{"id":"0607d5a1-f355-452f-9638-1a3bdc1cbaef","arxiv_id":"1908.09834","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":6,"one_line_summary":"A new calculation of freeze-in dark matter in U(1)B-L models shows XENON1T already constrains the parameter space and maps the targets for future experiments.","lead":"Dark matter in a model with a new B-L force could be produced slowly in the early universe via freeze-in. This paper shows that existing XENON1T data already exclude parts of this scenario and that future fixed-target and direct-detection experiments can probe the rest.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No significant objection identified","rationale":"The reader's weakest assumption was the thermal-equilibrium and plasma-mixing treatment. I checked those rather than re-reviewing the whole paper. A rough rate estimate for A' production from q qbar -> A' at T ~ mχ for the couplings in the relic target gives Γ/H well above unity (for g_BL ~ 1e-6, Γ/H ~ 10^2 at T ~ 1 TeV and grows at lower T), so the equilibrium premise is not a demonstrated weak point. The mass-mixing formulas are standard and consistently used in both the thermal masses and the rotation angle; any order-one uncertainty would shift the subdominant plasmon-decay term and the fit coefficients slightly, but it would not change the order of magnitude g_BL ~ 1e-6 or the qualitative direct-detection reach. The one unverifiable piece is the unshipped numerical code: Eq. (25) and the figures rest on a modified micrOMEGAS 5 implementation that the reader cannot rerun, and no error bars are given for the fit. This is a legitimate condition for acceptance, but it is not a demonstrated flaw in the physics. Therefore I do not find a load-bearing objection beyond what the reader already identified, and I leave the verdict unchanged.","tokens_in":12580,"tokens_out":39111,"duration_ms":450617,"concrete_test":"Release the modified micrOMEGAS 5 model files and recompute the r = 1, mχ = 30 GeV benchmark with g_BL = g_DM = 1.6e-6; compare the resulting Ωχ h^2 to Fig. 2(a) and to the prediction of Eq. (25). Agreement at the advertised level closes the main residual gap, while a large discrepancy would show the fit or implementation is unreliable.","verdict_should_be":"UNCHANGED","load_bearing_attack":"No significant objection identified. The central argument is internally consistent: Eq. (25) follows from the stated scaling of the two production channels, the thermal-equilibrium premise for A' is supported by the size of the relevant rates (q qbar -> A' gives Gamma/H >> 1 for g_BL ~ 1e-6 at T ~ mχ), and the direct-detection treatment uses the zero-temperature B-L couplings with the expected A^2 coherence. The main unverified element is that the numerical core is a modified micrOMEGAS 5 implementation that is not shipped with the paper. This is a reproducibility gap rather than a demonstrated error, and it is the same concern that motivates the conditional verdict.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies freeze-in production of a Dirac fermion dark matter candidate in a U(1)_{B-L} gauge extension with a light new gauge boson A'. It assumes that A' thermalises with the Standard Model plasma for g_BL ≳ 10^-7, and includes the resulting production channels f fbar → χχ, A'A' → χχ, and plasmon / hypercharge-plasmon decays, accounting for temperature-induced mixing between A' and the SM hypercharge/photon before and after electroweak symmetry breaking. The relic abundance is computed with a modified version of micrOMEGAs 5 and summarised by the approximate formula Ωχ h^2 ≈ (0.16 r^-4 + 0.12 r^-2)(g_BL / 2×10^-6)^4, which is stated to be independent of mA' for mA' < 1 GeV and only weakly dependent on mχ. Matching to the Planck abundance gives g_BL around 10^-6 for r of order unity. The paper then uses DDCalc 2 and XENON1T data to derive direct-detection constraints, finding that XENON1T already excludes part of the parameter plane for mχ ≈ 30 GeV and r = 3, and compares these with accelerator and fixed-target constraints.","tokens_in":12706,"tokens_out":18776,"duration_ms":195250,"significance":"If the numerical implementation is confirmed, the paper provides a concrete and falsifiable freeze-in target in the (mA', g_BL) plane and demonstrates an