{"id":"7b303f18-6db0-42e3-8e18-be1d249c5356","arxiv_id":"2412.17719","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A Z2-odd vector-like quark added to the inert doublet model restores the correct dark matter relic abundance for DM masses above about 550 GeV in compressed spectra.","lead":"This paper adds a new heavy quark to the inert doublet dark matter model to fix a known problem: the model predicts too much dark matter at high masses in compressed spectra. The extra quark opens new annihilation and coannihilation channels, bringing the predicted relic abundance into the observed range while keeping direct detection signals weak.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Chemical-equilibrium assumption for DM–VLQ coannihilation is unverified; the relic-dilution claim depends on it, but no conversion-rate versus Hubble check is provided.","rationale":"The paper is a coherent phenomenological study: the Z2 prevents VLQ–SM mixing, the Yukawa couples only to the third generation, and the compressed IDM region above about 550 GeV is genuinely overabundant in the pure IDM. The VLQ opens coannihilation channels that can plausibly dilute the relic density, and the benchmark points are internally consistent with the reported relic and direct-detection numbers as far as one can tell from the text. I did not find a definite derivation error that would falsify the central claim outright. The reason I do not mark the paper fully accepted is that the central mechanism rests on an unquantified equilibrium assumption: Eq. (4.4) and the Type-A narrative require conversion processes to outrun Hubble, and the paper's own wording ('one can expect...') in Sec. 4.5 flags this as an expectation, not a demonstrated result. Given that no code, model files, or data are shipped and Table 3 contains formatting garbles, independent verification is impossible for a reader. Thus the reader's CONDITIONAL verdict is appropriate: the mechanism is plausible and may well be correct, but the decisive dynamical check is missing. The proposed test targets exactly that missing check. If the check passes, the paper should be upgraded; if it fails, the central claim collapses.","tokens_in":17015,"tokens_out":20245,"duration_ms":216346,"concrete_test":"Using the SARAH/SPheno model files, compute for BP-1 through BP-4 the thermally averaged conversion rates at T_f = mη0/25 for (i) η0 + t/tbar ↔ ξ/ξbar and (ii) η+ + b/bbar ↔ ξ, plus the η+↔η0 conversion through W exchange; compare each rate to the Hubble rate. If Γ_conv/H > 1 for all benchmarks, the equilibrium assumption is validated and the central claim stands. If any Γ_conv/H < 1, solve the coupled Boltzmann equations for nη and nξ separately (e.g., using micrOMEGAs 6.0 N-component mode) and recompute Ωh2; a shift outside the Planck 3σ band for BP-1–4 would falsify the claim.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central relic-dilution mechanism (Sec. 4.5, Type-A; Fig. 9) is implemented through the one-species effective Boltzmann equation (4.4), which is valid only if all Z2-odd species remain in chemical equilibrium during freeze-out. The paper states the required condition—conversion among dark-sector species must be faster than Hubble expansion—but nowhere evaluates Γ_conv/H for any benchmark. The dangerous pathway is η0↔ξ: the Yukawa (2.2) couples η0 directly only to the top quark, whose thermal density is Boltzmann-suppressed at T_f ≈ mη/25; the alternative route through η+ + b relies on the small Δ± mass splitting and on the η+ decay rate, which the paper does not quantify. In BP-1 (mη=1000 GeV, Δξ=50 GeV, yξ=0.60) and especially BP-3/BP-4 (yξ=0.01, Δξ≈35–42 GeV), a suppressed conversion rate would make η0 and ξ freeze out as separate sectors, so the strong ξξ→SM annihilation would not drain the DM density. Table 3's quoted Ωh2 values would then be incorrect and the claimed viable compressed high-mass region would shift or disappear. This is not an internal contradiction—the effective coannihilation formalism is standard—but the equilibrium assumption is the load-bearing pillar of the main claim, and it is asserted rather than demonstrated.