of its parameter space that reproduce the observed relic abundance and fit the Galactic Centre excess. They compare fBE results with the standard number-density approach (nBE) and report that departures from kinetic equilibrium change the total relic abundance by roughly -20% to +50% in most of the interesting region, by more than 100% in some regions, and can change individual component abundances by up to an order of magnitude. They further show that these effects can shift the preferred GCE-fit region in the model's parameter space.","tokens_in":25200,"tokens_out":7210,"duration_ms":74617,"significance":"If the quantitative results hold, the paper provides a useful demonstration that the kinetic-equilibrium assumption can fail non-negligibly in multi-component dark sectors with conversion processes, and it offers a numerical framework for future two-component phase-space studies. The main strengths are the detailed derivation of the discretized collision terms for annihilations, elastic scatterings, and conversions; the explicit use of the full t-channel elastic collision term for the channels where the Fokker-Planck approximation is not justified; and the clear identification of conversion-driven freeze-out regimes. The paper is also candid about the limitations of the Fokker-Planck approximation in Appendix A. The principal caveat is that the magnitude of the headline deviations depends on how the subdominant elastic channels are treated and on the neglect of self-scattering, both of which need to be quantified more directly before the central numbers can be taken at face value.","major_comments":[{"comment":"The paper does not specify which elastic-scattering partners are treated with the full collision term, eq. (23), and which are treated with the Fokker-Planck approximation, eqs. (17)-(18), nor does it report the fractional contribution of the FP-treated channels to the total momentum-transfer rate. This matters because Appendix A itself states that the FP expansion fails when the scattering-partner mass is comparable to or larger than the DM mass and when the amplitude depends strongly on t; both conditions hold for scattering off the pseudoscalar s in the mass scans (M_s = 75-84 GeV versus M_chi = 30-44 GeV, with amplitudes t^2/(t-M_s^2)^2 in eq. (2)). If s is among the \"remaining particles\" treated with FP, the kinetic-decoupling epoch that drives the reported fBE-nBE deviations could shift. A channel with small gamma_X can still transfer significant momentum per event, so selection by the largest gamma_X does not by itself guarantee control of the error. Please report the channel decomposition and either evaluate the full collision term for all channels in the benchmark scans or quantify the resulting error on the headline deviation numbers.","section":"§4.2 and Appendix A"},{"comment":"Self-scattering of chi1 and chi2 is neglected with only the statement that its rate is smaller and that it may give sub-leading corrections. Since self-scattering directly contributes to kinetic equilibration, and the paper's central claims concern the size of kinetic-equilibrium violations, this neglect is load-bearing. A quantitative estimate of the self-scattering rate relative to the included elastic and conversion rates should be provided at least for the benchmark point and the scan endpoints; otherwise the reported deviations should be regarded as upper bounds whose reduction by self-scattering is unknown.","section":"§4.3, last paragraph"},{"comment":"The GCE-fit regions in figs. 2 and 3 are computed using nBE relic abundances, while the fBE-based GCE fits are shown only in the one-dimensional scans of figs. 4 and 6. Because the central message is that the fBE treatment shifts the GCE-preferred region, the two-dimensional comparison in figs. 2 and 3 does not directly show the fBE-preferred GCE region. The claim of a significantly shifted GCE region would be strengthened by recomputing the GCE fit with fBE abundances over at least one two-dimensional plane, or by explicitly stating that the shift is demonstrated only along the scanned lines.","section":"§5.1 and §5.4"}],"minor_comments":[{"comment":"In the second branch of the definition of Â_i, the block should presumably use (Â_χ2)_{i-N} rather than (Â_χ1)_{i-N}; as written, the χ2 evolution appears to use the χ1 kernel.","section":"§4.3, eq. (38)"},{"comment":"The right-panel caption begins \"Right panel:.