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Electroweak Baryogenesis and New TeV Fermions

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Marcela Carena, Ariel Megevand, Mariano Quiros, Carlos E.M. Wagner

High Energy Physics - Phenomenology · Submitted 26 Oct 2004 · 62 references

Pith's verdict: The phase-transition strengthening is a real, checkable result; the baryogenesis half rests on a term three orders of magnitude below the leading source, and the abstract's Higgs-mass envelope is wider than the body supports.

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arXiv IDhep-ph/0410352 (version 2)
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CitationAriel Megevand, Carlos E.M. Wagner, Marcela Carena, Mariano Quiros. "Electroweak Baryogenesis and New TeV Fermions." arXiv:hep-ph/0410352 (2004). https://pith.science/paper/6FESZ4ND
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The paper

The paper claims

Fermions with order-one couplings to the Higgs can strengthen the electroweak phase transition, not just bosons, and a TeV Higgsino–Wino–Bino sector built on that idea could simultaneously supply the baryon asymmetry, a dark matter particle

The reading

The standard story of electroweak baryogenesis says that only new bosons can make the electroweak phase transition strongly first order: bosons generate a cubic term $-(hT/12π)(hφ)^3$ in the finite-temperature potential, while fermions were thought to contribute nothing of the kind. This paper argues that the claim holds only for weakly coupled fermions. Once the Yukawa coupling of a new fermion to the Higgs exceeds about 1, the fermion is relativistic in the symmetric phase and Boltzmann-suppressed in the broken phase, so the two phases have different numbers of light degrees of freedom; that mismatch lowers the critical temperature and pushes $φ_c/T_c$ up toward and past 1, which is the condition for sphalerons not to wash out a baryon asymmetry. The authors build a concrete model of TeV-scale Higgsinos, Winos and Binos with arbitrary Yukawa couplings, show the transition can be strong enough for Higgs masses up to a few hundred GeV, and then argue that the same charginos carry the CP-violating currents, that the lightest neutralino is a viable dark matter candidate, and that the whole thing survives electroweak precision data and can be probed by electron electric dipole moment experiments.

What carries the argument

The load-bearing mechanism is the change in the number of light degrees of freedom across the phase boundary, $Δg_* = g_*^{symmetric} - g_*^{broken}$, driven by fermions whose mass is dominated by $hφ$. It converts a species that decouples during the transition into a shift of the critical temperature and hence of $φ_c/T_c$, replacing the bosonic cubic term as the source of the barrier. On top of this sit three secondary pieces of machinery: the chargino mass matrix $(M_2, h_1φ; h_2φ, μ)$ and its neutralino analogue, which fix where the CP-violating source lives; the derivative-expansion diffusion formalism for CP-violating currents, which in the single-Higgs-doublet, $m_A → ∞$, $tan β ≃ 1$ limit leaves only the sub-leading source $H_1∂_μH_2 + H_2∂_μH_1 ∝ ∂_μ v^2$; and the statistical factors $k_i$ whose top-Yukawa radiative corrections give a non-zero coefficient $A ∼ 4 × 10^{-3}$ in $n_L = A n_H$, the suppression that sets how large the CP phase must be.

Extended reading notes

Core claim

The paper's central claim is that strongly coupled fermions, not only bosons, can induce a strongly first order electroweak phase transition. The argument is thermodynamic rather than diagrammatic: a species with mass $m^2(φ) = μ^2 + h^2φ^2$ and $h > 1$ is light relative to the temperature in the symmetric phase and heavy in the broken phase, so the effective number of relativistic degrees of freedom $g_*$ drops across the wall. Requiring degenerate minima of the free energy then gives $V_{SM}(φ_m,T_c) = -π^2 Δg_* T_c^4/90$, which moves the critical temperature down and the order parameter up, with the estimate $(φ_c/T_c)^3 Δ(φ_c/T_c) = 2π^2 Δg_*/(45λ)$. The authors realize this with Higgsinos and gauginos of a split-supersymmetry-like low-energy theory, with mass eigenvalues $λ_± = (M_+ ± √(M_-^2 + h^2φ^2))^2$ for the degenerate case $M_1 = M_2 = M$, $h_1 = h_2 = h$, $h' = 0$. For $h = 2$, $m_H = 120$ GeV and $μ = -M = 200$ GeV they find a first order transition with $φ_c/T_c ≃ 1.75$, and the $φ_c/T_c = 1$ contour reaches Higgs masses near 400 GeV for $h = 3$, or about 175 GeV for the $h ≲ 2$ allowed by their proposed ultraviolet completion. Because such large Yukawa couplings destabilize the zero-temperature Higgs potential at TeV scales, the low-energy theory is only defined together with heavier stabilizing fields, which the authors take to be bosons with comparable couplings and degrees of freedom.

