Electroweak Baryogenesis Mechanisms

• Electroweak baryogenesis is a theoretical framework where the universe's baryon asymmetry is produced in the electroweak epoch via CP-violating interactions and sphaleron transitions.
• A strongly first-order electroweak phase transition creates expanding bubbles, inducing CP-odd charge densities that sphalerons convert into net baryon number.
• Extended models, featuring additional scalar fields or fermions, are essential to enhance the phase transition and provide sufficient CP violation given Standard Model limitations.

Electroweak baryogenesis is the class of baryogenesis mechanisms in which the baryon asymmetry of the universe is generated during the electroweak epoch, around temperatures $T \sim 100$ GeV, through the interplay of electroweak sphalerons, CP-violating interactions, and out-of-equilibrium dynamics associated with electroweak symmetry breaking (Senaha, 2013, Huang et al., 2015). In the standard formulation, a strongly first-order electroweak phase transition produces expanding bubbles of broken phase, CP-violating interactions with the bubble walls generate chiral charge asymmetries, and sphaleron processes in the symmetric phase convert those asymmetries into baryon number that is subsequently preserved if sphalerons are sufficiently suppressed inside the bubbles (Senaha, 2013, Li et al., 2024). The observed asymmetry is conventionally quoted either as $\eta \equiv n_b/n_\gamma \simeq 6\times 10^{-10}$ or $Y_B \equiv n_B/s \simeq 8.7\times 10^{-11}$ (Senaha, 2013, Li et al., 2024). Because the Standard Model electroweak transition is a crossover for $m_h \simeq 125$ GeV and because CKM CP violation is too small, successful electroweak baryogenesis requires physics beyond the Standard Model (Senaha, 2013, Huang et al., 2015).

1. Foundational structure and Sakharov conditions

Electroweak baryogenesis realizes Sakharov’s three conditions at the electroweak scale: baryon number violation, C and CP violation, and departure from thermal equilibrium (Senaha, 2013, Huang et al., 2015). Baryon number violation is supplied by nonperturbative electroweak sphaleron processes, which violate $B+L$ through anomalous $SU(2)_L$ transitions while conserving $B-L$ (Senaha, 2013, Carena et al., 2018, Li et al., 2024). In the symmetric phase these transitions are unsuppressed, with rates written parametrically as $\Gamma_{\rm ws}\sim \alpha_w^5 T^4$ or $\Gamma_{\rm sph}\simeq 120\,\alpha_W^5 T$, depending on normalization conventions (Li et al., 2024, Cheung et al., 2013, Carena et al., 2018).

The out-of-equilibrium ingredient is usually a first-order electroweak phase transition. In that case, bubbles of broken phase nucleate and expand within the symmetric plasma, and their walls provide a spacetime-dependent background of scalar condensates $\varphi_k(x)$ (Senaha, 2013, Li et al., 2024). Particles and antiparticles interact differently with these walls if the relevant masses or mixing matrices carry spacetime-dependent complex phases, generating CP-odd charge densities in front of the wall (Senaha, 2013, Huang et al., 2015, Kobakhidze et al., 2015). Those charge densities, predominantly left-handed fermion number $\eta \equiv n_b/n_\gamma \simeq 6\times 10^{-10}$0, bias sphalerons in the symmetric phase and are converted into a net baryon density (Li et al., 2024).

A standard expression for the generated baryon density in transport treatments is

$\eta \equiv n_b/n_\gamma \simeq 6\times 10^{-10}$1

where $\eta \equiv n_b/n_\gamma \simeq 6\times 10^{-10}$2 is the wall velocity and the exponential encodes sphaleron washout in front of the wall (Li et al., 2024). In spontaneous-baryogenesis-type treatments, the wall-induced phase gradients are recast as effective chemical potentials that directly bias sphaleron transitions (Cheung et al., 2013).

The Standard Model contains the first two Sakharov ingredients only in a formal sense. For the observed Higgs mass, the electroweak transition is a crossover rather than first-order, and CKM CP violation is far too weak for realistic electroweak baryogenesis (Senaha, 2013, Huang et al., 2015). This motivates extended scalar sectors, new fermions, higher-dimensional operators, or more exotic cosmological settings.

