Higgs Troika for Baryon Asymmetry

Hooman Davoudiasl; Ian M. Lewis; Matthew Sullivan

REVIEW 1 major objections 5 minor 37 references

Higgs Troika for Baryon Asymmetry

T0 review · 1 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper claims that adding two TeV-scale Higgs doublets and right-handed neutrinos can generate the observed baryon asymmetry through CP-violating decays, with new signals at colliders and in lepton-flavor experiments.

desk verdict A credible TeV-scale baryogenesis proof-of-concept built on an established scalar-decay mechanism, but the benchmark relies on an undefended initial condition: the modulus must produce H3 but not H2. read the letter →

arxiv 1909.02044 v2 pith:TVVC3VHY submitted 2019-09-04 hep-ph hep-ex

Hooman Davoudiasl , Ian M. Lewis , Matthew Sullivan This is my paper · ORCID

classification hep-phhep-ex

keywords baryonasymmetryHiggsTroikaleptogenesisCPviolationright-handedneutrinostwodoubletmodelelectroweaksphaleronsflavorphysics

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

The paper tries to account for the observed excess of matter over antimatter without invoking very heavy new particles. It extends the Standard Model with two additional Higgs doublets, with masses at or above the TeV scale, and right-handed neutrinos between roughly $0.1$ and $10$ TeV. The heaviest doublet $H_3$ decays out of equilibrium into lepton doublets and right-handed neutrinos, and complex Yukawa couplings, with $H_2$ running in the loop, make the decay of $H_3$ and its antiparticle differ in rate; the resulting $B-L$ asymmetry is processed by electroweak sphalerons into a baryon asymmetry. A benchmark with $m_3=1.5$ TeV, couplings near $1.4\times10^{-3}$, and 10 percent mass degeneracy between $H_2$ and $H_3$ gives $\epsilon\approx2\times10^{-7}$ and $n_B/s\approx9\times10^{-11}$, with testable consequences for the 125 GeV Higgs decay into muons and taus, the electron EDM, and $\mu\to e\gamma$.

What carries the argument

The central object is the 'Higgs Troika,' a set of three Higgs doublets: $H_1$ is the 125 GeV Standard-Model-like Higgs, and $H_2,H_3$ are new doublets with masses near the TeV scale and small vevs. The generator of the baryon asymmetry is the CP-violating partial-width asymmetry $\epsilon$, Eq. (13), which comes from the interference between the tree-level decay $H_3\to\bar L\nu_R$ and its one-loop bubble diagram mediated by $H_2$, enhanced when $m_2\simeq m_3$. Small vevs for $H_2,H_3$ are produced by a tadpole seesaw from soft breaking of a $Z_2$ symmetry, which keeps the new Yukawa couplings compatible with fermion masses and flavor constraints. The same Yukawa structure controls washout, low-energy flavor signals, and the expected collider signatures.

What would settle it

Concretely, compute the branching fractions of the modulus (the heavy scalar whose decay reheats the Universe) into $H_2H_2$ and $H_3H_3$ from the derivative coupling $(\Phi/\Lambda)D_\mu H_i^\dagger D^\mu H_i$; if the two rates are comparable for parameters matching the benchmark, the required $H_3$-only population fails and the $n_B/s\simeq9\times10^{-11}$ estimate no longer follows.

