{"id":"c3c95825-5676-418e-b414-a195ca542d2f","arxiv_id":"2607.20625","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"FCC-hh displaced-vertex searches could probe Higgs-portal scalars whose decays ended an early matter-dominated era at temperatures from ~1 GeV to the electroweak scale.","lead":"A light scalar that might have briefly dominated the early universe before decaying could leave a displaced-vertex signal at the proposed FCC-hh collider. The paper maps those collider searches onto the temperature at which that early matter era ended, finding reach from about 1 GeV up to the electroweak scale.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Cosmological interpretation rests on unproduced φ abundance: no mechanism in the minimal model makes φ dominate, so the FCC-hh→T_rh mapping is conditional on external initial conditions.","rationale":"The reader identified the same load-bearing assumption: the primordial abundance of ϕ and its dominance are assumed, not derived. I agree that this is the most central link: without it, the collider-to-cosmology map is not a consequence of the model but of an unspecified external scenario. I considered other potential concerns—the idealized zero-background N=3 sensitivity, the uncertain hadronic widths for 3-10 GeV scalars, and the finite-temperature formula's assumptions—but these would shift the reach boundary or the T_rh contours by order-one factors, whereas the dominance failure would sever the cosmological interpretation entirely. The paper explicitly acknowledges the assumption and the other limitations, and the analysis is internally consistent under that assumption. Therefore the reader's CONDITIONAL high-confidence verdict remains appropriate: accept the conditional statement, but flag that the cosmological relevance depends on an unproduced initial abundance. Recommendation: UNCHANGED.","tokens_in":16665,"tokens_out":10080,"duration_ms":94998,"concrete_test":"Within the minimal model (no new couplings beyond Eq. 2.1), compute the maximal ϕ abundance from thermal freeze-in in a radiation-dominated SM bath at the highest permitted pre-BBN temperature (e.g., T ~ 100 GeV), for representative FCC-hh reach points such as (mϕ=5 GeV, sinθ=10^-5) and (mϕ=10 GeV, sinθ=10^-4). Sum all Higgs-mediated 2→2 and 1→2 production processes (using the public UFO model and MadGraph/micrOMEGAs). Then evaluate mϕ Yϕ/s at the time when ϕ would decay (t ~ 1/Γ0) and compare with the radiation energy density. If ρϕ/ρR < 1 for every reach point, the assumed dominance cannot be realized by the minimal model's own interactions, confirming that the T_rh interpretation requires an external production mechanism not specified in the paper. If ρϕ/ρR ≥ 1 for some points, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that FCC-hh displaced searches can probe transition temperatures T_rh—depends on the assumption that ϕ dominated the energy density at some early time. The paper states this explicitly: 'We remain agnostic about the mechanism that produced the primordial abundance of ϕ and simply assume that, at some early time, its energy density dominates' (Sec. 2-3, p. 5); later, 'This is our working assumption' (Sec. 3, p. 5). The minimal Lagrangian (Eq. 2.1) contains only Higgs-portal interactions; it does not generate a dominant ϕ population. Through the same Higgs mixing, ϕ would be produced in the early universe by freeze-in, but the resulting yield is generically many orders of magnitude too small to dominate before decaying. A dominant abundance requires an external source (inflaton decay, modulus displacement, etc.) not present in the minimal model. Therefore Eq. (3.6), which connects sinθ and mϕ to T_rh, is not a prediction of the model but a map valid only under an imposed initial condition. If no viable production mechanism exists in the parameter region of Fig. 7 (mϕ ~ 3-15 GeV, sinθ ~ 6×10^-6 - 3×10^-3), the headline 'probe GeV-scale transition temperatures' loses its cosmological meaning. This is an acknowledged limitation, but it is the load-bearing link between collider observables and early-universe history.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a minimal Higgs-portal extension with a real singlet scalar φ that mixes with the SM Higgs, and assumes that φ dominated the energy density of the early Universe before decaying into SM states. Including a finite-temperature suppression of the decay width, Γφ(T)=Γφ(0) tanh(mφ/4T), the authors derive the transition temperature T_rh at the end of the φ-dominated era and express sin^2θ as a function of mφ and T_rh (Eq. 3.6). They then simulate gluon-fusion production and displaced decays of φ at the LHC and FCC-hh, using the DDC acceptance package for the central tracker, a forward tracker, and FOREHUNT. The projected reach is mapped onto the [mφ, T_rh] plane, giving the paper's central claim: FCC-hh displaced searches could probe early matter-domination transition temperatures from about the GeV scale up to the electroweak scale, within the broken-phase Higgs-portal description.","tokens_in":17076,"tokens_out":14468,"duration_ms":125931,"significance":"If the assumptions hold, this is a valuable and timely proof-of-principle: it connects a concrete, minimal LLP collider signature to a pre-BBN cosmological parameter. The finite-temperature derivation in Appendix A is clean, and