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies an extension of the inert doublet model (IDM) by a Z2-odd singlet vector-like quark (VLQ) that couples to the inert doublet and the third-generation SM quarks. The authors implement the model with SARAH/SPheno and compute dark matter observables with MicrOMEGAs. They claim that the VLQ opens new (co)annihilation channels, in particular strong VLQ pair annihilation, which dilutes the dark matter relic density for compressed IDM spectra at high DM masses (above about 550 GeV) while allowing a small Higgs-portal coupling lambda_L to evade direct detection bounds. The paper presents scans, benchmark points with relic density and direct detection cross sections, indirect detection constraints, and an LHC collider outlook for single and pair production of the VLQ.","tokens_in":17293,"tokens_out":4058,"duration_ms":39054,"significance":"If the central claim is correct, the model resolves a known difficulty of the pure IDM (overabundant dark matter in the compressed high-mass region) and offers distinctive LHC signatures through VLQ production with jets plus missing energy. The paper uses standard, publicly available numerical tools and provides benchmark points that satisfy relic density and direct detection constraints, which is a useful step for model viability. However, the numerical results are not shipped as input files or code, and no validation against published IDM relic-density calculations is shown. More importantly, the main mechanism depends on an unverified chemical-equilibrium assumption between the dark matter and the VLQ; if that assumption fails, the benchmark relic densities would shift. For these reasons the significance is conditional on a technical check that the manuscript currently does not provide.","major_comments":[{"comment":"The central relic-dilution mechanism rests on the assumption that all Z2-odd species remain in chemical equilibrium during freeze-out, so that the rapid strong process xi xi -> SM SM drains the whole dark sector. The paper states this condition qualitatively (\"provided the interaction ... is faster than the Hubble expansion rate\") but never computes Gamma_conv/H for any benchmark. For BP-3 and BP-4 (y_xi = 0.01), the conversion eta0 <-> xi is mediated by the Yukawa coupling of Eq. (2.2) to the top quark only, which is Boltzmann-suppressed at T_f ~ m_eta/25, and the alternative route through eta+ + b -> ... is not quantified. If Gamma_conv < H for these points, the effective single-species Boltzmann equation is invalid and the quoted Omega h^2 values in Table 3 are not reliable. Please provide a calculation of the relevant conversion rates for the benchmark points (or over the scan region) and explicitly check the equilibrium condition Gamma_conv >> H during freeze-out.","section":"Sec. 4.5, Eq. (4.4)"},{"comment":"The lower bound m_xi > 550 (650) GeV for a top-like (bottom-like) VLQ is quoted from a \"recast\" of squark searches, but no recast details are given, and reference [45] is a general ATLAS SUSY overview rather than a specific search with stated event selections and efficiencies. The collider outlook and the choice of VLQ masses in the benchmark points depend on this bound. Please provide the original search reference, the recast procedure (signal regions, efficiencies, background estimates), and the resulting exclusion limit, or state clearly that this is an approximate estimate.","section":"Sec. 3, Eq. (3.12)"},{"comment":"The numerical results are not independently reproducible from the manuscript: no SARAH model files, MicrOMEGAs input cards, or benchmark validation against published IDM relic-density calculations are provided. Since the central claim is a numerical statement about relic density and direct detection cross sections, the absence of these materials makes it impossible to verify the benchmark points in Table 3. Please make the model and input files available, and show at least one validation point against a known pure-IDM relic-density calculation.","section":"Table 3 and Sec. 4.3"}],"minor_comments":[{"comment":"The caption does not identify which panel corresponds to the pure IDM and which to the IDM+VLQ case; the text refers to the \"right panel\" but the caption is ambiguous. Please add explicit panel labels.","section":"Fig. 1 caption"},{"comment":"The entries in the lambda_L column for BP-3 and BP-4 (e.g., \"0.238 (0.03)0.114\") are unclear; please separate the pure-IDM and IDM+VLQ values into distinct columns with clear headings.","section":"Table 3"},{"comment":"The symbol Delta_xi is used but never defined; please define it as (m_xi - m_eta0_D)/m_eta0_D alongside the definitions of Delta_i in Eq. (4.2).","section":"Eq. (4.4)"},{"comment":"There are several typos, e.g., \"coannihhilating\" should be \"coannihilating\" and \"their is a mass-splitting\" should be \"there is a mass-splitting.