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Extended reading notes

Core claim

The central claim is that a 'Higgs Troika'—the observed 125 GeV Higgs plus two new doublets with small vacuum expectation values—can host baryogenesis near the TeV scale. In the decay asymmetry $\epsilon$ defined by Eq. (12), $H_3\to \bar L \nu_R$ interferes at one loop with the same final state through $H_2$; the resulting asymmetry is controlled by Eq. (13), which involves traces of products of Yukawa matrices and is enhanced when $m_2$ and $m_3$ are mildly degenerate because of the bubble-diagram contribution. For $m_2\simeq1.1 m_3$, $\lambda^\ell_3\simeq\lambda^\nu_3\simeq1.4\times10^{-3}$, and order-one phases, $\epsilon\simeq2\times10^{-7}$, which through Eq. (19) yields $n_B/s\simeq9\times10^{-11}$. The lepton number carried by doublets is reprocessed by sphalerons according to $\Delta B = (28/79)\Delta(B-L)$, while the right-handed neutrino remains a spectator. Washout is avoided by keeping the reheat temperature near $100$ GeV, so that the new doublets decay out of equilibrium and their couplings obey the no-washout bound $\lambda^\ell_a\lambda^\nu_a\lesssim10^{-6}$.

Load-bearing premise

The load-bearing premise is that the heavy scalar whose decay reheats the Universe produces the third Higgs doublet but essentially none of the second; if it produces both in comparable amounts, the second doublet's decays can wash out or cancel the lepton asymmetry, and the predicted baryon abundance no longer follows.

Editorial extensions

If this is right

If the mechanism is right, the baryon asymmetry is explained by TeV-scale particles, so no superheavy right-handed neutrinos or electroweak-scale phase transition is required.
The 125 GeV Higgs decay $h_1\to\mu^+\mu^-$ and $h_1\to\tau^+\tau^-$ should deviate from the Standard Model by up to about 20 percent, an amount the HL-LHC and HE-LHC can test.
The heavy doublets are pair-produced through gauge interactions; the LHC may see tens of events near $m_i\simeq1$ TeV, while a 27 TeV or 100 TeV collider would cover much of the favored mass range.
The flavor structure predicts electron EDM and $\mu\to e\gamma$ rates within about an order of magnitude of current bounds, so upcoming searches could observe them.
A light right-handed neutrino $\nu_{R3}$ at about 100 GeV would decay with a lifetime giving displaced vertices on the meter scale, a distinctive collider signature.

Reading between the lines

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

The success of the mechanism is tied to the near-degeneracy of $m_2$ and $m_3$; if that degeneracy is not coincidental, a UV symmetry enforcing it would sharpen the prediction for di-scalar production and flavor signals.
The required preferential production of $H_3$ over $H_2$ could be tested by computing the modulus decay branching ratio; a symmetry forbidding $\Phi H_2H_2$ would make the scenario more robust.
Because washout bounds tie $\lambda^\ell_a\lambda^\nu_a$ to the reheat temperature, independent cosmological determination of $T_{\rm rh}$ from primordial nucleosynthesis or the CMB would indirectly constrain the Yukawa couplings of the model.
A measurement of displaced $\nu_{R3}$ decays would connect the baryogenesis epoch to laboratory neutrino physics, potentially fixing the CP phase that sets $\epsilon$.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper is a serious proof-of-concept: two additional Higgs doublets plus TeV-scale right-handed neutrinos, with the third doublet (H3) decaying out of equilibrium to produce a lepton asymmetry that sphalerons convert to baryons. The construction is a new application of the neutrinogenesis mechanism of Refs [2,3], and the third doublet is motivated by a real problem — H1-mediated washout kills the two-doublet version. The flavor model with Z2 symmetry and small induced vevs is clean, and the benchmark point does satisfy the washout bound and gives ε ~2×10^-7 with 10% degeneracy, enough for the observed BAU. The authors are properly cautious about order-of-magnitude estimates, and they check annihilation versus decay rates for H3. They also ship the FeynRules model and plot data, which makes the collider numbers reproducible.

The phenomenological sections are the strongest part. The di-scalar production cross-sections depend only on gauge couplings, so they're robust; the expected h→μμ and h→ττ shifts of ~20% are concrete and testable at HL-LHC; the EDM and μ→eγ constraints are handled at the right level of precision for a proof-of-concept.