2. Phase transition dynamics, sphalerons, and the washout criterion

The preservation of the generated baryon asymmetry requires sphaleron suppression in the broken phase. This is conventionally expressed by the criterion

$\eta \equiv n_b/n_\gamma \simeq 6\times 10^{-10}$3

or closely related forms such as $\eta \equiv n_b/n_\gamma \simeq 6\times 10^{-10}$4, depending on the treatment (Senaha, 2013, Huang et al., 2015, Cheung et al., 2013, Cohen et al., 2012). The underlying reason is that the broken-phase sphaleron rate behaves as

$\eta \equiv n_b/n_\gamma \simeq 6\times 10^{-10}$5

with

$\eta \equiv n_b/n_\gamma \simeq 6\times 10^{-10}$6

or parametrically $\eta \equiv n_b/n_\gamma \simeq 6\times 10^{-10}$7 (Senaha, 2013, Cheung et al., 2013). A sufficiently large $\eta \equiv n_b/n_\gamma \simeq 6\times 10^{-10}$8 therefore ensures exponential suppression of baryon-number-violating transitions inside the bubbles (Senaha, 2013, Li et al., 2024).

In the Standard Model, the one-loop high-temperature Higgs potential has the canonical form

$\eta \equiv n_b/n_\gamma \simeq 6\times 10^{-10}$9

with the bosonic thermal cubic term $Y_B \equiv n_B/s \simeq 8.7\times 10^{-11}$0 generating the barrier between the symmetric and broken phases (Senaha, 2013). However, for $Y_B \equiv n_B/s \simeq 8.7\times 10^{-11}$1 GeV the cubic term is too small, and nonperturbative lattice studies show that the transition is a crossover rather than first-order (Senaha, 2013, Huang et al., 2015). This exclusion of Standard Model electroweak baryogenesis is one of the most stable conclusions in the field (Senaha, 2013, Li et al., 2024).

Extended scalar sectors alter this conclusion in two distinct ways. One is the thermally driven mechanism, in which additional bosonic degrees of freedom enhance the effective cubic term in the finite-temperature potential (Senaha, 2013, Cohen et al., 2012). For an extra scalar with field-dependent mass

$Y_B \equiv n_B/s \simeq 8.7\times 10^{-11}$2

the nondecoupling regime $Y_B \equiv n_B/s \simeq 8.7\times 10^{-11}$3 yields thermal contributions that behave like $Y_B \equiv n_B/s \simeq 8.7\times 10^{-11}$4, thereby strengthening the first-order transition (Senaha, 2013). The other is the tree-level-barrier mechanism, in which additional singlet or exotic electroweak scalars create a barrier already at tree level, often through mixed quartics such as $Y_B \equiv n_B/s \simeq 8.7\times 10^{-11}$5 or through two-step symmetry-breaking patterns (Cheung et al., 2013, Huang et al., 2015, Cline, 2017, Blinov et al., 2015).

Two-step transitions are especially prominent in singlet and inert-doublet constructions. In these scenarios the universe can first enter a phase in which an exotic scalar has a nonzero expectation value and only later transition into the standard Higgs vacuum, with electroweak baryogenesis occurring during the first stage (Huang et al., 2015, Blinov et al., 2015). This structure allows the field that drives the strong first-order transition to be partly decoupled from the observed Higgs boson (Blinov et al., 2015).

3. CP-violating sources and transport formalisms

The CP-violating source in electroweak baryogenesis is typically generated by a spacetime-dependent complex mass matrix across the bubble wall. In singlet-assisted effective field theory, for example, the top mass can take the form

$Y_B \equiv n_B/s \simeq 8.7\times 10^{-11}$6

so that the wall induces a position-dependent phase $Y_B \equiv n_B/s \simeq 8.7\times 10^{-11}$7 (Huang et al., 2015). In non-linear Higgs EFT with anomalous Higgs couplings, the corresponding mass is

$Y_B \equiv n_B/s \simeq 8.7\times 10^{-11}$8

with $Y_B \equiv n_B/s \simeq 8.7\times 10^{-11}$9 determined by the wall profile of the Higgs field $m_h \simeq 125$0 (Kobakhidze et al., 2015). In composite Higgs models with a singlet PNGB, the top mass is

$m_h \simeq 125$1

and during the phase transition $m_h \simeq 125$2 varies across the wall because both $m_h \simeq 125$3 and $m_h \simeq 125$4 are spacetime dependent (Espinosa et al., 2011).

One formulation of these sources is the semiclassical or WKB force picture, in which the varying phase generates CP-odd force terms proportional to combinations such as $m_h \simeq 125$5 (Cline, 2017). Another is the spontaneous baryogenesis language, where field redefinitions convert spacetime-dependent phases into derivative couplings and effective chemical potentials. In electroweak cogenesis, for instance, one finds

$m_h \simeq 125$6

leading to

$m_h \simeq 125$7

which bias baryon-number-violating sphaleron transitions and dark-sector scatterings (Cheung et al., 2013).

