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REVIEW 2 major objections 5 minor 60 references

Dark CP Violation and Gauged Lepton/Baryon Number for Electroweak Baryogenesis

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A light leptophilic Z' can explain the baryon asymmetry by carrying dark-sector CP violation into the Standard Model.

desk verdict A careful, phenomenologically rich EWBG model built on a clever dark-CP-transfer idea, but the anomalon decoupling premise is asserted, not quantified. read the letter →

arxiv 1908.04818 v2 pith:L5WX32SV submitted 2019-08-13 hep-ph hep-ex

Marcela Carena , Mariano Quirós , Yue Zhang This is my paper · ORCID
classification hep-phhep-ex
keywords electroweakbaryogenesisgaugedleptonnumberdarksectorCPviolationleptophilicZ'matterelectricdipolemomentfirst-orderphasetransitionweaksphaleron
topics Matter-Antimatter Asymmetry
open problems Matter-Antimatter Asymmetry
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish a new way to make electroweak baryogenesis work when all CP violation lives in a dark sector. The proposed model promotes lepton number to a gauged $U(1)_\ell$ symmetry, adds a dark fermion $\chi$ with a complex mass that varies across the bubble wall, and uses a light leptophilic $Z'$ (a new force carrier that couples to leptons) as the messenger to the Standard Model. The dark CP violation creates a chiral asymmetry in $\chi$; because $\chi_L$ and $\chi_R$ carry different $U(1)_\ell$ charges, that asymmetry produces a time-like $Z'$ background that acts as a chemical potential for Standard Model leptons. Weak sphalerons, the Standard Model processes that violate baryon and lepton number, biased by the anomaly in the low-energy lepton-number current, convert the lepton asymmetry into the observed baryon asymmetry $\eta_B \simeq 0.9\times 10^{-10}$. If the mechanism is right, it leaves concrete experimental targets: a leptophilic $Z'$ with mass roughly between 10 GeV and the TeV scale, a dark-matter fermion around a few hundred GeV, and electron electric dipole moments no larger than about $10^{-30}$ e cm from at least three loops.

What carries the argument

The load-bearing object is the time-like background of the $Z'$ gauge boson, $\langle Z'_0(z)\rangle$, generated by the net $U(1)_\ell$ charge density of the dark fermion $\chi$. Because $\chi_L$ and $\chi_R$ carry different $U(1)_\ell$ charges ($q+N_g$ and $q$, respectively), the CP-violating chiral asymmetry produced by the space-dependent phase of the $\chi$ mass is not neutral under the gauge symmetry, and the resulting charge density sources the background through Eq. (3.19). That background is CP odd and CPT odd, so it acts like a chemical potential $\mu_{LL}(z)=g'\langle Z'_0(z)\rangle$ for SM leptons. The companion ingredient is the anomalous low-energy current: after the anomaly-cancelling anomalons are integrated out (and assumed Boltzmann-suppressed at $T_n$), the $U(1)_\ell$ current is anomalous with respect to $SU(2)_L$, meaning lepton number is violated by the same quantum triangle diagrams that feed the sphaleron, and this is what allows weak sphalerons to convert the lepton-number bias into a net baryon asymmetry rather than merely reshuffling conserved charges.