the compact piecewise formulas and Eq. (3.6) are internally consistent. A notable strength is that the map is not circular: the same mixing angle controls both collider production/decay and the cosmological width, and no parameters are fitted to data. The paper is honest about its main limitations — the assumed φ-dominated epoch, the partonic hadronic-width approximation, and the idealized zero-background N=3 criterion. The significance is therefore that of a conditional sensitivity study; a fully model-independent prediction of the early-universe history would require a production mechanism for the φ abundance and a more robust treatment of low-mass hadronic widths.","major_comments":[{"comment":"The cosmological interpretation is explicitly conditional on the field φ having dominated the energy density at some early time. The paper states 'We remain agnostic about the mechanism that produced the primordial abundance of φ and simply assume that, at some early time, its energy density dominates' (Sec. 2–3, p. 5) and later 'This is our working assumption' (Sec. 3, p. 5). I agree that this is an intended working assumption, not an internal inconsistency. However, the minimal Lagrangian in Eq. (2.1) contains no mechanism that produces a dominant φ population; freeze-in through the same Higgs mixing typically gives a yield many orders of magnitude too small. The 'ordinary cosmic reheating' interpretation requires φ to be the inflaton/reheaton, which demands an inflationary sector not present in the truncated model. For the broader 'modulus-like' interpretation, a concrete early-univer","section":"Secs. 2–3, pp. 5, and Eq. (2.1)"},{"comment":"The mapping and the collider reach both depend on the zero-temperature width Γφ(0) ∝ sin^2θ Γ_SM^h(mφ), with Γ_SM^h computed from MadGraph partonic widths. The paper acknowledges that 'below the b-quark threshold, the Higgs-like scalar width is subject to hadronic uncertainties' and leaves 'a treatment with dedicated light-scalar hadronic widths for future work.' This is not a negligible detail: the main sensitivity region shown in Fig. 7 is roughly 3 GeV ≲ mφ ≲ 15 GeV, where the width is dominated by non-perturbative QCD for mφ below the b threshold. Since T_rh in Eq. (3.6) and the proper lifetime cτ in Fig. 4 both scale directly with Γ_SM, an uncontrolled O(1–5) uncertainty in the hadronic width translates directly into an uncertainty in the quoted Trh bands and in the reach contours. I request a quantitative estimate: for example, compare the partonic width with known light-scalar had","section":"Sec. 3, Fig. 1, and Eq. (3.6)"},{"comment":"The projected reach is based on N=3 signal events with no background model. The paper is transparent: 'We do not model these backgrounds here and therefore interpret the N=3 contour ... as an idealized zero-background benchmark.' For a low-mass scalar decaying to soft jets, realistic backgrounds at a 100 TeV pp machine — heavy-flavor vertices, material interactions, pile-up, and track fakes — could substantially alter the N=3 contours. I do not ask for a full detector simulation, but the central claim that FCC-hh 'could probe' these temperatures would be strengthened by either a crude background estimate for the central tracker or an explicit statement that the result is a best-case sensitivity projection rather than a discovery reach. As written, the concluding sentence 'FCC-hh displaced searches could probe...' is slightly stronger than what is demonstrated.","section":"Sec. 4, Eq. (4.5), and Fig. 6"}],"minor_comments":[{"comment":"The text notes that the part of the mapped reach with T_rh > T_EW is a 'formal extrapolation,' but the figure does not visibly distinguish these segments. Please use dashed curves or a shading change so the reader immediately sees that the broken-phase interpretation stops at T_EW.","section":"Sec. 5, Fig. 7 right panel"},{"comment":"Eq. (3.4) assumes a radiation-dominated Hubble rate, while at the equality of ρφ and ρ_R the total energy density is twice the radiation density. The resulting O(1) numerical factor (about 2^{1/4} in T_rh) is absorbed in the 'standard analytic estimate' wording. Please state explicitly that Eq. (3.5) is the conventional instant-reheating estimate, not the exact equality condition, to avoid confusion with the definition of T_rh given in the text.","section":"Eqs. (3.4)–(3.5)"},{"comment":"The terminology switches between 'inflaton,' 'reheaton,' and 'modulus-like field.' It would be helpful to specify which interpretation is used when the final map is presented in Fig. 7; for the inflaton/reheaton case the assumption of domination is automatic, whereas for the modulus case it is not.","section":"Sec. 2, Eq. (2.1)"}],"recommendation":"major_revision","confidential_remarks":"This is a promising and potentially publishable sensitivity study. My main concern is not the finite-T derivation or the internal consistency of the T_rh map, which are sound; it is that the headline cosmological statement rests on an externally assumed φ-dominated epoch and on a partonic hadronic width for masses where QCD is non-perturbative. These are acknowledged, but they are load-bearing for the numerical claims in Fig. 7. I would be comfortable with acceptance after the authors either supply production-mechanism context and a hadronic-width uncertainty band, or explicitly downgrade the abstract/conclusion claims to 'if such an epoch occurs, the map shows...' The idealized zero-background criterion is also worth a caveat in the abstract."