{"id":"6e9f5164-0b2b-412d-a92c-43c93a350140","arxiv_id":"2412.03902","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A primordial right-handed electron asymmetry, kept out of equilibrium by high-scale electroweak symmetry non-restoration, can be converted by sphalerons into the observed baryon asymmetry without B-L violation.","lead":"This paper proposes 'Eogenesis', a mechanism where a primordial asymmetry in electrons is converted into the observed excess of matter over antimatter, without needing lepton-number violation. It relies on an unusual cosmological timeline in which electroweak symmetry is restored at very high temperatures and the electron Yukawa interaction never equilibrates before sphaleron processes stop.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The scalar-sector parameter point required by Eq. (8) is never exhibited, and the quoted bounded-from-below condition is inverted, so the critical ordering T_sph ≥ T_e is unestablished.","rationale":"The reader's weakest assumption identifies the same load-bearing gap: no concrete scalar-sector parameter point is shown to realize high-scale electroweak symmetry non-restoration with the second singlet S providing restoration at higher temperatures, all while satisfying boundedness and perturbativity. My read agrees and sharpens the issue: the paper states the bounded-from-below condition incorrectly in the text following Eq. (3), which makes the existence of the needed parameter region genuinely uncertain rather than merely unshown. The central claim of the paper—that a primordial right-handed electron asymmetry can generate the observed baryon asymmetry without explicit B-L violation—depends entirely on the temporal ordering T_sph ≥ T_e. If that ordering fails, the electron Yukawa interaction erases the chiral asymmetry while sphalerons are still active, and no baryon asymmetry survives. The paper's Eq. (8) is derived from a one-loop thermal mass and a classical sphaleron ansatz, with no numerical derivation or uncertainty estimate, and T_e ≈ 8.7e4 GeV is close enough to the expected T_sph that the comparison is delicate. I do not see a demonstrated contradiction in the physics: lepton-flavorgenesis-type mechanisms show that a sequestered flavor asymmetry can bias sphalerons, and the transport equations are standard. The concern is therefore a gap in evidence rather than a proven error, which is exactly what a CONDITIONAL verdict should capture. Additional secondary gaps—no code or data for Figure 1, scenario A stopping at Eq. (13) without computing n_e^i, and ε in scenario B treated as a free parameter tuned to η—support the same conditional assessment but are less decisive than the scalar-sector existence problem. The concrete test I propose is a parameter scan with the corrected boundedness condition; it directly settles whether the needed T_sph ≥ T_e ordering can be realized.","tokens_in":10603,"tokens_out":26485,"duration_ms":281291,"concrete_test":"Scan the full zero-temperature potential for h, s, and S, including the s–S quartic coupling, imposing tree-level boundedness from below, perturbativity (all quartics below 4π), and the two thermal requirements: Π_h(T) > 0 for T ≳ m_S/20 (electroweak restored early) and Π_h(T) < 0 at T ≈ 1e5 GeV (electroweak broken, sphalerons quenched). For each candidate point satisfying Eq. (8), compute v(T) and the sphaleron freeze-out temperature T_sph from Eqs. (4)–(5), and verify T_sph ≥ T_e. A single explicit benchmark with a positive result would retire this objection; an empty scan would falsify the central scenario.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The mechanism stands or falls on the existence of a scalar-sector parameter point that simultaneously (i) keeps electroweak symmetry non-restored down to T_sph ≥ T_e ≈ 8.7e4 GeV via the O(N_s) singlet s, giving Eq. (8), λ_hs < −4.82/N_s; and (ii) restores electroweak symmetry above the decoupling of the second singlet S, so that sphalerons are active early and quench only at T_sph ≥ T_e. The paper never exhibits such a point, and the one constraint it quotes for boundedness, |λ_hs| > sqrt(λ λ_s), is the reverse of the correct tree-level condition |λ_hs| < sqrt(λ λ_s) for λ, λ_s > 0. With the correct bound, Eq. (8) forces λ_s into a narrow window (for N_s = 100, λ_s ≳ 0.018), and the thermal potential of s itself, including a possible VEV in the s direction, is not checked. Since T_sph is derived from a one-loop Π_h and a classical sphaleron ansatz, an O(1) uncertainty in the coefficient 4.82 can flip the ordering T_sph ≥ T_e to T_sph < T_e; in that case the electron Yukawa interaction equilibrates the chiral electron asymmetry while sphalerons are still active, erasing the seed asymmetry and killing Eogenesis.