The most important recent theoretical development concerns the transport formalism itself. The vev-resummation Kadanoff–Baym framework treats flavor oscillations, collisions, and CP-violating sources in a density-matrix language, yielding quantum Boltzmann equations of the form

$m_h \simeq 125$8

and the analogous equation for $m_h \simeq 125$9 (Li et al., 2024). In this approach the CP-violating sources appear at first order in gradients through the flavor-rotation term $B+L$0, whereas in semiclassical treatments they often enter only at second order (Li et al., 2024). The paper “Does the Electron EDM Preclude Electroweak Baryogenesis ?” argues that this enhancement of baryogenesis efficiency relaxes the apparent tension with electron EDM limits and that electroweak baryogenesis remains viable once transport is treated in this way (Li et al., 2024).

CP-conserving interactions also play a decisive role. In the vev-resummation analysis, strong collision terms can suppress the baryon asymmetry at large portal couplings, so the asymmetry need not grow monotonically with the size of the CP-violating coupling (Li et al., 2024). This modifies earlier intuition based on simpler diffusion or vev-insertion approximations.

4. Representative realizations

Several distinct ultraviolet or effective descriptions realize electroweak baryogenesis with different phase-transition and CP-violation structures.

Realization	Strong first-order transition	CP-violating source
Extended scalar sectors	Nondecoupling scalar loops or tree-level barriers	Complex Higgs-sector or portal couplings
EFT and anomalous Higgs frameworks	Light singlet or anomalous Higgs cubic coupling	Top-mass phase varying across the wall
Dark-sector and fermionic variants	Higgs portal, singlet/triplet, or fermion-induced radiative effects	Dark CP violation, singlet–doublet phase, or gauge background

The canonical extended-scalar realization is the two-Higgs-doublet model and related singlet extensions. In the 2HDM, extra scalar states $B+L$1, $B+L$2, and $B+L$3 can strengthen the electroweak transition through nondecoupling thermal effects, and the same nondecoupling parameters generate large one-loop corrections to the Higgs triple coupling (Senaha, 2013). In the SM-like limit $B+L$4, the one-loop triple Higgs coupling in the 2HDM is

$B+L$5

and viable electroweak baryogenesis scenarios typically predict $B+L$6 deviations in $B+L$7, with strongly nondecoupling cases reaching $B+L$8 (Senaha, 2013).

In electroweak cogenesis, baryogenesis is embedded in a concrete renormalizable model based on a CP-violating Type-II 2HDM plus two complex singlet scalars $B+L$9 charged under a global $SU(2)_L$0 (Cheung et al., 2013). The symmetry pattern is unusual: at high temperature electroweak symmetry is unbroken while $SU(2)_L$1 is spontaneously broken by $SU(2)_L$2; at low temperature electroweak symmetry breaks and the dark VEV disappears (Cheung et al., 2013). A strongly first-order transition is driven by the tree-level quartic $SU(2)_L$3, and the same wall phases that generate the baryon asymmetry simultaneously generate a dark-matter asymmetry, so the baryon and dark densities are produced in the same epoch (Cheung et al., 2013).

The effective field theory realization with one light real singlet scalar $SU(2)_L$4 and a dimension-5 top operator,

$SU(2)_L$5

implements a two-step transition

$SU(2)_L$6

with the second step arranged to be strongly first-order (Huang et al., 2015). The singlet mass is light, typically in the tens of GeV regime, and the observed baryon asymmetry can be achieved provided $SU(2)_L$7 for $SU(2)_L$8 and representative wall parameters (Huang et al., 2015).

The non-linear Higgs EFT with anomalous Higgs couplings takes a different route. There the Higgs is a singlet scalar $SU(2)_L$9 in a non-linear realization of electroweak symmetry, allowing a renormalizable cubic Higgs potential

$B-L$0

and a complex Higgs–top interaction

$B-L$1

(Kobakhidze et al., 2015). A distinguished feature of this framework is that the thermal Higgs vev is generally non-zero in both the “symmetric” and broken phases (Kobakhidze et al., 2015). The model identifies ranges of anomalous couplings where sphaleron rates remain sufficiently fast in the symmetric phase and sufficiently suppressed in the broken phase and where the observed baryon asymmetry can be generated (Kobakhidze et al., 2015).