\"","section":"Sec. 4.3"},{"comment":"Reference [31] is missing bibliographic details (journal, volume, pages); please complete it.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of a phenomenological journal and the main idea is interesting. The primary technical issue is the unverified chemical-equilibrium assumption underlying the coannihilation treatment; this is fixable with a dedicated calculation of conversion rates. I would also ask for the numerical inputs to be made available, since the current manuscript does not permit independent verification of the benchmark results. No concerns about novelty or citation fairness beyond the incomplete reference details."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read the paper. The genuinely new thing is the systematic scan of a compressed, high-mass inert doublet plus one Z2-odd singlet VLQ, with relic density, direct detection, indirect detection, and collider cross sections in one package. The mechanism—VLQ strong annihilation draining the whole dark sector if coannihilation keeps it in equilibrium—is physically sensible, and the benchmark points look internally consistent with what MicrOMEGAs would produce. That is real work, and it gives the subfield concrete benchmark points to test.\n\nThe soft spots are real but not fatal. The load-bearing assumption is chemical equilibrium between the DM and the VLQ during freeze-out, especially for Type-A benchmarks like BP-3 and BP-4, where y_xi = 0.01 and the mass gap is ~35–42 GeV. The paper states that conversion must be faster than Hubble expansion, but it never computes Gamma_conv/H for any benchmark. Given that the eta0–xi Yukawa couples through the top quark and the thermal density is Boltzmann-suppressed at T_f ~ m/25, this is not an idle worry. It is the one thing I would want checked before trusting the quoted Omega h^2 values. This is exactly the kind of thing a single-species effective Boltzmann equation assumes, and it can fail.\n\nSecond, the novelty claim is underargued. The intro says the VLQ-in-IDM role has not been addressed in previous studies, but refs [17] and [29] are related vector-like-quark/top-partner-plus-scalar-DM works. Maybe the compressed high-mass scan is new, but the paper does not say what is different from those. That should be easy to fix.\n\nThird, there are presentation problems. Table 3 has garbled entries (e.g., BP-3 lambda_L '0.238 (0.03)0.114'), and no code, data, or validation against published IDM relic benchmarks is shipped. The quoted squark recast bound is taken from an ATLAS SUSY paper, so at minimum a footnote on caveats is needed.\n\nBottom line: the central claim is plausible and the technical package is standard. The chemical-equilibrium check is the missing piece. I would send this to a serious referee, and I would expect the referee to ask for that check or an explicit multi-species treatment before acceptance. If you work on IDM extensions, this is worth reading in the meantime.","headline":"Useful scan of compressed high-mass IDM with a Z2-odd VLQ; the central relic-dilution mechanism is plausible but the chemical-equilibrium assumption is asserted rather than checked.","tokens_in":17891,"tokens_out":3329,"would_cite":false,"duration_ms":40460,"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":"Adding a $Z_2$-odd vector-like quark to the inert doublet model opens new annihilation channels that reconcile heavy, compressed scalar dark matter with the observed relic abundance and direct-detection limits.","keywords":["inert doublet model","vector-like quark","dark matter relic density","compressed mass spectrum","coannihilation","direct detection","Z2 symmetry","collider signatures"],"falsifier":"Solve the coupled Boltzmann equations for the individual number densities of $\\eta_D^0$, $\\eta_D^A$, $\\eta_D^\\pm$, and $\\xi$ in a Type-A benchmark without assuming equilibrium fractions; if any dark-sector conversion rate falls below the Hubble rate during freeze-out, the relic is not diluted and the benchmark fails. A collider counterpart is a search for a third-generation quark partner in the jets-plus-missing-energy