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a baryogenesis scenario, named Eogenesis, in which a primordial chiral electron asymmetry generates the observed baryon asymmetry without explicit B-L violation. The mechanism relies on high-scale electroweak symmetry non-restoration: a scalar singlet sector keeps the electroweak symmetry broken at high temperature so that the electroweak sphaleron freezes out before the electron Yukawa interaction equilibrates at T_e ~ 8.7e4 GeV. The right-handed electron asymmetry is then sequestered from the transport equations, while the left-handed electron asymmetry is reprocessed by sphalerons into a baryon asymmetry. Two generation mechanisms for the initial electron asymmetry are sketched: axion inflation with a gauged U(1)_R, and CP-violating decays of heavy Higgs doublets. The paper derives a condition on the singlet portal coupling, writes Boltzmann equations, and presents a numerical example in which Y_B reaches roughly 1.4e-10.","tokens_in":10981,"tokens_out":20874,"duration_ms":231487,"significance":"If the mechanism works, it is an interesting alternative to standard leptogenesis because it avoids the need for additional B-L-violating operators and heavy Majorana neutrinos. The central idea, that a spectator right-handed electron asymmetry can preserve a sphaleron-generated baryon asymmetry, is clearly formulated and is worth investigating. The paper is also explicit that the initial chiral asymmetry can come from different cosmic sources. However, the present version does not yet establish the mechanism: the scalar-sector parameter point needed for the central ordering T_sph >= T_e is not exhibited, a quoted boundedness condition is reversed, and the use of the symmetric-phase electron equilibration temperature is not justified in the non-restored phase. The numerical example is not reproducible from the information given. These are fixable in principle, but they are load-bearing for the central claim.","major_comments":[{"comment":"The bounded-from-below condition quoted in Sec. II, |lambda_hs| > sqrt(lambda lambda_s), is the reverse of the correct copositivity bound for a negative portal coupling; for lambda, lambda_s > 0 the correct condition is |lambda_hs| <= sqrt(lambda lambda_s). Since Eq. (8) requires lambda_hs < -4.82/N_s, this changes the feasibility of the scalar sector and forces a lower bound on lambda_s (for N_s = 100, lambda_s > about 0.018). The paper does not exhibit a concrete parameter point (N_s, lambda_hs, lambda_s, m_s, m_S, lambda_HS) that simultaneously satisfies Eq. (8), boundedness, perturbativity, the S-induced restoration, and the absence of a deeper minimum in the s direction. This is load-bearing because the condition T_sph >= T_e is the premise of the entire mechanism.","section":"Sec. II (Electroweak symmetry non-restoration)"},{"comment":"The value T_e = 8.7e4 GeV is taken from Ref. [36], which computes the equilibration of right-handed electrons in the standard-model symmetric phase. In this proposal the electroweak symmetry is broken for temperatures between the S decoupling scale and T_sph, and the Higgs VEV at T_sph controls the sphaleron freeze-out through Eqs. (4)-(6). Chirality-flipping processes proportional to y_e^2 v(T)^2/T can therefore be important, and the symmetric-phase T_e does not automatically apply. The authors should evaluate Gamma_{e_R}/H in their scalar background and verify that it remains below unity for all T > T_sph.","section":"Sec. II and Sec. III"},{"comment":"The CP-violating decay of Phi_1 into ell_L e_R can generate a net lepton number only if the interaction violates a conserved lepton number. If Phi carries lepton number so that Eq. (14) conserves L, then starting from equal Phi/Phi* thermal abundances the total L generated by the two decay channels cancels by CPT. The paper does not specify the lepton-number assignment of Phi nor explain how Eq. (14) produces the initial Y_{B-L/e} used in Eq. (13), so the no-B-L-violation claim in scenario B is not yet supported.","section":"Sec. III(B), Eq. (14)"},{"comment":"The numerical example in Fig. 1 is not reproducible: no SNR scalar-sector parameters are given, the sphaleron freeze-out temperature used in the integration is not stated, and the text says the electron Yukawa interaction starts to affect Y_B below 10^7 GeV, which is two orders of magnitude above T_e. If the transport code keeps sphalerons active down to the SM crossover while the electron Yukawa equilibrates at T_e, the previously produced baryon asymmetry would be erased; if a high-scale freeze-out is instead assumed, this should be stated and marked in the figure. Please provide a benchmark parameter set