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe paper does one clearly useful thing: it converts the proposed FCC-hh LLP sensitivity into a map onto the [mφ, T_rh] plane for a GeV-scale Higgs-portal scalar, including the finite-temperature Pauli-blocking suppression of the decay width. That specific mapping is new relative to the earlier vector-DM work (their ref [39]), and it is done transparently. The thermal width derivation in Appendix A is clean and reproduces the Adshead et al. tanh form; the piecewise T_rh formulas are consistent; and the collider analysis uses existing detector proposals rather than inventing new ones.\n\nThe paper is also honest about what it does not do: backgrounds are not modeled, the N=3 contour is an idealized zero-background benchmark, the hadronic width in the 3-10 GeV region is a MadGraph estimate with acknowledged uncertainties, and the analytic H=Γ estimate is used instead of full Boltzmann evolution. None of these are hidden.\n\nThe largest caveat, which the paper states without hiding, is that the cosmological interpretation requires φ to have dominated the energy density at some early time. In the minimal Lagrangian of Eq. (2.1) there is no production mechanism that yields a dominant abundance; freeze-in through the Higgs mixing is far too small. The authors call this a working assumption and note that φ could be the inflaton/reheaton or a modulus-like field. That is a legitimate parameterization of an early matter-dominated epoch, not an internal inconsistency, but it does mean the T_rh reach is conditional: if no cosmology produces the needed abundance, the map has no predictive power. The stress-test note frames this as load-bearing, and I think that is fair — but it is a limitation the authors already flag, and it is standard in reheating studies to leave the production mechanism unspecified.\n\nI would give the paper solid marks for clarity and internal consistency. It deserves a serious referee. The main things a referee would push on are the zero-background assumption, the light-scalar width uncertainties, and whether the authors can at least sketch a production mechanism (e.g., inflaton decay) that reaches domination in the shown parameter range.\n\nRecommendation: send it to peer review. It is a useful, honest projection that the community will want to see.","headline":"A clean mapping from FCC-hh displaced decays to the reheating temperature of a Higgs-portal scalar, honest about its conditional assumptions and worth a round of refereeing.","tokens_in":17514,"tokens_out":2285,"would_cite":true,"duration_ms":20681,"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":"Displaced-decay searches at FCC-hh could measure the temperature at which an early matter-dominated era ended, mapping scalar masses and Higgs mixing angles in the 3–15 GeV, 6×10^-6–3×10^-3 range onto reheating temperatures from roughly the","keywords":["early matter domination","reheating temperature","Higgs-portal scalar","long-lived particles","displaced vertices","FCC-hh","finite-temperature decay width","GeV-scale scalar"],"falsifier":"If FCC-hh runs at 100 TeV with 20 ab^-1 and finds zero displaced-vertex events in the region 3 GeV < m_φ < 15 GeV with 6×10^-6 < sinθ < 3×10^-3, the paper's central reach claim is falsified under its idealized background-free N=3 criterion. Conversely, a precise measurement of the Higgs mixing angle from another channel that is incompatible with the assumed single-angle link would break the map between collider lifetimes and T_rh.","tokens_in":16591,"feed_emoji":"⚛️","tokens_out":9451,"duration_ms":75250,"temperature":0.7,"pith_summary":"The paper aims to turn long-lived-particle searches at a future hadron collider into a direct probe of the Universe's pre-Big-Bang-nucleosynthesis expansion history. It studies a minimal extension of the Standard Model: a GeV-scale scalar that mixes with the Higgs boson, can dominate the energy density of the early Universe, and decays into Standard Model fermions. Because the same mixing angle controls both the cosmic decay rate and the collider production rate, the particle's displaced decays at FCC-hh can be translated into the reheating temperature T_rh at which the matter-dominated era ended. The key refinement is a finite-temperature decay width, suppressed by Pauli blocking and inverse decays, which lowers T_rh relative to vacuum-decay estimates. The central result is a map showing that FCC-hh displaced-vertex searches could probe transition temperatures from roughly the GeV scale up to the electroweak scale, within the broken-phase Higgs-portal description.","feed_headline":"FCC-hh displaced decays can reveal cosmic reheating temperatures","feed_subtitle":"A GeV-scale scalar that once dominated the universe would decay late; FCC-hh could see it and reveal the reheating temperature.","key_machinery":"The engine of the paper is the Higgs-mixing angle θ. After electroweak symmetry breaking, a real singlet scalar φ mixes with the Higgs boson, and every φ coupling to Standard Model fermions is proportional to sin θ. This one parameter governs three observables at once: the vacuum decay width Γ0 = sin²θ Γ_SM_h(m_φ), the