channel: excluding $m_\\xi$ in the 600--1000 GeV range at the predicted pair-production cross-sections would rule out the central parameter space.","tokens_in":16768,"feed_emoji":"🌌","tokens_out":9012,"duration_ms":81856,"temperature":0.7,"pith_summary":"The paper argues that adding a $Z_2$-odd singlet vector-like quark to the inert doublet model (IDM) makes the compressed, heavy dark-matter region viable. In the pure IDM, dark-matter masses above about 550 GeV with nearly degenerate inert scalars are overabundant, and the obvious fix of raising the Higgs-DM coupling $\\lambda_L$ is blocked by direct-detection bounds. The vector-like quark opens new annihilation and coannihilation channels, most importantly strong $\\xi\\xi\\to$ SM annihilations that, while the dark sector stays in equilibrium, drain the whole $Z_2$-odd sector and dilute the DM relic. With this new leverage, $\\lambda_L$ can be as small as $10^{-3}$ and DM masses around 800--1000 GeV satisfy the Planck relic abundance while evading current direct-detection limits, with collider signatures the LHC can reach.","feed_headline":"One new quark fixes heavy inert dark matter","feed_subtitle":"New annihilation channels restore the relic density and loosen direct-detection bounds, putting the model within LHC reach.","key_machinery":"The load-bearing machinery is the extended effective thermally averaged annihilation cross-section, Eq. (4.4), which adds DM-VLQ coannihilation and VLQ-VLQ annihilation terms to the pure IDM coannihilation sum. The mechanism that makes the high-mass region work is chemical equilibrium within the $Z_2$-odd sector: because $\\xi\\bar{\\xi}\\to$ SM is a strong process, $\\xi$'s number density drops rapidly, and if the dark-sector species maintain their equilibrium fractions through conversion reactions, the scalar DM abundance is dragged down with it. This is the Type-A dilution regime; Type-B and Type-C regimes, where DM-VLQ coannihilation and VLQ-mediated annihilation processes dominate respectively, provide additional reduction of the relic density at moderate and large $y_\\xi$. The same parameter controls the collider signal: the VLQ decays to a third-generation quark plus an inert scalar, producing jets and missing transverse energy.","core_discovery":"The paper's central claim is that a $Z_2$-odd singlet vector-like quark $\\xi$ with a Yukawa coupling to the inert doublet and the third-generation quark doublet restores the compressed inert doublet model at high DM masses. In the pure IDM the compressed region above roughly 550 GeV is overabundant because annihilation into weak gauge bosons is weakened by a destructive interference between the four-point contact diagram and scalar-mediated diagrams. With the VLQ, the effective annihilation cross-section gains three types of contributions---VLQ pair annihilation through QCD, DM-VLQ coannihilation, and VLQ-mediated t-channel enhancements---with the relative weights set by the Yukawa coupling $y_\\xi$ and the DM-VLQ mass gap. In the Type-A parameter region the quark's strong annihilation to SM quarks depletes the common dark sector, diluting the scalar DM relic; the benchmark points show DM masses of 800 and 1000 GeV with small inert-scalar splittings and $\\lambda_L\\simeq 0.001$--$0.01$ giving $\\Omega h^2\\simeq 0.12$ and spin-independent cross-sections around $10^{-47}\\,\\text{cm}^2$.","pith_inferences":["This suggests a general recipe: any strongly interacting $Z_2$-odd partner kept in chemical equilibrium with a weakly interacting WIMP can dilute an otherwise overabundant relic, so similar rescues should work in other minimal dark-matter models with a colored companion.","Because the benchmark region has $\\lambda_L\\sim10^{-3}$, the spin-independent direct-detection signal falls toward the neutrino floor; if no collider signal appears first, a low-threshold or direction-sensitive experiment would be needed to distinguish the DM signal from neutrinos.","A decisive internal check would be to solve the full coupled Boltzmann equations for each dark-sector species without assuming fixed equilibrium fractions; if the conversion rates are not fast enough in Type-A regions, the relic density would not be diluted as claimed and the allowed benchmarks would shift to larger $y_\\xi$ or smaller DM-VLQ mass gaps."],"forward_implications":["Compressed IDM spectra with DM masses in the 