Asymmetric Leptogenesis: Key Concepts

• Asymmetric leptogenesis is a framework that produces a lepton–antilepton imbalance through CP- and lepton-number violating processes, later transformed into baryon asymmetry by electroweak sphalerons.
• It encompasses various mechanisms including decay-driven, oscillation-driven, and annihilation-driven processes, as seen in type-I seesaw and dark-matter related models.
• The framework relies on transport equations and flavor dynamics, linking high-scale models with dark-sector co-genesis to explain the observed matter–antimatter asymmetry.

Asymmetric leptogenesis denotes a class of early-universe mechanisms in which a lepton–antilepton asymmetry is generated dynamically through CP- and lepton-number-violating processes, so that $n_L \neq n_{\bar L}$, and is then partially converted into baryon number by electroweak sphalerons. In its canonical realization the asymmetry is produced by out-of-equilibrium decays of heavy sterile neutrinos in the type-I seesaw, but the term also covers oscillation-driven, annihilation-driven, scalar-decay, and background-driven variants, including constructions tied to dark matter, modular flavor, or Dirac neutrino sectors (0802.2962, Stengel, 2014, Hernández et al., 2015, Heeck, 2013).

1. Core conceptual structure

The quantitative target of leptogenesis is the observed baryon asymmetry, commonly written as

$$\eta \equiv \frac{n_B-n_{\bar B}}{n_\gamma}\Big|_0 \simeq 6.2\times 10^{-10}, \qquad Y_{\Delta B}\equiv \frac{n_B-n_{\bar B}}{s}\Big|_0 \simeq 8.8\times 10^{-11},$$

with $s$ the entropy density (0802.2962). Asymmetric leptogenesis satisfies the Sakharov conditions through lepton-number violation, CP violation, and a departure from equilibrium. In the broadest usage represented in the literature, the asymmetry may be generated in visible leptons, right-handed neutrinos, or sectors that later communicate with the visible plasma, provided that a nonzero $B-L$ survives until sphaleron freeze-out (Stengel, 2014).

In the Standard Model plasma, electroweak sphalerons violate $B+L$ but conserve $B-L$, with selection rule

$\Delta B=\Delta L=\pm 3.$

A convenient basis is

$$Y_{\Delta_\alpha}\equiv \frac{1}{3}Y_{\Delta B}-Y_{\Delta L_\alpha},$$

which is conserved by sphalerons flavor by flavor in the regime where the charged-lepton flavors are resolved (0802.2962). Above the electroweak phase transition, the Standard Model equilibrium relations give

$$Y_{\Delta B}^{\rm SM}=\frac{28}{79}\sum_\alpha Y_{\Delta_\alpha},$$

while below the transition one has

$$Y_{\Delta B}^{\rm SM}=\frac{12}{37}\sum_\alpha Y_{\Delta_\alpha}$$

(0802.2962).

This structure makes clear why asymmetric leptogenesis is more general than “a lepton asymmetry first, baryons later” in a purely one-field sense. What matters is the generation and survival of the conserved charges that sphalerons reprocess. This suggests a unifying viewpoint: seemingly disparate models differ primarily in the microscopic source term, the transport equations, and the washout network, rather than in the overall charge bookkeeping.

2. Canonical high-scale leptogenesis and the role of flavor

In the type-I seesaw, one adds SM-singlet Majorana fermions $$\eta \equiv \frac{n_B-n_{\bar B}}{n_\gamma}\Big|_0 \simeq 6.2\times 10^{-10}, \qquad Y_{\Delta B}\equiv \frac{n_B-n_{\bar B}}{s}\Big|_0 \simeq 8.8\times 10^{-11},$$0 with Yukawa couplings $$\eta \equiv \frac{n_B-n_{\bar B}}{n_\gamma}\Big|_0 \simeq 6.2\times 10^{-10}, \qquad Y_{\Delta B}\equiv \frac{n_B-n_{\bar B}}{s}\Big|_0 \simeq 8.8\times 10^{-11},$$1 and Majorana masses $$\eta \equiv \frac{n_B-n_{\bar B}}{n_\gamma}\Big|_0 \simeq 6.2\times 10^{-10}, \qquad Y_{\Delta B}\equiv \frac{n_B-n_{\bar B}}{s}\Big|_0 \simeq 8.8\times 10^{-11},$$2. In the charged-lepton and singlet-mass basis, the relevant Lagrangian is

