Electromagnetic Leptogenesis

• Electromagnetic leptogenesis is a theoretical framework that employs CP- and lepton-number violating electromagnetic interactions to generate the Universe's matter–antimatter asymmetry.
• Mechanisms involve effective dipole operators, hypermagnetic helicity, and portal sectors, often requiring resonant enhancement in quasi-degenerate heavy neutrino systems.
• Key implications include testable signatures in collider experiments, astrophysical observations, and cosmological measurements, linking baryogenesis with dark matter and dark energy.

Electromagnetic leptogenesis is a theoretical framework in which the observed matter–antimatter asymmetry of the Universe is generated through mechanisms involving electromagnetic processes, either via electromagnetic dipole operators, hypermagnetic fields, or the interplay of new scalar, fermion, and gauge sectors with electromagnetic interactions. The term encompasses a variety of models, ranging from those positing effective dipole moments connecting sterile and active neutrinos, to scenarios where primordial (hyper)magnetic helicity, anomalies, and out-of-equilibrium decay processes convert lepton number asymmetry into baryon asymmetry at sub-GUT scales.

1. Fundamental Principles and Theoretical Frameworks

Electromagnetic leptogenesis leverages CP-violating, lepton-number violating processes that are enabled, mediated, or significantly affected by electromagnetic or related gauge interactions. The mechanisms are typically embedded in extensions of the Standard Model (SM), including:

• Dipole Operator Scenarios: Effective interactions of the form

$$\mathcal{L}_{\rm dipole} = \frac{\lambda_{ij}}{\Lambda} \overline{N_i^c} \sigma_{\mu\nu} \nu_j B^{\mu\nu}$$

where $N_i$ are heavy right-handed neutrinos, $\nu_j$ are sterile or active neutrinos, $B^{\mu\nu}$ is the hypercharge field strength, and $\Lambda$ is the cutoff scale. Here, lepton asymmetry is generated via two-body decays $N_i \to \nu_j + \gamma$ or $N_i \to \nu_j + Z$ (Choudhury et al., 2011, Borah et al., 22 Jan 2025, Takada, 9 Sep 2025).

• Hypermagnetic Field/Helicity Mechanisms: The Abelian (triangle) anomaly links (hyper)magnetic fields (pre-EWSB) or magnetic helicity to the time evolution of fermionic charge densities, so that the evolution and decay of helical hypermagnetic fields produce or track lepton (and baryon) number (Dvornikov et al., 2011, Long et al., 2013, Semikoz et al., 2016, Fukuda et al., 7 Oct 2024).
• Portal and Messenger Sectors: Models with additional particle content (“shadow fermions,” “messenger” scalars, new gauge sectors) connect the visible and hidden (dark) sectors, with lepton-number violation arising via exotic Yukawa couplings that also have electromagnetic cargo (0810.3341, Nevzorov, 2017, Chun et al., 2020).
• Resonant and Out-of-Equilibrium Enhancement: The efficiency of these mechanisms is frequently amplified in the presence of quasi-degenerate heavy states or resonant dynamics, e.g., the self-energy enhancement for nearly degenerate neutrinos or dark vector bosons (Choudhury et al., 2011, Chun et al., 2020, Takada, 9 Sep 2025).
• Operator Dimension and Gauge Invariance Constraints: Gauge invariance of the SM generally requires Higgs insertions, thereby elevating the relevant effective operators to dimension-6 (or higher) unless new fields (e.g., light sterile neutrinos) are introduced (Borah et al., 22 Jan 2025, Takada, 9 Sep 2025).

2. Mechanisms for Lepton Number Violation and CP Asymmetry

A common requirement for electromagnetic leptogenesis is the realization of CP- and lepton number-violating interactions that can produce a net lepton (or $B-L$) asymmetry:

• Dipole–Induced Two-Body Decays: For instance, the decay $N_i \to \nu_R + \gamma$ mediated by a dimension-5 electromagnetic dipole operator produces a lepton asymmetry in the sterile sector. Interference between tree-level and loop (vertex and self-energy) diagrams introduces CP violation, with asymmetry parameter

$$\epsilon_i \sim \frac{1}{4\pi} \frac{|\lambda|^2}{\Lambda^2} \sin(2\theta) M_i^2 F(x)$$

where $F(x)$ is a loop function sensitive to mass ratios and possible resonant enhancement (Borah et al., 22 Jan 2025).

• Hypermagnetic/Helicity-Induced Asymmetry: In the early Universe, the time evolution of hypermagnetic helicity is directly linked to lepton number through the anomaly:

$$\partial_\mu j_{e_R}^\mu = -\frac{g'^2}{16\pi^2}\, Y_{\mu\nu}\tilde{Y}^{\mu\nu}$$

which implies that the change in helicity $\mathcal{H}$ is compensated by the creation of fermionic asymmetry. The dynamical equations governing the chemical potentials, hypermagnetic field, and helicity are integro-differential and admit amplification schemes (e.g., $\alpha^2$-dynamo) (Dvornikov et al., 2011, Semikoz et al., 2016, Fukuda et al., 7 Oct 2024).