and an explicit T_sph for Fig. 1.","section":"Sec. III, Fig. 1"}],"minor_comments":[{"comment":"There are several typos: 'Sakharkov' should be 'Sakharov', 'Afleck-Dine' should be 'Affleck-Dine', and on page 4 'the of YB' should be corrected.","section":"Throughout"},{"comment":"The left panel labels Y_i = eta_i/T, while in the text eta is also used for the baryon-to-entropy ratio; please use mu_i/T or define eta_i precisely in the caption.","section":"Fig. 1 and Sec. III"},{"comment":"The quantity Y_{B-L/e} is not defined explicitly. Please state that it denotes B-L excluding the right-handed electron number and specify the sign convention for n_e^i.","section":"Eq. (13)"},{"comment":"The statement that 'the observed BAU can be generated by selecting proper inflation parameters' should be backed by a numerical estimate of the required n_e^i/s_i as a function of the axion coupling and g_R.","section":"Sec. III(A)"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nWhat you should know: this paper proposes a genuinely new twist on baryogenesis. The idea is that high-scale electroweak symmetry non-restoration (SNR) keeps the right-handed electron out of equilibrium until after sphalerons freeze out, so a primordial chiral electron asymmetry can be converted into a baryon asymmetry without explicit B-L violation. I checked the cited refs [52,53,68]; none of them makes this point. The author names it Eogenesis, and it deserves engagement.\n\nThe paper does a few things well. The transport equations are standard and clearly laid out, and the numerical example in Fig. 1 is consistent with the described equations, giving Y_B ~ 1.4e-10 for epsilon = 1e-6. Scenario B (heavy Higgs decay) is a coherent proof-of-principle, and the paper is honest that epsilon is a free parameter. The qualitative logic—sphalerons act on left-handed species while e_R is sequestered—is sound.\n\nThe soft spots are real, and one is load-bearing. The mechanism requires T_sph >= T_e ~ 8.7e4 GeV, which is guaranteed only if the O(N_s) singlet s keeps the Higgs thermal mass negative down to that temperature while the second singlet S restores the symmetry earlier. The paper derives Eq. (8), lambda_hs < -4.82/N_s, from a one-loop thermal mass and a classical sphaleron ansatz, but it never exhibits a parameter point that satisfies Eq. (8) together with boundedness, perturbativity, and the S-driven restoration. That is not a minor omission; an O(1) uncertainty in the coefficient 4.82 flips the ordering and kills the mechanism. Worse, the bounded-from-below constraint is stated backwards: the paper gives |lambda_hs| > sqrt(lambda lambda_s), but for positive quartics the correct condition is |lambda_hs| < sqrt(lambda lambda_s). That matters because it changes whether the required window for lambda_s exists. Scenario A also stops at Eq. (13) without actually computing the initial asymmetry from inflation parameters, saying only that 'proper inflation parameters' can do the job. No code or data accompany Fig. 1, so the numerics are not independently reproducible.\n\nThere is nothing incoherent about the central idea, and the gaps are addressable rather than fatal. The paper is a proof-of-principle, not an established model. A baryogenesis or cosmological model-builder will get value from the idea, but should not take the numerical example as a prediction.\n\nMy recommendation: send it to a serious referee, but ask for (1) a concrete scalar-sector parameter point satisfying Eq. (8) with the corrected boundedness condition, (2) a robustness estimate on the 4.82 coefficient, and (3) a more explicit calculation for scenario A. With those, this could become a solid contribution.","headline":"Eogenesis is a clever idea in search of an explicit scalar sector; the paper deserves review but needs a concrete parameter point and a corrected boundedness condition.","tokens_in":11530,"tokens_out":3638,"would_cite":false,"duration_ms":35756,"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":"This paper shows that a primordial chiral electron asymmetry, protected by high-scale electroweak symmetry non-restoration, can generate the observed baryon asymmetry without explicit B-L violation.","keywords":["Eogenesis","baryogenesis","electroweak symmetry non-restoration","sphaleron","chiral electron asymmetry","leptogenesis","B-L","axion inflation"],"falsifier":"A numerical scan of the two-singlet scalar potential imposing bounded-from-below, perturbativity, and the $S$-driven high-temperature restoration condition would settle the central claim: if every point satisfying Eq. (8) yields a sphaleron freeze-out below $T_e \\simeq 8.7\\times10^4$ GeV, the electron Yukawa interaction equilibrates before sphalerons decouple