$$\eta \equiv \frac{n_B-n_{\bar B}}{n_\gamma}\Big|_0 \simeq 6.2\times 10^{-10}, \qquad Y_{\Delta B}\equiv \frac{n_B-n_{\bar B}}{s}\Big|_0 \simeq 8.8\times 10^{-11},$$3

and integrating out the heavy singlets yields

$$\eta \equiv \frac{n_B-n_{\bar B}}{n_\gamma}\Big|_0 \simeq 6.2\times 10^{-10}, \qquad Y_{\Delta B}\equiv \frac{n_B-n_{\bar B}}{s}\Big|_0 \simeq 8.8\times 10^{-11},$$4

for the light Majorana neutrino mass matrix (0802.2962). The CP asymmetry arises from interference between tree-level and one-loop decay amplitudes, and in the hierarchical limit one obtains the Davidson–Ibarra bound

$$\eta \equiv \frac{n_B-n_{\bar B}}{n_\gamma}\Big|_0 \simeq 6.2\times 10^{-10}, \qquad Y_{\Delta B}\equiv \frac{n_B-n_{\bar B}}{s}\Big|_0 \simeq 8.8\times 10^{-11},$$5

for successful unflavored hierarchical leptogenesis (0802.2962).

The washout strength is parameterized by

$$\eta \equiv \frac{n_B-n_{\bar B}}{n_\gamma}\Big|_0 \simeq 6.2\times 10^{-10}, \qquad Y_{\Delta B}\equiv \frac{n_B-n_{\bar B}}{s}\Big|_0 \simeq 8.8\times 10^{-11},$$6

The regime $$\eta \equiv \frac{n_B-n_{\bar B}}{n_\gamma}\Big|_0 \simeq 6.2\times 10^{-10}, \qquad Y_{\Delta B}\equiv \frac{n_B-n_{\bar B}}{s}\Big|_0 \simeq 8.8\times 10^{-11},$$7 is strong washout; $$\eta \equiv \frac{n_B-n_{\bar B}}{n_\gamma}\Big|_0 \simeq 6.2\times 10^{-10}, \qquad Y_{\Delta B}\equiv \frac{n_B-n_{\bar B}}{s}\Big|_0 \simeq 8.8\times 10^{-11},$$8 is weak washout (0802.2962). In realistic calculations this is only the starting point. Finite-temperature effects modify decay kinematics and reaction densities, and spectator processes redistribute asymmetries among left-handed leptons, right-handed leptons, quarks, and Higgs fields. In the three-flavor regime these redistributions are encoded by matrices such as

$$\eta \equiv \frac{n_B-n_{\bar B}}{n_\gamma}\Big|_0 \simeq 6.2\times 10^{-10}, \qquad Y_{\Delta B}\equiv \frac{n_B-n_{\bar B}}{s}\Big|_0 \simeq 8.8\times 10^{-11},$$9

which enter the flavor-dependent washout terms (0802.2962).

Flavor is not merely a correction. In the $s$0 “asymmetric texture” model, unflavored leptogenesis vanishes because $s$1, whereas the fully flavored density-matrix treatment yields successful baryogenesis for right-handed neutrino masses of $s$2 GeV (Rahat, 2020). In that construction the sign of the baryon asymmetry also fixes the sign of the predicted Dirac phase, with $s$3, consistent with $s$4 (Rahat, 2020). This directly illustrates a recurring theme: the viability of asymmetric leptogenesis can depend decisively on flavor decoherence and flavor-specific washout.

3. Nonstandard microscopic realizations

The modern literature contains multiple source mechanisms beyond hierarchical heavy-neutrino decays. They differ in whether the asymmetry is seeded by decays, oscillations, annihilations, or a time-dependent background, and in which sector first stores the nonzero charge.