interesting complementarity between direct detection and accelerator searches. The extension of the thermal-mixing and plasmon-decay formalism to temperatures above the electroweak phase transition is a useful step beyond previous work, and the use of the public DDCalc code for direct-detection bounds is a strength. The headline analytic formula Eq. (25), the approximate independence of the abundance on mA', and the explicit XENON1T exclusion regions are all testable statements that will be useful to the community. The main limitations are the unreleased modified micrOMEGAs implementation and the lack of an explicit validity range for the analytic fit, both of which currently prevent full independent verification.","major_comments":[{"comment":"The central quantitative claim, that the freeze-in target is g_BL ≈ 2×10^-6 for r ≈ O(1), rests on the approximate formula Eq. (25), whose coefficients 0.16 and 0.12 are fitted to the authors' modified micrOMEGAs 5 implementation. The manuscript does not report the goodness of this fit, the residuals as a function of mχ and r, or the range of mA' over which the fit is valid, and the modified code is not made available. Because the relic-density target and all subsequent direct-detection constraints in Figs. 4–6 are built on this fit, I request that the authors either release the code, provide a benchmark table or plot comparing Eq. (25) with the full numerical solution over the parameter range r = 0.1–10, mχ = 1–1000 GeV and mA' = 1 MeV–100 GeV, or both. Without this, the accuracy of the headline coupling target cannot be independently assessed.","section":"§III, Eq. (25) and Figs. 2–4"},{"comment":"The paper states that A' enters thermal equilibrium with the SM bath only for g_BL ≳ 10^-7, citing Ref. [11], yet the left panel of Fig. 3 uses g_BL = 10^-8 while assuming an equilibrium A' abundance for the A'A' → χχ channel. This is internally inconsistent. Either Fig. 3(a) is an extrapolation that should be labelled as such, or the Boltzmann calculation should solve for the A' abundance self-consistently in this regime. Relatedly, the r^-4 term in Eq. (25) relies on the equilibrium A' abundance; for r small enough that the required g_BL falls below 10^-7, this term will overestimate the yield. Please state explicitly the range of r, and hence g_BL, over which Eq. (25) is intended to apply.","section":"§III, first paragraph and Fig. 3(a)"},{"comment":"The temperature-induced mixing angle is computed with the perturbative expression θ = δm^2 / (m_A^2 - m_A'^2), which assumes that the mass splitting is large compared to δm^2. When mA' becomes comparable to the plasma frequency after EWSB, or to the hypercharge thermal mass before EWSB, the mixing is resonant and the two-state system must be diagonalised exactly. The numerical scan in Fig. 5 reaches mA' values up to O(100 GeV), so for mχ = 30 GeV there will be temperatures around T ~ mA'/g where such level crossings occur. Please demonstrate that the relic-density calculation, and therefore the derived direct-detection exclusions, are insensitive to this effect, or implement the full mass-matrix diagonalisation in the Boltzmann solver.","section":"§II.A, Eq. (7)"}],"minor_comments":[{"comment":"The statement that freeze-in production is independent of mA' for mA' < 1 GeV is non-obvious; please give the physical reason (mA' much smaller than the relevant temperatures) and ideally show the numerical independence explicitly.","section":"§III, near Fig. 2"},{"comment":"Please define q'_eff explicitly, including color and generation factors, so that the signs and magnitudes in Table I are transparent to the reader.","section":"§II.A, Eq. (6)"},{"comment":"The caption of the right panel should state the range of r and mχ used for the 'Freeze-in relic density target' band (presently 0.3 < r < 3 and 1 GeV < mχ < 1 TeV) directly in the caption, not only in the main text.","section":"Fig. 4 caption"},{"comment":"The thermalisation condition g_BL ≳ 10^-7 is quoted from Ref. [11]; a short derivation or the relevant rate comparison would make the paper more self-contained.","section":"§III, first paragraph"},{"comment":"The text uses 'g′ × gDM' loosely as an effective coupling; please define this combination explicitly and clarify how it is related to