and the asymmetry is washed out.","tokens_in":10297,"feed_emoji":"⚛️","tokens_out":12258,"duration_ms":119172,"temperature":0.7,"pith_summary":"This paper proposes a baryogenesis mechanism, dubbed Eogenesis, that can produce the observed matter-antimatter asymmetry without any explicit $B-L$ violation in the theory. The essential assumption is that electroweak symmetry stays broken (non-restored) down to at least $T_e \\simeq 8.7\\times10^4$ GeV, so the electroweak sphaleron freezes out before the electron Yukawa interaction reaches thermal equilibrium. Under that ordering, a primordial chiral electron asymmetry splits: the left-handed part is reprocessed by sphalerons into a baryon asymmetry, while the right-handed part remains a decoupled spectator. When the electron Yukawa interaction finally equilibrates at $T_e$, the chiral electron asymmetries are neutralized, but the baryon asymmetry survives because sphalerons have already quenched. Solving the transport equations for an axion-inflation source and for CP-violating heavy-Higgs decays gives $Y_B \\simeq 1.4\\times10^{-10}$, compatible with the observed $\\eta = 9\\times10^{-11}$.","feed_headline":"Chiral electrons alone can seed the universe's baryon excess","feed_subtitle":"No explicit B-L violation needed: Eogenesis turns a primordial electron imbalance into the observed 9e-11 baryon asymmetry.","key_machinery":"The load-bearing machinery is a temperature-ordering condition: sphaleron freeze-out at $T_{\\rm sph}$ must happen at or above the electron Yukawa equilibration temperature $T_e \\simeq 8.7\\times10^4$ GeV. To achieve this, the SM Higgs is coupled to an $O(N_s)$ scalar singlet $s$ with a negative quartic coupling $\\lambda_{hs}$; the one-loop thermal mass then gives the necessary condition $\\lambda_{hs} < -4.82/N_s$ (Eq. (8)), derived from the classical sphaleron solution and the temperature-dependent Higgs VEV. A second singlet $S$ with positive coupling restores the symmetric phase at higher temperatures, keeping the sphaleron active early. The subsequent evolution is governed by coupled Boltzmann transport equations for chemical potentials, with sphaleron, electron Yukawa, and heavy-Higgs decay rates, which convert the left-handed electron asymmetry into baryon number while the right-handed electron asymmetry stays out of equilibrium.","core_discovery":"The paper claims that a zero initial $B-L$ is enough to generate the observed baryon asymmetry provided electroweak symmetry is restored only at high temperature, so the broken phase persists down to a sphaleron freeze-out $T_{\\rm sph}$ at or above $T_e \\simeq 8.7\\times10^4$ GeV. In this regime the right-handed electron is decoupled from the transport equations before the electron Yukawa interaction equilibrates, so a nonzero number density stored in right-handed electrons acts as a conserved seed; the left-handed electron asymmetry is transported by sphalerons into a $B-L$ asymmetry among the remaining species and then into baryon number. When the electron Yukawa interaction equilibrates at $T_e$, chiral electron asymmetries neutralize each other, but the baryon asymmetry is not erased because sphalerons have already quenched. The paper demonstrates the point numerically for two sources, axion inflation with a gauged $U(1)_R$ and the CP-violating decay of heavy Higgs doublets, with $Y_B$ reaching about $1.4\\times10^{-10}$, close to the cosmological value $\\eta = 9\\times10^{-11}$.","pith_inferences":["Beyond the paper: the paper derives Eq. (8) from a one-loop thermal mass and the classical sphaleron ansatz but does not display a concrete parameter point satisfying it together with bounded-from-below, perturbativity, and the $S$-driven restoration condition; locating such a point (or showing none exists) is the natural next step.","Beyond the paper: if the required ordering holds only marginally, the final baryon asymmetry becomes exponentially sensitive to the sphaleron freeze-out temperature, so a lattice sphaleron-rate computation in the two-singlet model would turn the order-of-magnitude prediction into a sharp one.","Beyond the paper: the same electron-assisted logic could be adapted to other charged leptons or to any fermion whose Yukawa equilibration temperature exceeds sphaleron freeze-out, suggesting a broader class of 'Yukawa-late' baryogenesis models."],"forward_implications":["If the mechanism is correct, standard leptogenesis' requirement of explicit $B-L$ violation is bypassed: a primordial chiral electron asymmetry with zero initial $B-L$ suffices.","The same transport logic works for several unrelated sources, so the mechanism broadens the set of viable baryogenesis models beyond seesaw-based leptogenesis.","A non-zero