Realization	Source process	Characteristic feature
Thermal type-I leptogenesis (0802.2962)	$s$5	hierarchical case typically requires $s$6 GeV
GeV-scale seesaw leptogenesis (Hernández et al., 2015)	sterile-neutrino oscillations and thermal production	sizeable asymmetries with non-degenerate masses and measurable active–sterile mixings
“WIMPy leptogenesis” (Stengel, 2014)	dark matter annihilation $s$7 followed by $s$8	$s$9; leptonic branching fraction may be small
LNV Dirac leptogenesis (Heeck, 2013)	scalar decay $B-L$0	neutrinos remain Dirac; predicted $B-L$1
Oscillating-Higgs leptogenesis (Enomoto et al., 2020)	non-perturbative neutrino production in a coherent Higgs background	required Higgs-oscillation and lightest-RHN scales above $B-L$2 GeV

In GeV-scale seesaw models, the dominant mechanism is the Akhmedov–Rubakov–Smirnov regime: sterile neutrinos with $B-L$3 GeV are produced slowly, oscillate coherently in the plasma, and generate flavor asymmetries while at least one sterile state remains out of equilibrium (Hernández et al., 2015). The relevant dynamics are quantum-kinetic rather than purely Boltzmann, and the asymmetry is controlled by a small set of CP invariants, notably $B-L$4, $B-L$5, $B-L$6, and $B-L$7 (Hernández et al., 2015).

At the opposite extreme, leptogenesis due to an oscillating Higgs field integrates out heavy right-handed neutrinos and uses the effective time-dependent Majorana mass of light neutrinos in a coherent Higgs background. The required lepton asymmetry is

$B-L$8

and the numerical analysis finds that both the Higgs-background oscillation scale and the lightest right-handed-neutrino mass must exceed $B-L$9 GeV (Enomoto et al., 2020). This is non-thermal and background-driven rather than decay-driven.

A further generalization appears in decay-based weak-washout models with both thermalized and nonthermal decay products. There the final lepton asymmetry can become largely insensitive to the decaying-particle mass and to the “large” Yukawa couplings because the explicit source enhancement is canceled by the coupling- and mass-dependence of the departure from equilibrium of the decaying particle (Kanemura et al., 4 Sep 2025). The resulting “mass–coupling effect” is specific to weak washout and does not automatically extend to strong washout or resonant regimes (Kanemura et al., 4 Sep 2025).

4. Asymmetric leptogenesis and dark-sector co-genesis

A major branch of the subject links leptogenesis to dark matter. The simplest distinction is between asymmetric leptogenesis from dark matter and asymmetric dark matter itself. In “WIMPy leptogenesis,” a Majorana WIMP $B+L$0 annihilates through

$B+L$1

so that the lepton asymmetry comes from dark matter annihilation, yet the relic dark matter abundance remains the usual symmetric WIMP abundance rather than a particle–antiparticle asymmetry (Stengel, 2014). The CP asymmetry arises from interference between CP-even and CP-odd tree-level operators, with the absorptive phase supplied by the width of the unstable intermediate state $B+L$2. In the narrow-width regime,

$B+L$3

rather than the more familiar $B+L$4, allowing the CP-violating leptonic annihilation branch to be as small as $B+L$5–$B+L$6 while still reproducing the observed baryon asymmetry (Stengel, 2014).

Triplet-based models go further and unify visible and dark asymmetries. In a scalar-triplet extension with a vector-like inert fermion doublet $B+L$7, the same out-of-equilibrium triplet decays produce both a lepton asymmetry and a dark-sector asymmetry, while the triplet vev generates type-II seesaw neutrino masses and a Majorana splitting for the dark fermion (Sahu, 2012). The asymmetry relations are

$B+L$8

leading to

$B+L$9

(Sahu, 2012). In the related inert-doublet analysis, asymmetric scalar doublet dark matter requires $B-L$0 TeV because post-EWSB oscillations otherwise erase the asymmetry, whereas an asymmetric vector-like fermion doublet around $B-L$1 GeV is much more viable and can satisfy the combined leptogenesis and direct-detection constraints (Arina et al., 2011).