gluon-fusion production cross-section at a proton collider (also suppressed by sin θ), and the proper decay length cτ. The bridge to cosmology is the in-medium decay width Γφ(T)=Γ0 tanh(m_φ/(4T)), derived from the Boltzmann collision term with Pauli blocking and inverse decays; using H(T_rh)=Γφ(T_rh) converts a measured lifetime into a reheating temperature. Equation (3.6) mak","core_discovery":"The paper's central claim is that a GeV-scale Higgs-portal scalar phi, if it once dominated the energy density of the early Universe, leaves a collider-visible remnant: because its decays are suppressed by a small Higgs mixing angle, it is long-lived and can decay inside FCC-hh detectors. The same mixing angle sets both its cosmic lifetime and its production rate at colliders, so observing displaced decays would fix the decay width and, through the relation H(T_rh)=Gamma_phi(T_rh), determine the temperature T_rh at which phi-matter gave way to radiation domination. The paper shows that the finite-temperature decay width Gamma_phi(T)=Gamma0 tanh(m_phi/4T) lowers T_rh relative to vacuum-decay","pith_inferences":["Inference: The map can be read backwards: a measured displaced-decay signal would fix m_φ and sinθ and therefore predict T_rh, which could then be compared with independent cosmological probes of early matter domination (e.g., gravitational-wave spectra) to test whether the scalar was indeed the agent that ended the matter-dominated era.","Inference: The tanh thermal suppression is derived for fermionic final states; extending the same plasma calculation to decays into gauge bosons would be needed before applying the map to scalar masses above the electroweak scale, where gauge-boson channels open.","Inference: Since the production mechanism of φ is left unspecified, a future measurement would not by itself distinguish ordinary inflaton reheating from a modulus-like matter component; complementary observables would be required to pin down the origin of the early matter dominance.","Inference: A detector-level background study would turn the idealized zero-background reach curves into actual exclusion or discovery limits; the same mapping machinery would carry over unchanged."],"forward_implications":["If a displaced vertex is seen at FCC-hh with mass and mixing in the quoted range, the corresponding reheating temperature must lie between roughly the GeV scale and the electroweak scale, meaning the early Universe went through a matter-dominated phase that ended before BBN.","A null result in the full reach region would rule out Higgs-portal scalars as the driver of an early matter-dominated era in this mass/mixing window, as well as Higgs-portal reheating with T_rh in that range.","The finite-temperature suppression means that for T_rh > m_φ/4, the lifetime implied by a given collider signal is longer than the vacuum estimate, so cosmological constraints derived from vacuum decays would overestimate T_rh.","The LHC's displaced-vertex searches cannot reach this model because production is too suppressed and the decay products are too soft, so FCC-hh is the practical path to test this cosmological scenario.","The reach lies above T_BBN ≈ 4 MeV, so the eras that could be probed are all consistent with standard BBN predictions."],"fun_headline_variants":["FCC-hh sees long-lived scalar's late decay, pinning reheating temperature","GeV-scale scalar decay at FCC-hh reveals reheating epoch","Displaced vertices at FCC-hh map cosmic reheating temperature","Long-lived Higgs-portal scalar: collider probe of early matter era","FCC-hh can spot scalar decay that set the reheating temperature"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing assumption is that the scalar φ actually dominated the total energy density of the Universe at some early time; the paper explicitly remains agnostic about how it was produced, so if φ's primordial abundance was too small—or if it never came to dominate—the observed displaced decays would carry no information about reheating or radiation domination.","fun_headline_variants_meta":{"raw":{"variants":["FCC-hh sees long-lived scalar's late decay, pinning reheating temperature","GeV-scale scalar decay at FCC-hh reveals reheating epoch","Displaced vertices at FCC-hh map cosmic reheating temperature","Long-lived Higgs-portal scalar: collider probe of early matter era","FCC-hh can spot scalar decay that set the reheating temperature"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000433,"raw_usage":{"total_tokens":2004,"prompt_tokens":666,"completion_tokens":1338,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":410,"completion_tokens_details":{"reasoning_tokens":1256}},"tokens_in":410,"tokens_out":1338,"duration_ms":9637,"temperature":1.0,"reasoning_tokens":1256,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T09:48:04.919263+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"If FCC-hh runs at 100 TeV with 20 ab^-1 and finds zero displaced-vertex events in the region 3 GeV < m_φ < 15 GeV with 6×10^-6 < sinθ < 3×10^-3, the paper's central reach claim is falsified under its idealized background-free N=3 criterion. Conversely, a precise measurement of the Higgs mixing angle from another channel that is incompatible with the assumed single-angle link would break the map between collider lifetimes and T_rh.","supporting_citations":[],"review_version":1}