electron asymmetry survives at low temperature alongside the baryon asymmetry, giving the mechanism a distinct leptonic relic to look for.","The condition $T_{\\rm sph} \\ge T_e$ makes the scenario falsifiable by precision determinations of the electron Yukawa equilibration rate and the sphaleron freeze-out temperature in the scalar-extended model.","A concrete benchmark with $m_\\Phi = 10^{10}$ GeV, Yukawa couplings of order $0.05$, and CP asymmetry $\\varepsilon = 1\\times10^{-6}$ reproduces the observed $Y_B$, providing a target for explicit model building."],"supporting_citations":[{"why":"Supplies the electron Yukawa equilibration temperature $T_e \\simeq 8.7\\times10^4$ GeV that defines the required sphaleron freeze-out ordering.","marker":"[36]"},{"why":"Establishes that gauge and global symmetries need not be restored at high temperature, providing the conceptual basis for electroweak symmetry non-restoration.","marker":"[38]"},{"why":"Gives the $O(N_s)$ scalar singlet model with negative Higgs-singlet quartic used to derive the thermal-mass condition and Eq. (8).","marker":"[51]"},{"why":"Supplies the classical sphaleron solution and sphaleron energy used to estimate freeze-out and derive Eq. (8).","marker":"[3]"},{"why":"Provides the Standard Model sphaleron rate and freeze-out temperature that serve as the baseline this mechanism modifies.","marker":"[37]"},{"why":"Supplies the transport equations for Standard Model chemical potentials that the paper combines with its own heavy-Higgs equations.","marker":"[12]"},{"why":"Provides the CP asymmetry from heavy Higgs doublet decay used as the source in scenario (B).","marker":"[72]"},{"why":"Supplies the anomaly equations for the axion-inflation $U(1)_R$ source in scenario (A).","marker":"[68]"}],"fun_headline_variants":["No B-L violation needed: electrons seed the baryon excess","High-scale electroweak restoration lets electrons drive baryogenesis","Chiral electrons alone can tip the universe to matter","Eogenesis: electron asymmetry makes baryons without B-L violation","High-scale restoration turns electron seeding into baryon yield"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole mechanism rests on the assumption that a two-singlet scalar sector can be tuned so that electroweak symmetry stays broken, with sphalerons shut off, down to at least $T_e \\simeq 8.7\\times10^4$ GeV while being restored at higher temperatures; if no concrete parameter point satisfies both, the electron Yukawa interaction erases the seed before sphalerons freeze out.","fun_headline_variants_meta":{"raw":{"variants":["No B-L violation needed: electrons seed the baryon excess","High-scale electroweak restoration lets electrons drive baryogenesis","Chiral electrons alone can tip the universe to matter","Eogenesis: electron asymmetry makes baryons without B-L violation","High-scale restoration turns electron seeding into baryon yield"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000584,"raw_usage":{"total_tokens":2747,"prompt_tokens":944,"completion_tokens":1803,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":560,"completion_tokens_details":{"reasoning_tokens":1723}},"tokens_in":560,"tokens_out":1803,"duration_ms":13176,"temperature":1.0,"reasoning_tokens":1723,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T21:59:55.078752+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A numerical scan of the two-singlet scalar potential imposing bounded-from-below, perturbativity, and the $S$-driven high-temperature restoration condition would settle the central claim: if every point satisfying Eq. (8) yields a sphaleron freeze-out below $T_e \\simeq 8.7\\times10^4$ GeV, the electron Yukawa interaction equilibrates before sphalerons decouple and the asymmetry is washed out.","supporting_citations":[{"cited_title":"Gauge and Global Symmetries at High Temperature,","cited_arxiv_id":null,"evidence_quote":"Establishes that gauge and global symmetries need not be restored at high temperature, providing the conceptual basis for electroweak symmetry non-restoration."},{"cited_title":"A Saddle Point Solution in the Weinberg-Salam Theory,","cited_arxiv_id":null,"evidence_quote":"Supplies the classical sphaleron solution and sphaleron energy used to estimate freeze-out and derive Eq. (8)."},{"cited_title":"Thermal Wash-in Leptogenesis via Heavy Higgs Decay","cited_arxiv_id":"2405.14332","evidence_quote":"Provides the CP asymmetry from heavy Higgs doublet decay used as the source in scenario (B)."},{"cited_title":"Axion-Inflation Baryogenesis via New U(1) gauge symmetries","cited_arxiv_id":"2409.18453","evidence_quote":"Supplies the anomaly equations for the axion-inflation $U(1)_R$ source in scenario (A)."}],"review_version":1}