The soft spot is exactly where the stress-test note points. The baryogenesis calculation starts from the assumption that the modulus Φ produces H3 but not H2. The interaction in Eq. (6) is written for a generic doublet, and in the Z2 flavor model Φ2 and Φ3 have identical quantum numbers. No coupling matrix or symmetry explains preferential production. If Φ also produces H2, the ratio r in Eq. (17) is diluted and H2 decays contribute an uncorrelated (possibly cancelling) Δ(B-L). The paper acknowledges this with a one-sentence 'could be a result' and a citation to Ref [9], but it's a load-bearing premise, not a derived feature. This is not an internal contradiction — it's an incompleteness in the model specification.

There are smaller issues: the 10% mass degeneracy and O(1) phases are tuned; the washout bound in Eq. (5) is satisfied only marginally (|λ_l λ_ν| ≈ 2×10^-6 vs the bound ~2.1×10^-6); and the low-energy constraints saturate within factors of order one. These are acceptable for a benchmark study, but they mean the model is not predictive in a sharp sense.

If I were refereeing, I would recommend publication after the authors either supply a mechanism for preferential Φ→H3 decay or revise the text to state clearly that this is an external initial condition whose model realization is deferred. The paper is worth a serious referee and would be useful to anyone working on TeV-scale baryogenesis or multi-Higgs models.

Referee Report

1 major / 5 minor

Summary. The paper proposes an extension of the Standard Model by two additional Higgs doublets H2 and H3, together with three right-handed neutrinos, and aims to generate the baryon asymmetry of the Universe through CP-violating, out-of-equilibrium decays of H3 into lepton doublets and right-handed neutrinos, with H2 providing the loop. A modulus field Phi is invoked to produce the H3 population non-thermally and to set a low reheating temperature Trh ~ 100 GeV; the resulting B-L asymmetry is then processed by electroweak sphalerons. The central quantitative benchmark, with m3 = 1.5 TeV, a 10% mass degeneracy between H2 and H3, and Yukawa couplings lambda_l3 ~ lambda_nu3 ~ 1.4e-3, lambda_l2 ~ 1, lambda_nu2 ~ 2e-6, gives epsilon ~ 2e-7 and nB/s ~ 9e-11, while satisfying the stated washout bounds. The paper also discusses flavor observables (EDMs, mu -> e gamma, mu -> 3e, tau -> 3mu) and collider signatures of the heavy scalars.

Significance. If the mechanism works as claimed, it is a relatively economical and testable alternative to high-scale leptogenesis: the new states are at the TeV scale, with potential signals in h -> mu mu, h -> tau tau, charged-lepton flavor violation, and di-scalar production at current and future colliders. The paper is transparent about the order-of-magnitude nature of the estimates, provides explicit benchmark numbers, and uses FeynRules/MadGraph to estimate annihilation cross sections. The internal arithmetic of the benchmark is consistent, and the use of external results for the CP-asymmetry formula and the sphaleron conversion factor is standard. The main weakness is that a load-bearing cosmological initial condition is assumed rather than derived.

major comments (1)

[THE BARYOGENESIS MECHANISM] The central quantitative result in Eqs. (17)-(19) depends on the assumption that a population of (H3,H3*) is produced non-thermally with no significant population of (H2,H2*). The modulus interaction in Eq. (6) is written for a generic Higgs doublet, and no charge assignment, symmetry, or coupling matrix is given that makes Phi decay preferentially into H3. If Phi couples to H2 and H3 with comparable strength, then the effective r in Eq. (17) is reduced, and the H2 analogue of Eq. (21) generates an additional, generally subdominant, contribution to B-L of either sign. Unless the authors supply a concrete mechanism for preferential Phi -> H3 decays, the benchmark value nB/s ~ 9e-11 is not a consequence of the specified model but of an extra initial condition. I recommend either adding a symmetry/coupling construction that realizes the preferential decay, or recomputing nB/s with a comparable H2 population and showing that the mechanism still works.

minor comments (5)