What would settle it

A direct finite-temperature computation of the $U(1)_\ell\times SU(2)_L^2$ anomaly coefficient with the anomalon fields present at the nucleation temperature $T_n$, rather than assuming them to be Boltzmann-suppressed, would settle the mechanism: if the coefficient is not strongly suppressed, Eq. (3.24) gives zero asymmetry and the working points of Fig. 5 cannot reproduce $\eta_B\simeq 0.9\times 10^{-10}$.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that the observed baryon asymmetry can be generated by a chain that starts and ends in the visible sector but is sourced entirely by dark-sector CP violation. During a strong first-order electroweak phase transition, the complex scalar $S$ changes its VEV across the bubble wall and makes the phase of the $\chi$ mass spacetime-dependent. That phase gradient produces opposite chiral asymmetries in $\chi_L$ and $\chi_R$ via diffusion. Their different $U(1)_\ell$ charges give a net lepton-number charge density, which creates the CP- and CPT-odd background $\langle Z'_0\rangle$; this background enters as a chemical potential for all SM leptons. The final lepton number is nonzero only because the low-energy effective theory has an anomalous $U(1)_\ell$ current with respect to $SU(2)_L$: the heavy anomalons are integrated out and decoupled from the plasma, and the Wess-Zumino terms restore gauge invariance. Since sphalerons preserve $B-L$, the lepton asymmetry becomes an equal baryon asymmetry, and the paper exhibits working parameter space in Fig. 5 with $M_{Z'}$ roughly in the 10 GeV to TeV range.

Load-bearing premise

The mechanism relies on the heavy particles that would cancel the quantum anomaly in the lepton-number symmetry being so rare in the hot plasma at the phase transition that the light theory still behaves anomalously; the paper assumes this Boltzmann suppression without computing it in detail.

Editorial extensions

If this is right

  • A leptophilic $Z'$ with mass roughly between 10 GeV and the TeV scale and small coupling is a smoking-gun signature; current constraints from colliders, beam dumps, neutrino experiments, $(g-2)_\mu$, and meson decays already carve out the allowed window, and future Higgs factories can extend it.
  • The dark fermion $\chi$ can account for the thermal relic dark matter with mass around a few hundred GeV, mainly through annihilation into the real and imaginary parts of $S$, while remaining consistent with direct-detection limits.
  • The electron electric dipole moment is generically below the current bound: the leading contribution appears at three loops, $d_e\sim 10^{-30}(\lambda_{SH}\lambda^2 g'^4 q^2)\sin(2\theta_\lambda)\,e\,{\rm cm}$, and if $S$ keeps a small VEV the prediction can come closer to the present limit while still passing it.
  • If the low-energy $U(1)_\ell$ current is not anomalous at the phase transition, the final asymmetry vanishes exactly (Appendix B), so the mechanism intrinsically requires the anomalons to be out of the plasma.
  • The same mechanism is presented for gauged $L_\mu+L_\tau$ and, in outline, for gauged baryon number $U(1)_B$, so the construction is not tied to the three-flavor lepton-number choice.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A consequence the paper leaves implicit is that the $Z'$ is not just a signal but the control knob, because the baryon yield scales roughly as $g'^2/M_{Z'}^2$; searches in the allowed window are therefore a direct quantitative test of the baryogenesis mechanism.
  • The finite-temperature anomaly treatment is the most vulnerable link: a full plasma calculation of the Wess-Zumino coefficient could shrink or shift the working region in Fig. 5 even if the zero-temperature logic is sound.
  • If the same trick works for gauged baryon number as the paper sketches, the idea may generalize to any spontaneously broken symmetry whose low-energy current becomes anomalous after heavy fermions decouple, broadening the model space for electroweak baryogenesis.
  • The mechanism also suggests that a transient CP-odd, CPT-odd vector background is sufficient for baryogenesis, which could motivate analogous constructions that avoid permanent Lorentz or CP violation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper proposes a new electroweak baryogenesis mechanism in an extension of the Standard Model where lepton number is promoted to a gauged U(1)_ℓ symmetry. The UV theory contains anomalons that cancel gauge anomalies, and below the lepton-number-breaking scale the effective theory contains the SM, a leptophilic Z′ boson, a dark fermion χ, and a complex scalar S. During a first-order electroweak phase transition, a space-dependent phase in the χ mass generates chiral asymmetries in χ; these asymmetries create a CP- and CPT-odd Z′_0 background, which acts as a chemical potential for SM leptons. Because the low-energy U(1)_ℓ current is assumed to be anomalous with respect to SU(2)_L (after the anomalons have decoupled), this chemical potential biases weak sphalerons and produces a net baryon asymmetry. The authors scan the parameter space (Eq. 3.27), find points reproducing η_B ≃ 0.9 × 10^{-10}, and then study the phenomenology of the Z′, the dark matter candidate χ, EDMs, and LHC signals, also discussing the cases L_μ + L_τ and gauged baryon number.