Load-bearing premise

The baryon-asymmetry claim assumes that the sub-leading CP-violating source, suppressed to a coefficient of about $4 × 10^{-3}$ by top-Yukawa corrections to the statistical factors, is computed accurately enough by a diffusion formalism the authors themselves say is good only up to corrections of order one.

Editorial extensions

If this is right

  • The MSSM requirement of a light right-handed stop and a Higgs below about 120 GeV is a property of weakly coupled fermions, not of electroweak baryogenesis as such; strongly coupled TeV Higgsinos relax it to Higgs masses of a few hundred GeV.
  • With all squarks heavy, reproducing $η_{BBN} = (8.7 ± 0.3) × 10^{-11}$ requires CP-violating phases of order one; if a right-handed stop sits near 100 GeV the required phase drops to about $10^{-2}$, and at 500 GeV to about $0.1$.
  • The lightest neutralino is mostly Higgsino with mass near $|μ|$, and its Z-coupling is proportional to $(h_2^2 - h_1^2)/(h_1^2 + h_2^2)$, so a small but non-zero splitting $h_-$ is needed both for the relic density and to keep the $T$ parameter inside the precision-electroweak ellipse.
  • For $h_+ ≲ 2$ and order-one phases, the predicted electron electric dipole moment lies below the present $1.7 × 10^{-27}$ e cm bound but within reach of a bound near $10^{-29}$ e cm.
  • The construction can be embedded in a softly broken supersymmetric model with an extra asymptotically free $SU(2)$ gauge sector that becomes strong at the TeV scale, keeping the large Yukawa couplings perturbative up to high energies.

Reading between the lines

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

  • If the mechanism works as claimed, the same logic applies to any new fermion with a large Higgs Yukawa coupling, so vector-like quarks or mirror leptons with $h ≳ 1.5$ would be alternative phase-transition engines, and existing collider searches for such states acquire a cosmological motivation they are not usually given.
  • The two claims have very different robustness: the phase-transition result is a one-loop free-energy computation that lattice studies could check directly for $h ≃ 2$, whereas the baryon-asymmetry number passes through a sub-leading source three orders of magnitude below the leading one, so a future treatment that keeps the full $O(1)$ corrections could move $η$ substantially in either direction.
  • The dark matter and precision-electroweak requirements pull $|μ|$ toward the $Z$ resonance region and $h_-$ toward small values, which means the scenario is most naturally probed by a combination of a Higgs-mass measurement, a $T$-parameter extraction, and a direct-detection or invisible-width measurement rather than by any single observation.
  • Because the stabilizing sector is introduced by hand and only its gross features (degrees of freedom and coupling strength) enter, the phase-transition prediction is fairly insensitive to the ultraviolet completion, which makes it a more portable claim than the specific embedding into an extended gauge group.
Original abstract

New fermions, strongly coupled to the Standard Model Higgs boson provide a well motivated extension of the Standard Model (SM). In this work we show that, once new physics at heavier scales is added to stabilize the Higgs potential, such an extension of the SM can strengthen the first order electroweak phase transition and make the electroweak baryogenesis mechanism feasible. We propose a SM extension with TeV Higgsinos, Winos and Binos that satisfy the following properties: a) The electroweak phase transition is strong enough to avoid sphaleron erasure in the broken phase for values of the Higgs mass mH < 300 GeV; b) It provides large CP-violating currents that lead to the observed baryon asymmetry of the Universe for natural values of the CP-violating phase; c) It also provides a natural Dark Matter candidate that can reproduce the observed dark matter density; d) It is consistent with electroweak precision measurements; e) It may arise from a softly broken supersymmetric theory with an extra (asymptotically free) gauge sector; e) It may be tested by electron electric dipole moment experiments in the near future.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,223 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.40 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.92 · compares with prior results 0.09 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