[Eq. (29)] The (3,1) entry of the rotation matrix appears as mu_13^3/m_3^2; this should presumably be mu_13^2/m_3^2, consistent with the statement that the rotation is accurate to order mu^2/m_2,3^2.
[Fig. 2] In panel (a) the two labels 'hih±i' are identical; one of them should read 'aih±i', and the caption should distinguish ai h_i^± from h_i h_i^±.
[Eq. (25)] The notation Gamma(H3 -> SM) is misleading because the displayed expression includes only the charged-lepton channel (lambda_l3)^2, not the neutrino channel (lambda_nu3)^2. Since both channels contribute to the total width, the expression should be (|lambda_l3|^2 + |lambda_nu3|^2) m3/(16 pi gamma), which only strengthens the subsequent inequality.
[A BENCHMARK MODEL OF FLAVOR] The benchmark value lambda_nu2 ~ 2e-6 in Eq. (20) is the coupling to nu_R3, while the neutrino-mass discussion uses y_nu2 ~ 1e-3 for couplings to nu_R1,2. The notation should be made explicit (e.g., lambda^{nu_R3}_2 versus lambda^{nu_R1,2}_2) so that the two parts of the parameter space are not confused.
[THE BARYOGENESIS MECHANISM] The washout bound in Eq. (3) is presented as a general constraint before the right-handed neutrino mass hierarchy is introduced; the later discussion correctly explains that the bound is evaded for m_R1,2 >> Trh by Boltzmann suppression, but the earlier statement should be qualified to avoid the apparent contradiction with lambda_nu1 ~ 1e-5 needed for neutrino masses.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the baryogenesis estimate is an explicitly chosen benchmark using external formulas, not a prediction forced by an input.

full rationale

The paper's derivation chain is self-contained against external results and contains no step that reduces by construction to its own inputs. The asymmetry parameter epsilon in Eq. (13) is taken from the independent neutrinogenesis literature (Refs. [2,3]); the sphaleron conversion factor in Eq. (16) is taken from Harvey-Turner (Ref. [13]); and the observed BAU in Eq. (2) is used only as a target for a proof-of-concept benchmark (Eq. (20)), not fitted into the formula for epsilon or n_B/s. The benchmark values are chosen, not extracted from the output, and the final estimates in Eqs. (18)-(19) follow from standard decay and entropy relations. The assumption that a modulus produces H3 but not H2 is an unproved initial condition, but it is explicitly identified as an assumption ('We will assume...') and is not defined in terms of, or equivalent to, the BAU result; if it fails, the benchmark would not apply, which is a model-construction limitation rather than circularity. The self-citations (Refs. [4,9]) are contextual or illustrative (related ideas and an example of preferential decay) and are not the load-bearing derivation of the central claim. Therefore no circular step can be exhibited.

Assumptions & free parameters 9 free parameters · 8 assumptions · 3 invented entities

The model's viability rests on a large set of chosen parameters: the heavy scalar masses and their near-degeneracy, the benchmark Yukawa couplings, the right-handed neutrino spectrum, the modulus parameters, the CP phases, and the energy fraction r. None of these are predicted by an underlying symmetry; they are selected to satisfy washout bounds, flavor constraints, and the observed BAU simultaneously. The most fragile invented element is the modulus Phi, which must populate H3 but not H2.

free parameters (9)