the coupling ratio r.","section":"§IV, Eq. (26)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of the journal and the central physics idea is attractive. The main obstacle to acceptance is reproducibility: the central fit Eq. (25) depends on a modified, unreleased numerical code, and one of the illustrative figures appears to violate the paper's own thermalisation assumption. These issues are fixable with additional documentation, benchmark comparisons, or a code release, and I would be willing to review a revised version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This paper is better than the conditional verdict suggests. It is a clean, well-explained pheno paper that turns freeze-in in a U(1)B-L extension into a concrete experimental target: after the A' thermalizes, the relic density fixes g_BL at roughly 1e-6 with only mild mass dependence, and a quick DDCalc run shows XENON1T already excludes part of the plane at m_chi ~30 GeV, r=3. I think the central claim holds up.\n\nThe genuinely new pieces are the treatment of thermal mixing before and after EWSB, the inclusion of hypercharge plasmon decays at T>Tc, and the direct detection constraints that come out of combining the relic density requirement with the scattering formula. Individual ingredients are known—Dvorkin-Lin-Schutz and An-Huo-Liu did the sub-MeV case—but the extension to B-L and to GeV-TeV DM is a real step. The formula (25) follows from the scaling arguments and reproduces the numerics in Figs. 2 and 3. They also use DDCalc, so the XENON1T curves are reproducible in principle.\n\nThe main soft spot is the same one the reader flagged: the micrOMEGAs implementation is not shipped. That is a reproducibility gap, not an error. The physics input is standard and the approximations are clearly stated, but I would want the authors to either release the modified code or spell out the numerical procedure in enough detail for someone to re-implement it. The fit coefficients 0.16 and 0.12 in Eq. (25) also have no uncertainty attached—minor, since the rounding doesn't change the target band qualitatively. The thermalization assumption for A' is cited to Evans-Gori-Shelton rather than re-derived; I consider that acceptable, and the rates in that regime are large enough.\n\nI also want to note the authors are honest about the limitations: the direct detection constraints apply only to freeze-in production and vanish for r<0.3. They don't oversell.\n\nI'd send this to a competent pheno referee. The missing code should be requested, but neither that nor the approximate fit is enough to sink it. It deserves a serious referee; I'd probably accept with minor revisions if the code question is addressed.","headline":"A solid, well-explained pheno paper that turns freeze-in in U(1)B-L into a concrete XENON1T target; the central argument holds and it deserves a serious referee despite a moderate reproducibility gap.","tokens_in":13238,"tokens_out":2313,"would_cite":true,"duration_ms":23730,"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":"In a U(1)B-L gauge extension, a thermalized dark photon produces freeze-in dark matter with a nearly mass-independent relic abundance, fixing g_BL around 10^{-6} for r ~ 1.","keywords":["freeze-in","dark photon","U(1)B-L","dark matter","relic abundance","direct detection","thermal mixing","gauge extension"],"falsifier":"A measurement that fixed the dark matter relic abundance while ruling out the entire predicted horizontal band ($g_{BL}$ near $10^{-6}$ for $1\\,\\mathrm{MeV} < m_{A'} < 1\\,\\mathrm{GeV}$) in fixed-target searches would falsify the scenario; alternatively, a precise finite-temperature computation showing that $A'$ does not thermalize for $g_{BL} \\sim 10^{-6}$ would invalidate the production calculation.","tokens_in":12386,"feed_emoji":"🌌","tokens_out":11799,"duration_ms":100024,"temperature":0.7,"pith_summary":"The paper claims that in a $U(1)_{B-L}$ gauge extension with a MeV-scale dark photon $A'$ that thermalizes with the Standard Model plasma, the observed dark matter abundance can be produced by freeze-in with the gauge coupling fixed near $g_{BL} \\sim 10^{-6}$, nearly independent of the dark matter mass and of the dark photon mass. The equilibrium population of $A'$ opens a new production channel, $A'A' \\to \\chi\\chi$, alongside SM-fermion annihilation and plasmon decays. In the parameter region that reproduces the relic abundance, $A'$ is long-lived enough for fixed-target searches and light enough to enhance direct-detection rates, and existing XENON1T data already exclude a slice of the plane. This matters because it turns a very weakly coupled freeze-in model into a concrete, testable target for both accelerator and direct searches.","feed_headline":"Dark photon freeze-in fixes its coupling near one part per million","feed_subtitle":"Relic abundance is nearly mass-independent, so XENON1T and fixed-target runs already test the predicted plane.","key_machinery":"The central object is the temperature-induced mass mixing between the dark photon $A'$ and the Standard Model $U(1)$ gauge fields, parametrized by $\\theta_{BL} = (q'_{\\rm eff}/q_{\\rm eff})(g'/e)$ after electroweak symmetry breaking and $\\theta_{BL} = (8/11)(g_{BL}/g_Y)$ before it, where $q_{\\rm eff}$ and $q'_{\\rm eff}$ are the effective charge and charge-mixing degrees of freedom of the plasma. This mixing gives $A'$ its couplings to SM fermions and is the source of plasmon and hypercharge-plasmon decays into dark matter. The second ingredient is the pair of freeze-in production channels, SM-fermion annihilation $\\bar f f \\to \\chi\\bar\\chi$ (scaling as $g_{BL}^2 g_{DM}^2$) and dark-photon annihilation $A'A' \\to \\chi\\bar\\chi$ (scaling as $g_{DM}^4$), whose competition is controlled by $r = g_{BL}/g_{DM}$. The approximate scaling $Y \\propto g^4 M_{\\rm Pl}/m_\\chi$ makes the final abundance nearly mass-independent.","core_discovery":"For a Dirac fermion dark matter candidate $\\chi$ charged under $U(1)_{B-L}$ with mediator $A'$, the authors find that freeze-in production from a thermalized $A'$ bath gives a relic abundance $\\Omega_\\chi h^2 \\approx (0.16 r^{-4} + 0.12 r^{-2})(g_{BL}/(2\\times 10^{-6}))^4$, where $r = g_{BL}/g_{DM}$. The yield is almost independent of $m_\\chi$ and independent of $m_{A'}$, so the relic-density requirement selects a narrow horizontal band in the $g_{BL}$--$m_{A'}$ plane, around $g_{BL} \\sim 10^{-6}$ for $r$ of order unity. The calculation includes temperature-induced mixing between $A'$ and the SM hypercharge boson before electroweak symmetry breaking and with the photon afterward, and includes decays of the resulting plasmon mass eigenstates into $\\chi\\chi$ when kinematically open. Translating the relic abundance to direct detection, the authors find XENON1T excludes a noticeable region near $m_\\chi = 30$ GeV for $r = 3$, with future experiments extending the reach.","pith_inferences":["The same thermal-mixing framework could be applied to a scalar or Majorana dark matter candidate; the $A'A' \\to \\chi\\chi$ channel would have different velocity and coupling factors, so the exact target band would shift by an order-one amount that this paper does not compute.","For $g_{BL}$ between roughly $10^{-8}$ and $10^{-7}$, the assumed $A'$ thermalization becomes marginal; in that sub-range the freeze-in yield would be suppressed and the derived direct-detection constraints would not apply in their stated form.","The horizontal target band suggests a model-independent experimental strategy: any experiment covering $g_{BL}$ near $10^{-6}$ for MeV-scale mediators tests freeze-in across a wide dark matter mass range, independent of the mediator mass.","In $B-L$ extensions where right-handed neutrinos are lighter than $A'$, the $A'$ decays to neutrinos would shorten its lifetime and weaken fixed-target signals; the paper assumes heavy right-handed neutrinos and does not explore this branch."],"forward_implications":["The relic-density target in the $g_{BL}$--$m_{A'}$ plane is an exactly horizontal band, independent of $m_{A'}$, for dark matter masses between about 1 GeV and 1 TeV.","In the target region, $A'$ is long-lived enough to be searched for in fixed-target and beam-dump experiments such as SeaQuest, SHiP, FASER, and NA62.","Direct-detection rates are enhanced whenever $m_{A'}$ is below about 16 MeV for a recoil threshold of 1.1 keV, so XENON1T already excludes $m_\\chi$ around 30 GeV for $r = 3$, and LZ will extend the reach.","For $r \\gg 1$, the direct-detection cross-section and the relic abundance depend on