\" with an extra period and no description; the sentence should be completed.","section":"§5.1, fig. 2 caption"},{"comment":"The notation \"1 (f_eq)^{-1}\" and \"1 (f_eq)^{-1}\" is ambiguous; please define these as diagonal matrices diag(1/f_eq) or use an explicit diagonal-matrix symbol.","section":"§4.2, eq. (26)"},{"comment":"The adaptive grid size N is stated to vary between 40 and 100, but no convergence test with respect to N or the q-grid mapping parameters q_A,i and q_B,i is shown. A short convergence study for at least one benchmark would support the claimed few-percent numerical accuracy.","section":"§4.4"},{"comment":"The assumption that the pseudoscalar s remains in kinetic equilibrium with the SM bath is stated without a quantitative estimate. Since s is a scattering partner for the DM species, a brief estimate of its relevant scattering or decay rate would make the assumption easier to assess.","section":"§4, opening paragraph"}],"recommendation":"major_revision","confidential_remarks":"The central idea and numerical framework are valuable, but the Quantitative headline numbers rest on the treatment of subdominant elastic channels and on neglected self-scattering. Before acceptance I would want to see the channel decomposition and at least a bounding estimate of the FP error and of self-scattering effects for the benchmark and scan endpoints. The code being available only in a future DRAKE release also limits reproducibility; making a version available with the paper would help."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear [colleague],\n\nQuick take: this is a legitimate step forward, not a headline grab. The authors extend DRAKE to solve the full phase-space Boltzmann equation for two dark-sector states including 2↔2 conversions, and apply it to a double-Coy model. That capability is new—earlier fBE two-component studies either omitted conversions or used moment approximations. The derivation of the discretized collision terms is careful and the FP approximation is stress-tested in Appendix A, which is more than most papers do. The concrete results—deviations between fBE and nBE of order tens of percent in most of the GCE-preferred region, with larger per-component effects and a dramatic reversal of the GCE fit at the benchmark point—are plausible and internally consistent.\n\nThe soft spots are real but not fatal. First, the paper uses the Fokker-Planck form for 'remaining' elastic scattering channels without naming them or reporting their fractional contribution to the total momentum-transfer rate. Appendix A shows FP can fail badly when the scattering partner is heavier than the DM or the amplitude is t-dependent—conditions that apply to scattering off the pseudoscalar s. In practice those channels likely have small γX and thus contribute little, but we shouldn't have to infer that; the authors should show it. If a full-collision-term rerun for one benchmark shifts the headline numbers, the paper needs a revised figure. Second, the 'more than 100%' total deviation and 'order of magnitude' per-component effects are asserted in the abstract but never pinned to a single displayed point with the parameters and ratio spelled out. Given the few-percent numerical accuracy and ~100-point scans, the headline should be tied to a concrete example. The neglected self-scattering is a known limitation and probably subleading, but again the justification is a statement, not a quantitative check.\n\nNone of this undermines the central point—that conversions plus early kinetic decoupling can make nBE quantitatively wrong in this class of models. The GCE-fit reversal may be the most important phenomenological result, and it deserves independent confirmation once the code is public.\n\nWho should read it: anyone computing relic densities in multi-component dark sectors, especially with pseudoscalar mediators. I'd bring it to our reading group and I'd cite it once the code is out.\n\nRecommendation: send it to a serious referee. Condition acceptance on the authors reporting which channels use FP and their γ-fractions, and on a demonstration that the one headline benchmark is robust to using the full elastic collision term.","headline":"A serious step forward for fBE relic calculations in multi-component dark sectors; the FP-channel disclosure gap is fixable and shouldn't block a solid referee.","tokens_in":25770,"tokens_out":4028,"would_cite":true,"duration_ms":37068,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["95.35.