Significance. If the underlying assumptions hold, this is an original and potentially important mechanism: it provides a new way to communicate dark-sector CP violation to the visible sector through an anomalous vector current, while keeping electron EDM contributions suppressed to at least three loops (Eq. 4.19). The paper gives concrete, falsifiable predictions—a light leptophilic Z′ with 10 GeV ≲ M_Z′ ≲ O(TeV), a fermionic dark matter candidate near a few hundred GeV, and distinctive multi-lepton signals—and it combines existing Z′, dark matter, EDM, and collider constraints in a thoughtful way. The transport calculation from the CP-violating source S_CPV to η_B (Eqs. 3.11–3.25) is explicit and internally consistent, and Appendix B usefully proves that the final asymmetry vanishes if the low-energy U(1)_ℓ current is not anomalous. The main caveats are that the strong first-order phase transition is assumed rather than computed, and that the anomalon decoupling at the nucleation temperature is not quantified; both are load-bearing for the central claim.

major comments (2)
  1. [Sec. 3.1, Eq. (3.27)] The baryogenesis calculation is carried out in a prescribed bubble-wall background with v(T_n)/T_n ≳ 1, wall width L_w, velocity v_ω, and profile |S(z)| = s_0[1 + tanh(z/L_w)]/2 (Eqs. 3.8, 3.9), but the existence of such a strong first-order transition is assumed, not demonstrated. The paper states 'we will just assume hereafter that they are such that they provide a strong enough first order phase transition' and defers the detailed calculation to future work. Because the transport result Eq. (3.24) is an integral over this background, the central existence claim depends on this assumption. I ask that the paper either provide at least one explicit finite-temperature benchmark showing v(T_n)/T_n ≳ 1 with the stated profile, or state clearly that the result is conditional on the existence of such a transition. The sphaleron rate in Eq. (3.23) is likewise taken from the SM, with the caveat after Eq. (3.23) that it depends on the S–H potential parameters, and this dependence is not quantified.
  2. [Footnote 1, Sec. 4.1, App. B] The mechanism requires that at the nucleation temperature the anomalons are Boltzmann-depleted, so that the low-energy U(1)_ℓ current is anomalous with respect to SU(2)_L; Appendix B shows that if the current is not anomalous the final asymmetry vanishes exactly. The only support for the decoupling is footnote 1 and the qualitative statement that v_Φ is above a few times the electroweak scale, while the scan (3.27) allows T_n up to 500 GeV and does not impose m_a/T_n. For v_Φ ~ 1–4 TeV, the Boltzmann factor exp(-m_a/T_n) ranges from ~0.14 to ~3 × 10^{-4} at T_n = 500 GeV, so at the upper end of the scanned temperatures the decoupling is marginal. Moreover, the finite-temperature effective anomaly coefficient and the role of Wess-Zumino terms in the dense plasma are asserted rather than computed. Please quantify the decoupling condition, impose it in the scan, and discuss the finite-temperature treatment of the anomalous current.
minor comments (5)
  1. [Eq. (3.26) and Fig. 5] The scan imposes η_B = 0.9 × 10^{-10} as the selection criterion, so the result is an existence proof over parameter space rather than a prediction from measured inputs; the text should state this more explicitly in the abstract and conclusions.
  2. [Sec. 4.2, Eq. (4.6)] The ∆N_eff constraint v_Φ ≳ 10 TeV for M_Z′ ≫ T_QCD would remove part of the Fig. 5 blue region, and the paper notes this but does not show how many EWBG-favored points survive; a quantitative statement or a plot showing the surviving region would be helpful.
  3. [Appendix A] The solution of the rate equation leading to Eq. (3.24) is deferred to App. A, but in the manuscript as provided the appendix text is not included, so the derivation is not fully checkable; the published version should contain the claimed appendix.
  4. [Eq. (4.19)] The three-loop EDM estimate is a power-counting estimate with no explicit loop functions or logarithms; since this suppression is one of the paper's selling points, a slightly more explicit expression or a reference to a full loop calculation would strengthen the claim.
  5. [Eqs. (3.6) and (4.13)] The relation between the phase θ in the mass term (3.6) and the phase θ_λ used in the Yukawa interactions (4.13) is not repeated at the later point, which may confuse readers; a brief restatement of the phase conventions near Eq. (4.13) would improve clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the observed baryon asymmetry is used as a scan target, not as a derived prediction, and the core derivation is self-contained.