m3 = 1.5 TeV
Chosen heavy Higgs mass; sets the decay boost E3 approximately 50 TeV and satisfies Trh much less than m3; also enters the washout bound of Eq (5).
m2/m3 = ~1.1 (10% degeneracy)
Enhances epsilon in Eq (21) to about 2e-7; the asymmetry is too small unless the masses are within about 10%, and this tuning is not derived from a symmetry.
lambda_l2, lambda_nu2, lambda_l3, lambda_nu3 = 1, 2e-6, 1.4e-3, 1.4e-3
Benchmark Yukawas in Eq (20) set to satisfy the washout bound Eq (5) and to maximize epsilon; lambda_l3 and lambda_nu3 are chosen equal and maximal at about 1.4e-3.
mR1, mR2, mR3 = 10 TeV, 10 TeV, 100 GeV
mR1 and mR2 are heavy to suppress production at Trh around 100 GeV and to generate two about 0.1 eV neutrino masses; mR3 is light enough to appear as a final state in H3 decays.
v2/vEW = ~0.01 (v2 ~ 2.5 GeV)
Needed for an O(1) tau Yukawa to Phi2 and for lambda_nu1 around 1e-5 from y_nu2 around 1e-3; the small vev emerges from a tadpole seesaw, but its magnitude is chosen.
mPhi, Lambda = 100 TeV, 3e13 GeV
Chosen to give Trh around 100 GeV via Eq (7); the energy scale E3 is set by mPhi/2.
r = less than or about 1; benchmark assumes order one
n(B-L)/s is proportional to r in Eq (18), so a value close to 1 is needed for the benchmark epsilon around 2e-7.
CP phases phi and omega = O(1) for phi; sin omega ~ 0.1
The phase phi maximizes epsilon in Eq (21); the smaller phase omega is chosen to satisfy electron EDM and mu to e gamma constraints.
quartic scalar couplings of H3 = ~0.1
Used in the annihilation cross-section estimate of Eq (23); the values are assumed but not derived from the scalar potential.

assumptions (8)

standard math Standard sphaleron conversion Delta B = (28/79) Delta(B-L) applies during the unbroken phase at T > 100 GeV.
Used in Eq (16), taken from Ref [13].
domain assumption The CP asymmetry from heavy scalar decays is given by the interference formula Eq (13), with the bubble diagram dominating over the triangle diagram when m2 and m3 are mildly degenerate.
Equation (13) is from the neutrinogenesis literature [2,3]; the triangle suppression is assumed valid for the 10% degeneracy benchmark.
domain assumption A modulus Phi with derivative coupling to Higgs doublets dominates the early universe and reheats to Trh around 100 GeV.
Equations (6)-(7); standard non-thermal modulus cosmology, but no specific UV origin is given.
ad hoc to paper Phi decays preferentially into H3 with negligible H2 production.
Needed so that only H3 decays generate the asymmetry; no mechanism is given, and Ref [9] is cited only as a possibility.
domain assumption Washout 2 to 2 processes are Boltzmann suppressed and obey the parametric bounds of Eq (3) and Eq (5).
Needed to protect the generated asymmetry; these are order-of-magnitude estimates.
domain assumption The light neutrino sector contains only two massive states near 0.1 eV, with the third effectively massless.
Resolves the mR less than 10 MeV conflict; allowed by neutrino data but not derived.
ad hoc to paper The charged-lepton Yukawa flavor structure follows the modified ansatz lambda_ij ~ min(mi,mj)/m_tau.
Used to satisfy LFV and EDM constraints; modified from Ref [21] with no dynamical origin.
domain assumption New quartic scalar couplings make only non-leading contributions to the mechanism.
Footnote 2 states this was checked, but the check is not shown in the paper.

invented entities (3)

Two additional Higgs doublets Phi2 and Phi3, with mass eigenstates H2 and H3, forming the 'Higgs Troika'. independent evidence
purpose: Provide CP-violating out-of-equilibrium decays into lepton doublets and right-handed neutrinos, generating the B-L asymmetry.
Predicts di-scalar production at colliders, shifts in h1 to mu mu and tau tau branching ratios, plus LFV and EDM signals.
Three right-handed Majorana neutrinos nuR1, nuR2, and nuR3. independent evidence
purpose: Generate two light neutrino masses via a seesaw and provide the nuR3 final state in H3 decays that carries asymmetry outside sphaleron processes.
nuR3 decays can give displaced vertices, and neutrino masses are indirect evidence; the 0.1 to 10 TeV mass range is testable in principle.
Modulus Phi with derivative coupling (Phi/Lambda) D_mu H_i^† D^µ H_i.
purpose: Create a matter-dominated epoch, reheat to 100 GeV, and produce the H3 population non-thermally.
No signatures are predicted for Phi; it is a device to set the initial condition and reheat temperature, and it is the least constrained element of the model.