+d"],"model":"deepseek-v4-flash","headline":"The paper shows that in a two-component dark sector with conversions, the standard kinetic-equilibrium calculation of relic abundances is off by more than 100% in some regions and 20–50% in the GCE-preferred region, with per-constituent…","keywords":["two-component dark matter","kinetic equilibrium","full Boltzmann equation","phase-space distribution","conversion processes","relic abundance","Galactic Centre excess","Fokker-Planck approximation"],"falsifier":"Recompute the benchmark and GCE-region points using the full, unexpanded elastic-scattering collision term of eq. (20) for $\\chi_i + s \\to \\chi_i + s$ instead of the Fokker-Planck form, and see whether the >100% and 20–50% fBE-versus-nBE deviations persist; a cheaper check would directly compare the Fokker-Planck operator with the full operator at $M_s = 75$–$84$ GeV, $M_\\chi = 30$–$44$ GeV and freeze-out temperatures, along the lines of the paper's appendix.","tokens_in":24643,"feed_emoji":"🌌","tokens_out":10284,"duration_ms":89572,"temperature":0.7,"pith_summary":"The paper asks whether the standard assumption of kinetic equilibrium distorts relic abundance predictions in a two-component dark sector with conversion processes. It solves the full Boltzmann equation for the phase-space distributions of two pseudoscalar-coupled fermions in a minimal extension of the Coy dark matter model, including annihilations, elastic scatterings, and 2-to-2 conversions. In the parameter regions that reproduce the observed relic abundance and fit the Galactic Centre excess, the standard number-density treatment is off by more than 100% in some places and typically by −20% to +50%; the abundance of each constituent separately can change by up to an order of magnitude. This matters because the predicted gamma-ray flux from the Galactic Centre scales with the square of the per-constituent density, so the preferred fit region shifts when the phase-space treatment is used.","feed_headline":"Kinetic-equilibrium bias can skew dark matter relic abundance by 100%","feed_subtitle":"Full Boltzmann calculation shows conversions between dark sector states change relic densities and the Galactic Centre fit.","key_machinery":"The load-bearing object is the discretised, coupled full Boltzmann equation for the two phase-space densities $f_{\\chi_1}(q,x)$ and $f_{\\chi_2}(q,x)$ (the paper's eq. 40). Annihilations enter as a pre-tabulated matrix term $f_{\\mathrm{eq}}(A_M f_{\\mathrm{eq}}) - f(A_M f)$; elastic scatterings enter either through a Fokker-Planck operator or, where that approximation is unreliable, through the full $t$-dependent collision term written as a matrix $E_M$; conversions enter through a three-index matrix $\\hat A$ that couples the two species and is evaluated on the fly because it depends on the unknown distributions. The conversion collision term is the structurally new piece: it is cubic in $f$, involves momenta of both particles, and requires interpolation when a final-state energy falls off the grid.","core_discovery":"The central discovery is that conversions between the two dark matter states do not merely change particle numbers; they imprint a non-thermal shape on the momentum distributions, and that shape feeds back into the rates. The benchmark shows a second bump in the $\\chi_2$ distribution generated by $\\chi_1\\to\\chi_2$ conversion, lying at momenta that additionally fuel resonant annihilations, so the final total abundance is lower than the standard treatment predicts (for the benchmark, $\\Omega h^2 = 0.126$ with the standard calculation versus $0.097$ at the phase-space level). Across the studied parameter space the fBE-vs-nBE deviation in total abundance exceeds 100% in some regions and is typically −20% to 50% where the model fits the GCE, with per-component deviations reaching an order of magnitude. The preferred GCE-fit region moves accordingly: for the benchmark at conversion strength $c\\simeq 1$ the reduced $\\chi^2$ degrades from 0.51 (nBE) to 62 (fBE).","pith_inferences":["If the 20–50% bias is representative, global fits of two-component dark matter that assume kinetic equilibrium may systematically mis-infer couplings by tens of percent; re-running such fits with the phase-space solver could shift best-fit regions beyond current observational precision.","The mechanism identified, conversions feeding a resonant or sub-threshold annihilation channel at specific momenta, should be generic: any model with a conversion amplitude peaking in $s$ and an annihilation resonance at a different momentum is a candidate for similarly large fBE effects, and the same solver could test that directly.","The Fokker-Planck limitation documented for pseudoscalar scattering suggests that the magnitude of the reported deviations may depend on the elastic-scattering treatment; switching to full collision terms for the $s$-mediated scattering in the GCE region would quantify this.","For indirect detection, the factor-change in