full rationale

The paper does not claim to predict the numerical value of eta_B from first principles; it computes the generated asymmetry from the diffusion and sphaleron equations and then uses the observed value as a selection criterion in the parameter scan. Specifically, Eq. (3.24) gives Delta n_LL from the Z' background and sphaleron rate, Eq. (3.25) defines eta_B, and Eq. (3.26) is then applied as the target condition in the scan range of Eq. (3.27). The text is explicit that the blue points in Fig. 5 'show the working parameter space where the observed baryon asymmetry ... can be generated.' This is standard EWBG bookkeeping: the target value selects viable parameters rather than serving as an input that is later renamed as a prediction. The load-bearing physics steps, namely the dark-sector CP-violating source S_CPV, the generation of a chiral asymmetry in chi, the Z' background chemical potential for SM leptons, and the anomalous lepton-number current that biases sphalerons, are derived from the model's Lagrangian and anomaly-structure assignments, not assumed equal to the final asymmetry. Appendix B proves that the asymmetry vanishes if the low-energy current is not anomalous, which strengthens rather than circularizes the argument. The self-citations to Ref. [1] are historical pointers to an earlier presentation; the present paper contains the derivation, including the diffusion Green's function and the Appendix B proof, so no load-bearing claim reduces to a self-citation. The Boltzmann decoupling of the anomalons is asserted in footnote 1 and Sec. 4.1 without quantitative control of m_a/T_n; that is a robustness or correctness caveat, but it is not a circular reduction of the derived asymmetry to its own inputs. No equation in the paper defines one target quantity in terms of itself, and no fitted parameter is renamed as a prediction. The independent phenomenological outputs, such as the predicted leptophilic Z' mass window, the dark matter mass range, and the suppressed electron EDM, are not used as inputs in the baryogenesis calculation, further supporting the conclusion that the derivation is self-contained.

Assumptions & free parameters 8 free parameters · 8 assumptions · 5 invented entities

The model adds a new gauge group U(1)_ℓ with a Z' boson, a dark fermion χ, a complex scalar S, a high-scale breaking scalar Φ, and a set of anomalon fermions. The baryogenesis claim rests on parameters that are scanned to match the observed asymmetry (g', M_Z', m_0, s_0, λ, θ, L_w, v_ω) and on the assumed scalar potential parameters behind the phase transition. The most important unproven premise is the Boltzmann decoupling of the anomalons, without which the asymmetry vanishes by the paper's own Appendix B. The Z' and χ carry independent falsifiable handles, while Φ and the anomalons do not.