550--1000 GeV range, inert-scalar splittings of a few GeV, and tiny $\\lambda_L$ become consistent with both the observed relic density and current direct-detection limits.","The vector-like quark masses that produce the correct relic density sit close to the DM mass, with DM-VLQ mass gaps of roughly 35--120 GeV in the benchmark scans, and the recast lower bounds $m_\\xi>550$ (650) GeV for top-like (bottom-like) quarks put much of this region within LHC reach.","The model predicts associated and pair production of the VLQ at the LHC, with final states containing top or bottom quarks plus missing energy from inert scalars; the paper reports pair-production cross-sections up to order a picobarn but leaves a full search strategy for future work.","Indirect-detection constraints from gamma-ray telescopes do not restrict the new allowed region in the 500--1000 GeV DM mass range considered, so the model's main observable test is at colliders.","Depending on $y_\\xi$, the VLQ decay can be prompt or long-lived, which changes the collider signature from prompt jets plus missing energy to displaced vertices."],"supporting_citations":[{"why":"Defines the inert doublet model and its Z2-stabilized scalar dark matter candidate, the starting point the paper extends.","marker":"[3–5]"},{"why":"Establishes the compressed-spectrum regime, its relic-density behavior, and the two-dark-species setup that motivates sharing the dark sector.","marker":"[13, 18, 19]"},{"why":"Supplies the observed relic abundance the benchmark points are required to match.","marker":"[20]"},{"why":"Provides the current spin-independent direct-detection bound that forces the Higgs-DM coupling to be small.","marker":"[2]"},{"why":"Gives the recast LHC lower bounds on a Z2-odd third-generation quark that decays to a quark plus missing energy.","marker":"[45]"},{"why":"Computes relic density and direct-detection observables for the model including the vector-like quark.","marker":"[47]"},{"why":"Supplies the effective-theory treatment for the one-loop box diagrams in the direct-detection calculation.","marker":"[50]"}],"fun_headline_variants":["Vector-like quark rescues heavy inert dark matter","New quark restores relic density for heavy DM","One quark eases heavy dark matter constraints","Quark addition unlocks heavy inert DM for LHC"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole mechanism rests on the assumption that the inert-scalar DM and the vector-like quark stay in chemical equilibrium during freeze-out, so the quark's rapid strong annihilations drag the DM relic down with it; if the conversion reactions that enforce this equilibrium are slower than the expansion of the Universe in some parameter regions, the predicted relic density would not be diluted.","fun_headline_variants_meta":{"raw":{"variants":["Vector-like quark rescues heavy inert dark matter","New quark restores relic density for heavy DM","One quark eases heavy dark matter constraints","Quark addition unlocks heavy inert DM for LHC"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000658,"raw_usage":{"total_tokens":3021,"prompt_tokens":965,"completion_tokens":2056,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":581,"completion_tokens_details":{"reasoning_tokens":1997}},"tokens_in":581,"tokens_out":2056,"duration_ms":14464,"temperature":1.0,"reasoning_tokens":1997,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T05:14:57.560785+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Solve the coupled Boltzmann equations for the individual number densities of $\\eta_D^0$, $\\eta_D^A$, $\\eta_D^\\pm$, and $\\xi$ in a Type-A benchmark without assuming equilibrium fractions; if any dark-sector conversion rate falls below the Hubble rate during freeze-out, the relic is not diluted and the benchmark fails. A collider counterpart is a search for a third-generation quark partner in the jets-plus-missing-energy channel: excluding $m_\\xi$ in the 600--1000 GeV range at the predicted pair-production cross-sections would rule out the central parameter space.","supporting_citations":[{"cited_title":"and et al","cited_arxiv_id":null,"evidence_quote":"Supplies the observed relic abundance the benchmark points are required to match."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the current spin-independent direct-detection bound that forces the Higgs-DM coupling to be small."}],"review_version":1}