New fermions, strongly coupled to the Standard Model Higgs boson provide a well motivated extension of the Standard Model (SM). In this work we show that, once new physics at heavier scales is added to stabilize the Higgs potential, such an extension of the SM can strengthen the first order electroweak phase transition and make the electroweak baryogenesis mechanism feasible. We propose a SM extension with TeV Higgsinos, Winos and Binos that satisfy the following properties: a) The electroweak phase transition is strong enough to avoid sphaleron erasure in the broken phase for values of the Higgs mass mH < 300 GeV; b) It provides large CP-violating currents that lead to the observed baryon asymmetry of the Universe for natural values of the CP-violating phase; c) It also provides a natural Dark Matter candidate that can reproduce the observed dark matter density; d) It is consistent with electroweak precision measurements; e) It may arise from a softly broken supersymmetric theory with an extra (asymptotically free) gauge sector; e) It may be tested by electron electric dipole moment experiments in the near future.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 New fermions, strongly coupled to the Standard Model Higgs boson provide a well motivated extension of the Standard Model (SM). background 1.00 0.05 0.04 asserted 0.99
s1 In this work we show that, once new physics at heavier scales is added to stabilize the Higgs potential, such an extension of the SM can strengthen the first order electroweak phase transition and make the electroweak baryogenesis mechanism feasible. contribution 0.53 0.89 0.77 asserted 0.92
s2 We propose a SM extension with TeV Higgsinos, Winos and Binos that satisfy the following properties: a) The electroweak phase transition is strong enough to avoid sphaleron erasure in the broken phase for values of the Higgs mass mH < 300 GeV; b) It provides large CP-violating currents that lead to the observed baryon asymmetry of the Universe for natural values of the CP-violating phase; c) It also provides a natural Dark Matter candidate that can reproduce the observed dark matter density; d) It is consistent with electroweak precision measurements; e) It may arise from a softly broken supersymmetric theory with an extra (asymptotically free) gauge sector; e) It may be tested by electron electric dipole moment experiments in the near future. contribution 0.95 0.74 0.42 asserted 0.64

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from argument 0.53.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Curves of constant φc/Tc = 1 and mH = 120 GeV, for a fermion with mass m2 = µ 2 + h 2φ 2 and g degrees of freedom. From top to bottom the curves correspond to h = 1.5, 2, 2.5, and 3. 3 Higgsinos and gauginos: the phase transition In this section we will consider the particular case of Higgsinos (H˜ 1,2), Winos and Binos (W˜ a , B˜) coupled to the SM Higgs doublet H with the Lagrangian L = H †  h2 σaW˜ a + h ′ 2 B˜  H˜ 2 + H T ǫ  −h1 σaW˜ a + h ′ 1 B˜  H˜ 1 + M2 2 W˜ aW˜ a + M1 2 B˜B˜ + µ H˜ T 2 ǫH˜ 1 + h.c. (3.1) where ǫ = iσ2 and the Yukawa coupling
Figure 2. The free energy at different temperatures for h = 2, mH = 120 GeV and µ = −M ≃ 200 GeV. phase, hence the VEV φc has a smaller value, which corresponds in the M → ∞ limit, to that of the electroweak phase transition in the Standard Model. 0 100 200 300 400 0 0.25 0.5 0.75 1 1.25 1.5 1.75 PSfrag replacements φc/Tc M [GeV]
Figure 3. φc/Tc for mH = 120 GeV and h = 2 as a function of M = −µ in GeV. In
Figure 4. Yukawa coupling h necessary to get φc/Tc = 1 for mH = 120 GeV as a function of M = −µ in GeV. the condition φc/Tc ∼ 1. Observe that the top-quark, with 12 degrees of freedom (similar to the chargino-neutralino system) and a Yukawa coupling ht ≃ 0.7 in our normalization, is not able to generate such a strong first-order phase transition in the SM. It is well known that the value of the Higgs mass plays a prominent role in the strength of the phase transition in the Standard Model and extensions thereof. Up to now we have fixed it to a “minimal” value, mH = 120 GeV. However our…
Figure 5. Contours of φc/Tc = 1 in the (M, mH )-plane for h = 1.6, 2, 2.5, 3 and M = −µ. The vertical line corresponds to the experimental lower bound, for a SM-like Higgs, of mH = 115 GeV. and Majorana masses Mi . We have concentrated on the case h ′ i = 0, in which the Bino state decouples from the other low energy states. Similar results for the phase transition would be obtained in any model in which the Bino would decouple from the low energy theory, for instance if h ′ i ≪ hi and M1 is much larger than the weak scale. Although the Bino is absent at low energies, there is still a state…
Figure 6. Values of φc/Tc as a function of δh, for a fixed value of the average value h+ = 2, mH = 120 GeV and M = −µ = 50 GeV. Up to this point we have discussed the electroweak phase transition in the absence of CP-violating phases. However for the baryogenesis mechanism to work we need a non￾vanishing CP-violating phase in the parameters of the theory that will trigger baryon number generation. As in the MSSM studies, we shall consider real Yukawa couplings (related to gauge couplings in the MSSM) and Majorana gaugino masses, and a complex mass parameter µ = |µ|e iϕ. To conclude this…
Figure 7. φc/Tc for h = 2 and |µ| = M = 50 GeV as a function of ϕ = arg(µ). GeV and Yukawa couplings h+ = 2, h− = 0. The plot at ϕ = π is consistent with the corresponding results that can be read off from
Figure 8. The ratio η/ηBBN as a function of the Yukawa coupling h for µ = −M2 exp(iϕ), M2 = 50 GeV, maximal CP-violating phase, sin ϕ = 1, and bubble parameters Lω = 10/Tc, vω = 0.1. Left-handed squarks and right-handed sbottoms are heavy (in the few TeV range). The lower (upper) solid line corresponds to heavy (light) right-handed stops, mT > ∼ 1 TeV (mT ≃ 100 GeV). Dashed line corresponds to right-handed stops with mT ≃ 500 GeV. The amount of generated baryon number density can be increased if some squark is light enough to be in equilibrium with the thermal bath during the phase…
Figure 9. Electric dipole moment of the electron as a function of |µ| for maximal CP￾violating phase, sin ϕ = 1, and h− = 0. The Higgs boson mass and Yukawa couplings are fixed to mH = 120 GeV, h+ = 1.5 (solid line); mH = 120 GeV, h+ = 2 (dashed line); and mH = 200 GeV, h+ = 2 (dot-dashed line). in addition, as shown in
Figure 10. Values of the µ parameter leading to a value of the neutralino relic density consistent with the central value of the WMAP observation, as a function of h−, for µ = −M2 exp(iϕ) and M2 = |µ|, assuming that the average value of the Yukawa couplings h+ is fixed to the value h+ = 2 (solid lines) and h+ = 1.5 (dashed lines). Lower and upper lines for each set of h+ values correspond to ϕ = 0 and ϕ = π/2, respectively. for each set of h+ values correspond to two different values of the CP-violating phase, ϕ = 0 and ϕ = π/2 respectively. Larger values of |h−| lead to larger values of |µ|.…
Figure 11. Chargino and neutralino contributions to the T-parameter as a function of h−, assuming that the average values of the Yukawa couplings has been fixed to h+ = 2 (solid line) and h+ = 1.5 (dashed line) and considering M = −µ determined as a function of h− from
Figure 12. 68 % (solid lines) and 95 % (dashed lines) C.L. allowed values of the S and T parameter based on the fit to the precision electroweak data in Ref. [60], for three different values of the Higgs mass: 115 GeV, 200 GeV and 300 GeV. from above from the requirement of a successful generation of the baryon asymmetry. For instance, for h+ = 2,