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Cite this review

Pith. "Pith review of Higgs Troika for Baryon Asymmetry." pith.science (2026). https://pith.science/paper/TVVC3VHY

@misc{pith2026190902044,
  author       = {Pith},
  title        = {Pith review of: Higgs Troika for Baryon Asymmetry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TVVC3VHY}},
  note         = {Machine review of arXiv:1909.02044}
}

abstract

To explain the baryon asymmetry of the Universe, we extend the Standard Model (SM) with two additional Higgs doublets with small vacuum expectation values. The additional Higgs fields interact with SM fermions through complex Yukawa couplings, leading to new sources of CP violation. We propose a simple flavor model with $\mathcal{O}(1)$ or less Yukawa couplings for quarks and charged leptons, consistent with current flavor constraints. To generate neutrino masses and the baryon asymmetry, right-handed neutrinos in the $\sim 0.1-10$ TeV range couple to the "Higgs Troika." The new Higgs doublet masses could be near the TeV scale, allowing for asymmetric decays into Standard Model lepton doublets and right-handed neutrinos. The asymmetry in lepton doublets is then processed into a baryon asymmetry, similar to leptogenesis. Since the masses of the new fields are near the TeV scale, there is potentially a rich high energy collider phenomenology, including observable deviations in the 125 GeV Higgs decay into muons and taus, as well as detectable low energy signals such as the electron EDM or $\mu\rightarrow e\gamma$. Hence, this is in principle a testable model for generation of baryon asymmetry, similar in that respect to "electroweak baryogenesis."

Figures

Figures reproduced from arXiv: 1909.02044 by the authors.

**Figure 2.** FIG. 2: Production cross sections for heavy scalars (a) [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

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The washout bound then implies ε≪ 4× 10−10, which suggests that baryogenesis is not feasible

First consider λν 2λf 2≪ (λf ′ 2 )2. The washout bound then implies ε≪ 4× 10−10, which suggests that baryogenesis is not feasible

work page
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The washout bound to- gether with ε & 10−9 then implies that λν 2 & 2.8λf

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(4) This bound is inconsistent with our starting as- sumption implying that a baryon asymmetry can- not be generated with this hierarchy of couplings. The results are similar for λf 2≪λν 2∼λf ′ 2

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triangle

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work page
[5]

The couplings ofH2 are not so tightly constrained and can be generically larger than those of H3

Together with the washout condition this cre- ates the boundλ𝓁,ν 3 ≲ 1.4×10−3. The couplings ofH2 are not so tightly constrained and can be generically larger than those of H3. Hence, the above model could easily lend itself to collider searches. In particular, if the cou- plings to quarks are not too small, one of the heavy Higgs states could be produced...

work page
[6]

The Yukawa interactions are then yu 1 ˜Φ∗ 1 ¯Qu +yd 1Φ∗ 1 ¯Qd + ∑ b=2,3 yν b ˜Φ∗ b ¯LνR +y𝓁 bΦ∗ b ¯L𝓁

The Higgs doublets Φ 2,3 and lepton dou- blets L are odd under a Z2 symmetry while all other ﬁelds are even. The Yukawa interactions are then yu 1 ˜Φ∗ 1 ¯Qu +yd 1Φ∗ 1 ¯Qd + ∑ b=2,3 yν b ˜Φ∗ b ¯LνR +y𝓁 bΦ∗ b ¯L𝓁. (26) The organizing principle for the charged fermion ﬂavor is that the largest Yukawa coupling for quarks and charged leptons should be order on...