free parameters (8)
  • g' (U(1)_ℓ gauge coupling) = about 1e-5 to 1e-2 (EWBG-favored, Fig. 5)
    Scanned over 1e-6 to 0.1; values are selected so the computed η_B matches the observed 0.9e-10. This is a free coupling of the new gauge group, not predicted from first principles.
  • M_Z' (Z' mass) = 10 GeV to O(TeV) (allowed window)
    Scanned from 1e-3 to 1e3 GeV; the baryogenesis requirement η_B ∝ g'^2/M_Z'^2 plus experimental limits select the window. It sets the range of the Z'_0 background in Eq. (3.19).
  • m_0 (zero-temperature χ mass) = favored m_0 > M_Z'/2
    Scanned from 1e-3 to 1e3 GeV. It must be nonzero for the phase of M_χ(z) to vary, i.e., for the CP source in Eq. (3.14); it also sets the dark matter mass today.
  • s_0 (S VEV scale in symmetric phase) = 100-500 GeV (shared with the T_n scan)
    Sets the change in |S(z)| across the wall and hence the gradient of arg M_χ, which is the CP source. Scanned, not derived.
  • λ = |λ_c| (dark Yukawa modulus) = 0.01-1; relic density window sqrt(m_0/1.4 TeV) < λ < sqrt(m_0/1.0 TeV)
    Controls Γ_m, the diffusion constant, and S_CPV. It is also selected to match the dark matter relic density through Eq. (4.15).
  • θ (phase of λ_c) = nonzero, e.g. π/3 in Fig. 4
    The CP source S_CPV is proportional to sin θ; scanned over (-π/2, π/2). It is chosen nonzero to generate the asymmetry.
  • L_w, v_ω (bubble wall width and velocity) = L_w in (1/T_n, 10/T_n), v_ω in (0.05, 0.5)
    Bubble wall parameters; η_B depends on them through the diffusion length and the source. They are scanned over generous ranges.
  • λ_SH, μ_S, λ_S, v_S (scalar potential parameters) = not scanned explicitly; chosen to make r, a non-degenerate and to enable a strong FOPT
    λ_SH is the Higgs portal; μ_S^2 breaks the r-a degeneracy, which is required for CP violation (Sec. 4.4). The first-order phase transition is assumed to hold for these values (Sec. 3.1).
assumptions (8)
  • domain assumption The anomalon content of Tab. 1 cancels the U(1)_ℓ-SM gauge anomalies in the UV.
    Standard model-building requirement for a gauged, otherwise anomalous symmetry; the paper takes this set as the minimal UV completion.
  • ad hoc to paper Heavy anomalons are Boltzmann-suppressed at the nucleation temperature T_n, leaving the low-energy U(1)_ℓ current anomalous with respect to SU(2)_L.
    Footnote 1 and Sec. 3.3. This is the premise that makes the mechanism work; Appendix B states the asymmetry vanishes if the current is not anomalous.
  • domain assumption Wess-Zumino terms restore SM gauge invariance after integrating out the anomalons, and do not affect the tree-level baryogenesis processes.
    Sec. 2. The paper argues loop-momentum conventions are irrelevant because all relevant processes are tree level.
  • ad hoc to paper The H-S scalar potential (3.1) admits a strong first-order phase transition with v(T_n)/T_n ≳ 1 for the chosen parameters.
    Sec. 3.1 and footnote 6. Assumed, with the detailed calculation explicitly left for a future publication; references [11,22] are cited for the mechanism.
  • standard math The semiclassical transport formalism of Refs. [4,6] (diffusion equation with source S_CPV) applies to the χ chiral asymmetry.
    Sec. 3.3, Eqs. (3.11)-(3.14). The CP-violating source is computed in this framework.
  • domain assumption The weak sphaleron rate is unsuppressed outside the bubble and exponentially suppressed inside, with Γ_0 ≃ 120 α_w^5 T_n and the SM value B ≃ 1.96 for M_sph.
    Eq. (3.23). The paper notes (citing [28]) that the singlet modifies the rate, but uses the SM form.
  • ad hoc to paper The S-field VEV profile across the wall is |S(z)| = s_0[1 + κ tanh(z/L_w)]/2 with κ = 1.
    Eq. (3.9). A modeling choice for the wall profile; the authors state qualitative results should hold for κ ≠ 1.
  • domain assumption χ is stable because of an exact Z_2 symmetry (χ → -χ) in the Lagrangian.
    Sec. 4.3. Required for χ to be the dark matter candidate.
invented entities (5)
  • Z' gauge boson (U(1)_ℓ) independent evidence
    purpose: Messenger that carries the dark chiral asymmetry to SM leptons via a time-like background; creates the lepton chemical potential that biases sphalerons.
    Predicts a leptophilic Z' in the 10 GeV to O(TeV) mass window with coupling about 1e-5 to 1e-2, testable in colliders, beam dumps, neutrino experiments and meson decays; the g'-M_Z' correlation in Fig. 5 is a falsifiable target.
  • Dark fermion χ (dark matter candidate) independent evidence
    purpose: Provides the CP-violating chiral asymmetry near the bubble wall and serves as the dark matter candidate.
    Predicts a dark matter mass near a few hundred GeV, annihilation through the dark scalars with λ in the window (4.15), and loop-suppressed direct detection; concrete targets for dark matter searches.
  • Complex scalar S (dark Higgs, mass eigenstates r and a) independent evidence
    purpose: Its VEV variation makes the χ mass phase vary (the CP source), and it assists the phase transition via the Higgs portal.
    Yields LHC signals gg to rr/aa with multi-lepton final states and CP-violating angular correlations (Sec. 4.5); masses set by Eq. (4.12).
  • Anomalons (ν_R, L'_L, e'_R, L''_R, e''_L)
    purpose: Cancel gauge anomalies in the UV; integrated out below v_Φ and Boltzmann-depleted at T_n.
    No specific searchable signature is given; their role is consistency, with masses around v_Φ at the TeV scale.
  • Scalar Φ
    purpose: Spontaneously breaks U(1)_ℓ at high scale, giving the Z' and anomalon masses and generating the CP-violating δV(S) terms.
    No direct falsifiable handle; constrained only indirectly through v_Φ and kinetic mixing (Eq. 4.4).