Figures reproduced from arXiv:hep-ph/0410352 by the authors.

References
How the literature uses it

45 arXiv papers cite this in 70 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 52 sentences without a confident label

Uses its method or tool 1 paper
  • The functions $P_a(ϕ^2)$ in [ref] depend on renormalization conditions, which are chosen to be [equation] which up to a field independent term set the functions $P_a(ϕ^2)$ to [ref] [equation] [equation]

    The minimal fermionic model of electroweak baryogenesis · Singlet-doublet model at finite temperatures · 0.87

Cites it as support 2 papers
  • However, models with fermions can give strong enough phase transitions, as shown in Ref. [ref] for the case of fermions with large Yukawa coupling $h$ and heavier stabilizing bosons.

    Velocity of electroweak bubble walls · Gravitational waves and baryogenesis · 0.98

  • Second it also would increase the strength of the phase transition, see [ref] .

    How much space is left for a new family? · Introduction · 0.98

Cites it as background 15 papers
  • Methods to strengthen the first-order phase transition beyond the SM and MSSM are now widely discussed [ref] .

    Four Generations, the Electroweak Phase Transition, and Supersymmetry · Introduction · 0.95

  • Some recent examples are [ref] .

    Beyond MSSM Baryogenesis · Introduction · 0.87

  • In the DTF, the SM is enlarged with two colorless fermions, a vectorlike $SU(2)_L$ doublet and a majorana $SU(2)_L$ triplet, both being odd an exact $Z_2$ symmetry[This symmetry can be recognized as remnant symmetry at the end of the symmetry breaking chain of the SO(10) group to the SM [ref] .] which is imposed in order to render stable the lightest $Z_2$-odd particle[This particle setup has been also considered in studies associated to strengthening the electroweak phase transition [ref] , presicion test in future colliders [ref] , electroweak precision tests [ref] , generation of neutrino masses [ref] , fake split-supersymmetry [ref] , and UV completion of doublet fermion DM [ref] .].

    Phenomenology of doublet-triplet fermionic dark matter in nonstandard cosmology and multicomponent dark sectors · Introduction · 0.80

Discussion

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