work page
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strong CP problem

The Higgs potential is then −µ2H† 1H1 +m2 2H† 2H2 +m2 3H† 3H3 +λ(H† 1H1)2 +···(30) That is, H2,3 are the doublet mass eigenstates appearing in Eqs. (11-13), as we desired. The Yukawas in Eq. (11) are related to those in Eq. (26) via λu,d 1 ≈yu,d 1 , λ u,d 2,3≈yu,d 1 v2,3/vEW, λ𝓁 1≈y𝓁 2v2/vEW, λ 𝓁 2,3≈y𝓁 2,3, λν 1≈ (yν 2v2 +yν 3v3)/vEW, λν 2,3≈yν 2,3, (31)...

work page 2000

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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The washout bound then implies ε≪ 4× 10−10, which suggests that baryogenesis is not feasible

First consider λν 2λf 2≪ (λf ′ 2 )2. The washout bound then implies ε≪ 4× 10−10, which suggests that baryogenesis is not feasible

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The washout bound to- gether with ε & 10−9 then implies that λν 2 & 2.8λf

Next, λν 2 ≪ λf 2 ∼ λf ′ 2 . The washout bound to- gether with ε & 10−9 then implies that λν 2 & 2.8λf

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[4] [3]

The results are similar for λf 2≪λν 2∼λf ′ 2

(4) This bound is inconsistent with our starting as- sumption implying that a baryon asymmetry can- not be generated with this hierarchy of couplings. The results are similar for λf 2≪λν 2∼λf ′ 2

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triangle

Finally, assume all couplings are similar λf 2∼λν 2∼ λf ′ 2 . The washout bound implies thatε ≲ 4×10−10. That is, baryogenesis is still not feasible. This conclusion leads us to require a third Higgs doublet ﬁeld H3, to avoid reliance on a light H1, whose interac- tions are constrained 1. Successful baryogenesis requires that the reheat tem- perature Trh,...

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[6] [5]

The couplings ofH2 are not so tightly constrained and can be generically larger than those of H3

Together with the washout condition this cre- ates the boundλ𝓁,ν 3 ≲ 1.4×10−3. The couplings ofH2 are not so tightly constrained and can be generically larger than those of H3. Hence, the above model could easily lend itself to collider searches. In particular, if the cou- plings to quarks are not too small, one of the heavy Higgs states could be produced...

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[7] [6]

The Yukawa interactions are then yu 1 ˜Φ∗ 1 ¯Qu +yd 1Φ∗ 1 ¯Qd + ∑ b=2,3 yν b ˜Φ∗ b ¯LνR +y𝓁 bΦ∗ b ¯L𝓁

The Higgs doublets Φ 2,3 and lepton dou- blets L are odd under a Z2 symmetry while all other ﬁelds are even. The Yukawa interactions are then yu 1 ˜Φ∗ 1 ¯Qu +yd 1Φ∗ 1 ¯Qd + ∑ b=2,3 yν b ˜Φ∗ b ¯LνR +y𝓁 bΦ∗ b ¯L𝓁. (26) The organizing principle for the charged fermion ﬂavor is that the largest Yukawa coupling for quarks and charged leptons should be order on...

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strong CP problem

The Higgs potential is then −µ2H† 1H1 +m2 2H† 2H2 +m2 3H† 3H3 +λ(H† 1H1)2 +···(30) That is, H2,3 are the doublet mass eigenstates appearing in Eqs. (11-13), as we desired. The Yukawas in Eq. (11) are related to those in Eq. (26) via λu,d 1 ≈yu,d 1 , λ u,d 2,3≈yu,d 1 v2,3/vEW, λ𝓁 1≈y𝓁 2v2/vEW, λ 𝓁 2,3≈y𝓁 2,3, λν 1≈ (yν 2v2 +yν 3v3)/vEW, λν 2,3≈yν 2,3, (31)...

work page 2000