Other cogenesis constructions alter the mediator sector or the CP source. In a non-commutative $B-L$2 model based on $B-L$3, heavy-neutrino decays simultaneously produce visible and dark asymmetries, with automatic matter parity stabilizing W-odd dark matter; the resulting dark masses are $B-L$4 for singlet fermion or scalar candidates and $B-L$5 for a vector candidate $B-L$6 (Dong et al., 2018). In low-scale spontaneous leptogenesis, a dynamical majoron phase sources both the baryon asymmetry and the dark matter asymmetry, predicting

$B-L$7

when the dark asymmetry reaches equilibrium, and

$B-L$8

when it does not (Takahashi et al., 5 Jan 2026). In a modular $B-L$9 type-III seesaw, the same modulus $\Delta B=\Delta L=\pm 3.$0 fixes the neutrino texture, the resonant CP asymmetries, and the baryon–dark matter ratio, yielding

$\Delta B=\Delta L=\pm 3.$1

(Abhishek et al., 3 Feb 2026).

5. Transport equations, resonance, and parametric control

Across realizations, asymmetric leptogenesis is fundamentally a transport problem. In hierarchical thermal leptogenesis the simplest equations track the lightest singlet abundance $\Delta B=\Delta L=\pm 3.$2 and the conserved charges $\Delta B=\Delta L=\pm 3.$3, with source terms proportional to the CP asymmetries $\Delta B=\Delta L=\pm 3.$4 and washout terms controlled by inverse decays and $\Delta B=\Delta L=\pm 3.$5 scatterings (0802.2962). In annihilation-driven models the source instead scales with the departure of the dark matter number density from equilibrium. For WIMPy leptogenesis one may write schematically

$\Delta B=\Delta L=\pm 3.$6

which makes explicit the competition between source and washout (Stengel, 2014).

Resonant leptogenesis replaces hierarchical suppression with quasi-degeneracy. In the modular left-right asymmetric inverse-seesaw model, the six heavy Majorana states form three quasi-Dirac pairs satisfying

$\Delta B=\Delta L=\pm 3.$7

and the lightest pair $\Delta B=\Delta L=\pm 3.$8 dominates the asymmetry (Kumar et al., 30 Apr 2025). The CP asymmetry is

$\Delta B=\Delta L=\pm 3.$9

with a resonant denominator in $$Y_{\Delta_\alpha}\equiv \frac{1}{3}Y_{\Delta B}-Y_{\Delta L_\alpha},$$0, and the washout parameters lie in the strong-washout range

$$Y_{\Delta_\alpha}\equiv \frac{1}{3}Y_{\Delta B}-Y_{\Delta L_\alpha},$$1

(Kumar et al., 30 Apr 2025). Numerically, the model yields

$$Y_{\Delta_\alpha}\equiv \frac{1}{3}Y_{\Delta B}-Y_{\Delta L_\alpha},$$2

with successful baryogenesis for

$$Y_{\Delta_\alpha}\equiv \frac{1}{3}Y_{\Delta B}-Y_{\Delta L_\alpha},$$3

(Kumar et al., 30 Apr 2025).

By contrast, the mass–coupling effect in weak-washout decay-based leptogenesis shows that even large variations in mass and Yukawa magnitude need not change the final asymmetry appreciably. In that class of models,

$$Y_{\Delta_\alpha}\equiv \frac{1}{3}Y_{\Delta B}-Y_{\Delta L_\alpha},$$4

and the dimensionless CP source obeys $$Y_{\Delta_\alpha}\equiv \frac{1}{3}Y_{\Delta B}-Y_{\Delta L_\alpha},$$5, where $$Y_{\Delta_\alpha}\equiv \frac{1}{3}Y_{\Delta B}-Y_{\Delta L_\alpha},$$6 is the departure from equilibrium of the decaying particle (Kanemura et al., 4 Sep 2025). Numerical and analytic solutions give the late-time scaling

$$Y_{\Delta_\alpha}\equiv \frac{1}{3}Y_{\Delta B}-Y_{\Delta L_\alpha},$$7

for $$Y_{\Delta_\alpha}\equiv \frac{1}{3}Y_{\Delta B}-Y_{\Delta L_\alpha},$$8–few, which cancels the explicit $$Y_{\Delta_\alpha}\equiv \frac{1}{3}Y_{\Delta B}-Y_{\Delta L_\alpha},$$9 and $$Y_{\Delta B}^{\rm SM}=\frac{28}{79}\sum_\alpha Y_{\Delta_\alpha},$$0 dependence of the source term (Kanemura et al., 4 Sep 2025). This suggests that large sectors of the mass–coupling plane can reproduce essentially the same asymmetry once a benchmark point is viable, but also that simply increasing masses or Yukawas is not, by itself, a reliable route to enhancing leptogenesis.