per-constituent abundances means that gamma-ray constraints from dwarfs or the Galactic Centre should be recomputed with fBE-inferred densities before drawing conclusions about the model's viability."],"forward_implications":["In the studied model, standard number-density relic calculations are not reliable at the percent level: deviations reach more than 100% in some resonant and sub-threshold regions and 20–50% in the GCE-preferred region.","The abundance of the subdominant constituent can change by up to an order of magnitude, so observables proportional to the square of the density, such as gamma-ray fluxes from annihilations, can be affected far more than the total abundance.","The GCE-preferred parameter region shifts when phase-space abundances are used; the benchmark at conversion strength $c\\simeq 1$ goes from a good fit (reduced $\\chi^2=0.51$) to a bad one (reduced $\\chi^2=62$).","Conversion-driven freeze-out can make the final abundance nearly independent of the annihilation parameter $a$, a regime that only the phase-space analysis fully resolves.","The numerical framework developed here can be applied to other two-component models with conversions, removing the kinetic-equilibrium assumption in future relic and indirect-detection predictions."],"supporting_citations":[{"why":"Provides the phase-space Boltzmann solver and numerical framework that this work extends to two species with conversions, and the reference for resonant-annihilation fBE deviations.","marker":"[7]"},{"why":"Supplies the reduction of elastic-scattering collision integrals to two dimensions for amplitudes depending on a single Mandelstam variable, used in the full non-Fokker-Planck collision terms.","marker":"[4]"},{"why":"Defines the Coy dark matter model, the pseudoscalar-mediated fermion setup on which the two-component extension is built.","marker":"[30]"},{"why":"Reports the Galactic Centre gamma-ray excess that the model and the GCE fit are targeting.","marker":"[31]"},{"why":"Provides the observed differential gamma-ray flux and errors used as the GCE fit data.","marker":"[46]"},{"why":"Documents the expected fBE-versus-nBE behaviour for resonant annihilation, against which the broader deviation range here is compared.","marker":"[6]"},{"why":"Sets the observed relic abundance $\\Omega h^2=0.12$ used for the relic-density contours.","marker":"[17]"},{"why":"Derives the Fokker-Planck elastic-scattering operator whose validity limits are analysed in the appendix.","marker":"[40]"}],"fun_headline_variants":["Dark matter conversions shift relic abundance by up to 100%","Phase-space effects alter dark matter relic density predictions","Conversions in dark sector skew relic abundance and GCE fit","Non-kinetic equilibrium dark matter changes relic abundance","Full phase-space analysis reveals 100% relic abundance bias"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation's headline numbers rest on the Fokker-Planck approximation being accurate for the elastic-scattering processes that set when kinetic decoupling happens; the paper's appendix shows this approximation can fail when the scattering partner is as heavy as the dark matter (as the pseudoscalar $s$ is in the GCE-favoured region), so if those rates are misestimated, the size of the reported abundance shifts could change.","fun_headline_variants_meta":{"raw":{"variants":["Dark matter conversions shift relic abundance by up to 100%","Phase-space effects alter dark matter relic density predictions","Conversions in dark sector skew relic abundance and GCE fit","Non-kinetic equilibrium dark matter changes relic abundance","Full phase-space analysis reveals 100% relic abundance bias"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000197,"raw_usage":{"total_tokens":1361,"prompt_tokens":939,"completion_tokens":422,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":555,"completion_tokens_details":{"reasoning_tokens":342}},"tokens_in":555,"tokens_out":422,"duration_ms":4230,"temperature":1.0,"reasoning_tokens":342,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T23:51:55.559764+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the benchmark and GCE-region points using the full, unexpanded elastic-scattering collision term of eq. (20) for $\\chi_i + s \\to \\chi_i + s$ instead of the Fokker-Planck form, and see whether the >100% and 20–50% fBE-versus-nBE deviations persist; a cheaper check would directly compare the Fokker-Planck operator with the full operator at $M_s = 75$–$84$ GeV, $M_\\chi = 30$–$44$ GeV and freeze-out temperatures, along the lines of the paper's appendix.","supporting_citations":[],"review_version":1}