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Cite this review

Pith. "Pith review of Dark CP Violation and Gauged Lepton/Baryon Number for Electroweak Baryogenesis." pith.science (2026). https://pith.science/paper/L5WX32SV

@misc{pith2026190804818,
  author       = {Pith},
  title        = {Pith review of: Dark CP Violation and Gauged Lepton/Baryon Number for Electroweak Baryogenesis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L5WX32SV}},
  note         = {Machine review of arXiv:1908.04818}
}
abstract

We explore the generation of the baryon asymmetry in an extension of the Standard Model where the lepton number is promoted to a $U(1)_\ell$ gauge symmetry with an associated $Z^\prime$ gauge boson. This is based on a novel electroweak baryogenesis mechanism first proposed by us in Ref. \cite{Carena:2018cjh}. Extra fermionic degrees of freedom - including a fermionic dark matter $\chi$ - are introduced in the dark sector for anomaly cancellation. Lepton number is spontaneously broken at high scale and the effective theory, containing the Standard Model, the $Z^\prime$, the fermionic dark matter, and an additional complex scalar field $S$, violates CP in the dark sector. The complex scalar field couples to the Higgs portal and is essential in enabling a strong first order phase transition. Dark CP violation is diffused in front of the bubble walls and creates a chiral asymmetry for $\chi$, which in turn creates a chemical potential for the Standard Model leptons. Weak sphalerons are then in charge of transforming the net lepton charge asymmetry into net baryon number. We explore the model phenomenology related to the leptophilic $Z^\prime$, the dark matter candidate, the Higgs boson and the additional scalar, as well as implications for electric dipole moments. We also discuss the case when baryon number $U(1)_B$ is promoted to a gauge symmetry, and discuss electroweak baryogenesis and its corresponding phenomenology.

Figures

Figures reproduced from arXiv: 1908.04818 by the authors.