6. Phenomenology, model discrimination, and open problems

The phenomenology of asymmetric leptogenesis is correspondingly diverse. In resonant modular left-right models, heavy-neutrino exchange can give

$$Y_{\Delta B}^{\rm SM}=\frac{28}{79}\sum_\alpha Y_{\Delta_\alpha},$$1

while the same parameter region predicts

$$Y_{\Delta B}^{\rm SM}=\frac{28}{79}\sum_\alpha Y_{\Delta_\alpha},$$2

all below current bounds (Kumar et al., 30 Apr 2025). In modular $$Y_{\Delta B}^{\rm SM}=\frac{28}{79}\sum_\alpha Y_{\Delta_\alpha},$$3 type-III seesaw, the low-energy predictions are especially sharp: $$Y_{\Delta B}^{\rm SM}=\frac{28}{79}\sum_\alpha Y_{\Delta_\alpha},$$4 with successful co-genesis at $$Y_{\Delta B}^{\rm SM}=\frac{28}{79}\sum_\alpha Y_{\Delta_\alpha},$$5 GeV (Abhishek et al., 3 Feb 2026).

Dirac implementations alter the expected experimental signatures more radically. In leptogenesis with lepton-number-violating Dirac neutrinos, the right-handed neutrino asymmetry is transferred to the visible sector by a neutrinophilic two-Higgs-doublet model, while standard neutrinoless double beta decay is absent because the neutrinos remain Dirac (Heeck, 2013). The same framework predicts an entropy-suppressed contribution of the right-handed neutrinos corresponding to

$$Y_{\Delta B}^{\rm SM}=\frac{28}{79}\sum_\alpha Y_{\Delta_\alpha},$$6

(Heeck, 2013). That combination—Dirac neutrinos, no standard $$Y_{\Delta B}^{\rm SM}=\frac{28}{79}\sum_\alpha Y_{\Delta_\alpha},$$7, and a mild excess in relativistic degrees of freedom—is qualitatively different from the signatures of type-I or type-II Majorana leptogenesis.

Dark-sector probes are equally model dependent. In the inert-doublet triplet scenario, a small Majorana splitting in the dark sector leads to inelastic scattering off nuclei. Updated Xenon100 limits strongly disfavor asymmetric scalar doublet dark matter of $$Y_{\Delta B}^{\rm SM}=\frac{28}{79}\sum_\alpha Y_{\Delta_\alpha},$$8 mass, whereas an asymmetric vector-like fermion doublet around $$Y_{\Delta B}^{\rm SM}=\frac{28}{79}\sum_\alpha Y_{\Delta_\alpha},$$9 GeV remains viable (Arina et al., 2011). In WIMPy leptogenesis, by contrast, the CP-violating annihilation channel into leptons can be only a tiny fraction of the total annihilation cross section, so direct or indirect leptonic signatures may be correspondingly suppressed even when baryogenesis is successful (Stengel, 2014).

Several conceptual issues remain unsettled. Precise predictions require consistent treatment of finite-temperature effects, spectator processes, flavor decoherence, and, in resonant settings, field-theoretic resummation and quantum kinetic equations (0802.2962). Some recent scaling results are explicitly limited to weak washout and can fail in strong washout, resonant, or flavor-sensitive regimes (Kanemura et al., 4 Sep 2025). A common misconception is that asymmetric leptogenesis is either synonymous with high-scale Majorana-decay leptogenesis or with asymmetric dark matter. The literature now includes oscillation-driven GeV-scale scenarios, annihilation-driven leptogenesis from dark matter, Dirac neutrino realizations with $$Y_{\Delta B}^{\rm SM}=\frac{12}{37}\sum_\alpha Y_{\Delta_\alpha}$$0, spontaneous leptogenesis sourced by a majoron background, and models in which dark matter remains a symmetric relic despite generating the lepton asymmetry (Hernández et al., 2015, Stengel, 2014, Heeck, 2013). Taken together, these developments indicate that “asymmetric leptogenesis” is best understood as a general framework for generating and transporting a nonzero lepton-sector charge asymmetry, rather than as a single model or scale.