the same combination $g_{BL}^2 g_{DM}^2$, so direct searches directly probe the freeze-in parameter space; for $r \\ll 1$ the direct-detection rate is suppressed by $r^2$.","Before the electroweak phase transition, hypercharge plasmon decays add a non-negligible production source, so the full thermal history must be split at $T_c = 164$ GeV."],"supporting_citations":[{"why":"It establishes that the dark photon enters thermal equilibrium with the Standard Model bath for $g_{BL} \\gtrsim 10^{-7}$, which is the premise for using an equilibrium $A'$ abundance.","marker":"[11]"},{"why":"It supplies the general temperature-induced mass mixing between $U(1)$ gauge bosons that defines the mixing angle $\\theta_{BL}$ used throughout the production calculation.","marker":"[22]"},{"why":"It introduces the plasmon-decay contribution to freeze-in production for sub-MeV dark matter, which this paper extends to heavier dark matter and to temperatures above the electroweak phase transition.","marker":"[24]"},{"why":"It provides the accelerator, beam-dump, and neutrino-experiment constraints against which the relic-density target is compared.","marker":"[18]"},{"why":"It shows that a sufficiently light mediator enhances direct-detection cross-sections, motivating the event-rate calculation presented here.","marker":"[8]"},{"why":"It gives the finite-temperature fermion and boson masses used to treat the plasma before and after electroweak symmetry breaking.","marker":"[29]"},{"why":"It sets the framework for dividing freeze-in production into pre- and post-electroweak-phase-transition regimes.","marker":"[30]"},{"why":"It provides the numerical Boltzmann solver used to integrate the freeze-in abundance over the full thermal history.","marker":"[31]"},{"why":"It supplies the measured relic abundance $\\Omega h^2 = 0.12$ used to fix the couplings $g_{BL}$ and $g_{DM}$.","marker":"[32]"},{"why":"It provides the XENON1T data from which the direct-detection exclusions in Fig. 5 and Fig. 6 are derived.","marker":"[36]"}],"fun_headline_variants":["Dark photon freeze-in pins coupling at one part per million","XENON1T already tests freeze-in dark matter via dark photons","Freeze-in dark matter: relic density nearly mass-independent","Dark photon freeze-in selects coupling near 10^-6 independent of mediator mass"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central calculation assumes that the dark photon reaches thermal equilibrium with the Standard Model bath at temperatures near the dark matter mass, which requires $g_{BL} \\gtrsim 10^{-7}$; if the coupling is below that or the interaction rate is overestimated, the $A'A' \\to \\chi\\chi$ channel and the plasmon-decay contributions would be too large.","fun_headline_variants_meta":{"raw":{"variants":["Dark photon freeze-in pins coupling at one part per million","XENON1T already tests freeze-in dark matter via dark photons","Freeze-in dark matter: relic density nearly mass-independent","Dark photon freeze-in selects coupling near 10^-6 independent of mediator mass"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000581,"raw_usage":{"total_tokens":2738,"prompt_tokens":952,"completion_tokens":1786,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":568,"completion_tokens_details":{"reasoning_tokens":1712}},"tokens_in":568,"tokens_out":1786,"duration_ms":11855,"temperature":1.0,"reasoning_tokens":1712,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T11:00:44.412467+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A measurement that fixed the dark matter relic abundance while ruling out the entire predicted horizontal band ($g_{BL}$ near $10^{-6}$ for $1\\,\\mathrm{MeV} < m_{A'} < 1\\,\\mathrm{GeV}$) in fixed-target searches would falsify the scenario; alternatively, a precise finite-temperature computation showing that $A'$ does not thermalize for $g_{BL} \\sim 10^{-6}$ would invalidate the production calculation.","supporting_citations":[{"cited_title":"KeV Scale Frozen-in Self-Interacting Fermionic Dark Matter","cited_arxiv_id":"1812.05699","evidence_quote":"It introduces the plasmon-decay contribution to freeze-in production for sub-MeV dark matter, which this paper extends to heavier dark matter and to temperatures above the electroweak phase transition."}],"review_version":1}