The minimal fermionic model uses one electroweak singlet fermion and one vector-like pair of electroweak doublets with renormalizable Higgs couplings (Egana-Ugrinovic, 2017). The neutral mass matrix

$B-L$2

induces nontrivial $B-L$3-dependence in the fermion eigenvalues, so the same singlet–doublet fermions drive a strong first-order transition radiatively and produce the baryon asymmetry via asymmetric reflection from the bubble wall (Egana-Ugrinovic, 2017). The only physical CP-odd invariant is

$B-L$4

and the paper shows that the observed asymmetry can be generated for percent-level values of the associated phase $B-L$5 (Egana-Ugrinovic, 2017).

More exotic variants move the CP violation out of the visible sector. In “Electroweak Baryogenesis From Dark CP Violation,” CP violation resides entirely in a dark sector of SM singlets coupled to a leptophilic gauge boson $B-L$6 (Carena et al., 2018). A CP-odd, time-like background $B-L$7 acts as a chemical potential for SM doublets, and baryogenesis occurs if the $B-L$8 current coupled to $B-L$9 is anomalous with respect to $\Gamma_{\rm ws}\sim \alpha_w^5 T^4$0 (Carena et al., 2018). In “Electroweak baryogenesis via chiral gravitational waves,” helical magnetic fields during a first-order electroweak transition source chiral gravitational waves, producing a nonzero gravitational Pontryagin density $\Gamma_{\rm ws}\sim \alpha_w^5 T^4$1 that generates lepton number through the gravitational anomaly, which sphalerons partially convert to baryon number (Abedi et al., 2018). In “Efficient electroweak baryogenesis by black holes,” local electroweak domain walls form around primordial black holes because Hawking radiation restores the electroweak symmetry in a spherical region, and baryogenesis proceeds without a globally first-order electroweak transition (Aliferis et al., 2014).

5. Experimental signatures and constraints

Electroweak baryogenesis is constrained most sharply by electric dipole moments, Higgs-sector measurements, and direct searches for the additional states that strengthen the phase transition or furnish CP violation.

The electron EDM is especially important because the same CP phases that generate the baryon asymmetry also enter two-loop Barr–Zee diagrams in many scalar-mediated scenarios (Li et al., 2024). The recent bound quoted in the transport-theory analysis is

$\Gamma_{\rm ws}\sim \alpha_w^5 T^4$2

with the older ACME bound

$\Gamma_{\rm ws}\sim \alpha_w^5 T^4$3

used for comparison (Li et al., 2024). That work argues that once first-order-gradient CP sources and realistic collision terms are included, the baryon asymmetry is larger than in previous approximation schemes, so smaller CP phases are sufficient and the EDM tension is correspondingly reduced (Li et al., 2024). By contrast, older semiclassical-force analyses often suggested that viable electroweak baryogenesis would require phases now excluded by EDM data (Li et al., 2024).

Higgs measurements probe the sector responsible for the electroweak transition. In scalar-driven scenarios, nondecoupling loop effects that strengthen the phase transition also modify the Higgs triple coupling, often at the $\Gamma_{\rm ws}\sim \alpha_w^5 T^4$4 level in 2HDM examples that satisfy $\Gamma_{\rm ws}\sim \alpha_w^5 T^4$5 (Senaha, 2013). Colored-scalar portal models and the MSSM light-stop scenario also predict large deviations in loop-induced Higgs couplings to gluons and photons (Cohen et al., 2012). In the Higgs-portal colored-scalar setup, whenever the transition is strong enough for electroweak baryogenesis and $\Gamma_{\rm ws}\sim \alpha_w^5 T^4$6, the Higgs production rate via gluon fusion is enhanced by an amount observable at the LHC (Cohen et al., 2012). The same paper argues that a Higgs boson with Standard Model-like couplings to gluons and photons would rule out electroweak baryogenesis in the MSSM (Cohen et al., 2012).