Figure 1
Figure 1. A schematic picture showing our model setup and the role played by each part in our proposed EWBG mechanism. In a recent short article [1], we presented the basic idea of a new EWBG mechanism in which the role of messenger of the CP asymmetry can be played by a Z 0 gauge boson that couples to both the SM and the dark sector. The low-energy effective theory is a dark sector model containing a Dirac fermion χ (charged… view at source ↗
Figure 2
Figure 2. Representative diagrams showing the loop generated electron EDM in two classes of models, where CP violation occurs through the interactions from electroweak charged particles (left panel) or SM gauge singlets that couple to the Z 0 (right panel). The gray blobs represent the loop generated hFµνF µν and hZ0 µνZ 0µν effective vertices in the two cases, respectively. In the former case, the contribution to EDMs can oc… view at source ↗
Figure 3
Figure 3. Schematic plot of the phase transitions. The left plot shows the change of S and H VEVs during the steps 3 and 4 discussed in the text. The right plot, shows their VEV profiles in front of and behind the expanding bubble wall (shadowed region) during the electroweak phase transition in step 4. The bubble interior is for z < 0. A schematic picture of the phase transitions in steps 3 and 4 is depicted in [PITH_FULL_I… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Left panel: Chiral charge asymmetry in χL (opposite for χR) particles around the bubble wall, with parameters m0 = s0 = Tn = 100 GeV, MZ0 = 1 GeV, λ = 0.3, θ = π/3, Lω = 5/Tn, vω = 0.1. Right panel: ∆n EQ LL (z)/g02T 3 n for the same values of the parameters. For this …
Figure 5
Figure 5. Figure 5: The parameter space of our model (assuming Ng = 3) that could generate the observed baryon asymmetry of the universe is covered by the blue points, in the g 0 versus MZ0 parameter space. The colorful shaded regions have been excluded by the existing constraints from LE…
Figure 6
Figure 6. Figure 6: Feynman diagrams for dark matter thermal freeze out (first row) and direct detection (second row) in the model we consider. Time flows from left to right. 20 [PITH_FULL_IMAGE:figures/full_fig_p021_6.png]
Figure 7
Figure 7. Figure 7: Confronting the electroweak baryogenesis favored parameter space (shown by the blue and magenta points) with dark matter observables, assuming the χ particle, which sources CP violation in baryogenesis, is also the dark matter candidate. All the blue and magenta points…
Figure 8
Figure 8. Figure 8: Two-loop generated hZ0 µνZ˜0µν vertex. It is worth noting that the non-degeneracy between r and a is the key for the coefficient of this operator to be nonzero, otherwise the coupling structure in (4.13) would lead to a complete cancellation between the two diagrams in…
Figure 9
Figure 9. Figure 9: Two-loop generated electron EDM, from the hZ0 µνZ˜0µν vertex (represented by the gray blob). In our model, the hZ0 µνZ˜0µν is generated at two loop level, see [PITH_FULL_IMAGE:figures/full_fig_p027_9.png]
Figure 10
Figure 10. Figure 10: Feynman diagrams for the loop induced decay of r, a into two Z 0 bosons (upper left) and the production process gg → rr (or aa) via an off-shell Higgs boson (upper right). The cross section for the latter at √ s = 13 TeV LHC is shown in the lower panel. each pair of t…
Figure 11
Figure 11. Figure 11: Scanned points (blue) in the g 0 – MZ0 plane, compatible with the observed baryon asymmetry of the universe assuming Ng = 2 . The colorful shaded regions have been excluded by the existing constraints from the CCFR, Borexino experiments, and the K → πνν¯ and B → Kµµ d…
Figure 12
Figure 12. Figure 12: The parameter space of the gauged U(1)B model that could generate the observed baryon asymmetry of the universe (blue points), in the g 0 – MZ0 plane. The colorful shaded regions have been excluded by the existing constraints from LHC dijet searches (red), hadronic wi…

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