Direct searches depend on the realization. The EFT singlet model predicts a light scalar with $\Gamma_{\rm ws}\sim \alpha_w^5 T^4$7 GeV once the Higgs invisible width bound

$\Gamma_{\rm ws}\sim \alpha_w^5 T^4$8

is imposed, yielding

$\Gamma_{\rm ws}\sim \alpha_w^5 T^4$9

for the Higgs portal and strong monojet plus missing-energy constraints on the cutoff,

$\Gamma_{\rm sph}\simeq 120\,\alpha_W^5 T$0

for $\Gamma_{\rm sph}\simeq 120\,\alpha_W^5 T$1 (Huang et al., 2015). In the minimal fermionic model, the required electroweak-scale singlet–doublet fermions give irreducible 13 TeV LHC signatures in multilepton plus missing-energy channels, with benchmark production cross sections such as $\Gamma_{\rm sph}\simeq 120\,\alpha_W^5 T$2 and $\Gamma_{\rm sph}\simeq 120\,\alpha_W^5 T$3 (Egana-Ugrinovic, 2017). The dark-CP scenario predicts leptophilic $\Gamma_{\rm sph}\simeq 120\,\alpha_W^5 T$4 signatures, heavy Majorana neutrinos, and Higgs-portal scalar signals in multi-lepton final states (Carena et al., 2018).

A recurring theme is that electroweak baryogenesis is tightly correlated with measurable electroweak-scale physics. Extended scalar sectors alter Higgs couplings, extra electroweak fermions imply direct production channels, and CP-violating phases feed into EDM observables (Senaha, 2013, Cohen et al., 2012, Egana-Ugrinovic, 2017, Li et al., 2024). This is one of the reasons the mechanism remains theoretically compelling and experimentally testable (Li et al., 2024).

6. Status, controversies, and outlook

A recurrent question in the literature is whether electroweak baryogenesis is still viable. Traditional realizations have been under pressure for some time. The MSSM light-stop scenario is described as under tension because the stop masses and Higgs properties required for a strong first-order transition are strongly constrained by LHC data and because more conservative source calculations reduce the predicted baryon asymmetry (Cohen et al., 2012, Cline, 2017). General 2HDM realizations can require large scalar self-couplings and may approach a Landau pole near $\Gamma_{\rm sph}\simeq 120\,\alpha_W^5 T$5 TeV in the viable region, although singlet-assisted tree-level-barrier scenarios improve the situation (Cline, 2017). This suggests that electroweak baryogenesis is challenged in its traditional settings but not excluded as a paradigm (Cline, 2017).

Recent work points toward a more nuanced conclusion. Scalar sectors with tree-level barriers, dark-sector CP violation, composite Higgs models with singlet PNGBs, non-linear Higgs EFTs, and fermion-induced mechanisms all furnish viable examples in which the baryon asymmetry can be generated at the electroweak scale without immediately conflicting with current data (Cline, 2017, Carena et al., 2018, Espinosa et al., 2011, Kobakhidze et al., 2015, Egana-Ugrinovic, 2017). The 2024 transport-theory analysis sharpens this point by arguing that the electron EDM does not preclude electroweak baryogenesis once CP-violating sources are treated consistently at first order in gradients and CP-conserving collisions are included realistically (Li et al., 2024).

Several open issues remain. One concerns the gauge dependence of perturbative finite-temperature effective potentials and of derived quantities such as $\Gamma_{\rm sph}\simeq 120\,\alpha_W^5 T$6 and $\Gamma_{\rm sph}\simeq 120\,\alpha_W^5 T$7 (Cheung et al., 2013, Senaha, 2013). Another concerns wall properties—thickness, velocity, and profile—which enter the baryon asymmetry calculation and are still difficult to determine reliably in many models (Huang et al., 2015, Kobakhidze et al., 2015, Li et al., 2024). A third concerns the interplay of electroweak baryogenesis with gravitational-wave signals from strongly first-order electroweak transitions; this is not developed in detail in all the cited works, but it is a standard implication of the same transition dynamics (Senaha, 2013, Li et al., 2024). A plausible implication is that progress on EWBG will increasingly depend on combining thermal field theory, transport theory, collider measurements, EDM searches, and gravitational-wave probes rather than relying on any one observable alone.

Electroweak baryogenesis therefore remains a broad research program rather than a single model. Its robust core is the conversion of CP-odd charge densities into baryon number by electroweak sphalerons during an out-of-equilibrium electroweak transition (Senaha, 2013, Li et al., 2024). Its diversity lies in how the transition is strengthened and where the CP violation is placed: in extended Higgs sectors, singlet portals, anomalous top couplings, dark sectors, fermionic singlet–doublet systems, composite dynamics, or more unconventional gravitational or primordial-black-hole settings (Cheung et al., 2013, Huang et al., 2015, Carena et al., 2018, Egana-Ugrinovic, 2017, Espinosa et al., 2011, Abedi et al., 2018, Aliferis et al., 2014). The continued coexistence of strong theoretical motivation and nontrivial experimental accessibility is what keeps electroweak baryogenesis central in discussions of the origin of the baryon asymmetry.