• Messenger-Induced Lepton Violation: In models with extended hidden sectors and real representations (e.g., $SU(2)_Z$ shadow fermions), Majorana masses for shadow fermions violate lepton number. CP violation arises through interference of tree and loop diagrams in decays such as messenger scalar $\to$ shadow fermion + lepton (0810.3341).

3. Operator Structure, Gauge Symmetry, and Model Constraints

The fundamental structure of the effective interaction in electromagnetic leptogenesis models is determined by SM gauge invariance:

• Operator Dimension: For purely SM fields, gauge invariance requires the electromagnetic dipole to arise as a dimension-6 operator:

$$O_{NB} = (\overline{L} \sigma^{\mu\nu} N)\tilde{H} B_{\mu\nu}$$

so that after EWSB, the dipole coupling is proportional to $v/M_\Psi^2$, resulting in decay widths and CP asymmetries scaling as $v^2/M_\Psi^4$ (Takada, 9 Sep 2025).

• Suppression and Resonance: The combined effect of operator dimension, loop suppression from UV matching, and RG running often suppresses the lepton asymmetry. Quasi-degenerate heavy neutrino masses are necessary for resonant enhancement of the self-energy diagrams, offering a path to realistic baryon asymmetry despite the otherwise “structural” suppression (Takada, 9 Sep 2025).
• Flavor and Portal Structure: The realization of lepton flavor violation (LFV), dark sector–visible sector communication, and asymmetry transfer (sterile $\rightarrow$ active) is sensitive to the flavor structure of the couplings and the presence of additional messenger fields or Higgs doublets (Choudhury et al., 2011, Borah et al., 22 Jan 2025, Nevzorov, 2017).

4. Boltzmann Evolution, Washout, and Phenomenological Viability

To convert the CP-violating microphysics into a cosmologically relevant baryon asymmetry, the dynamics of lepton number production, washout, and transfer are treated using coupled Boltzmann equations:

• Flavour-Dependent Evolution: At electroweak and lower scales, charged lepton Yukawa interactions decohere flavor, requiring full flavor-resolved kinetics (Takada, 9 Sep 2025).
• Asymmetry Transfer and Washout: The efficiency of transferring an asymmetry from the sterile to the active sector (for conversion by electroweak sphalerons) depends on the size of couplings (e.g., Yukawa with a neutrinophilic Higgs). Overly rapid washout from inverse processes or new washout channels (e.g., large radiatively induced Majorana masses) must be avoided (Borah et al., 22 Jan 2025, Takada, 9 Sep 2025).
• Freeze-Out Asymmetry: In the non-resonant, hierarchical regime, the freeze-out baryon asymmetry obtained after evolving the system is dramatically suppressed, $Y_B^{\rm FO} \lesssim 10^{-17}$, many orders below the observed value $Y_B^{\rm obs}\simeq 8.7\times 10^{-11}$ (Takada, 9 Sep 2025). Efficient baryogenesis in electromagnetic leptogenesis frameworks thus generally requires additional enhancements—most notably resonant CP violation due to mass degeneracy.

5. Experimental Signatures and Cosmological Implications

Electromagnetic leptogenesis models make concrete predictions for laboratory and astrophysical observations:

• Photon and $Z$ Signatures: Heavy RHNs decaying via dipole operators can produce monochromatic photons, accessible in collider or fixed-target experiments (Borah et al., 22 Jan 2025, Choudhury et al., 2011).
• Warm Dark Matter and Sterile Neutrinos: The presence of light sterile neutrino states in the keV range, produced as decay products or via mixing, provides a viable warm dark matter candidate, subject to constraints from X-ray and cosmological data (Borah et al., 22 Jan 2025, Nevzorov, 2017).
• Effective Degrees of Freedom: Additional relativistic species before recombination (implying $\Delta N_{\rm eff}$) offer a testable prediction for CMB-S4–class experiments (Borah et al., 22 Jan 2025).
• Lepton Flavor Violation and LFV Decays: Effective dipole and transition moments may induce charged LFV processes (e.g., $\mu \to e \gamma$) or affect neutrinoless double beta decay rates and kinematics (Chun et al., 2017).
• Primordial Magnetic Fields and Helicity: The prediction of relic magnetic fields with nontrivial helicity provides observationally accessible probes via astrophysical techniques, such as blazar observations, CMB polarization, and cross-correlations (Long et al., 2013).

6. Model Extensions and Cosmological Unification

Electromagnetic leptogenesis is embedded in a variety of broader theories, often linking baryogenesis to other cosmological sectors:

• Connection to Dark Energy and Hidden Sectors: Models with hidden gauge groups (e.g., $SU(2)_Z$) and axion-like particles generate dark energy via instanton-induced potentials, while “shadow” fermions act as cold dark matter. Messenger scalars bridge these sectors to the SM and mediate both asymmetry production and dark matter genesis (0810.3341).
• Portal-Enabled Unification: Scenarios with messenger fields, extra U(1) gauge groups (e.g., $U(1)_{B-L}$, $U(1)_D$), and exotic matter content unify mechanisms for leptogenesis, dark matter, and potential dark radiation, stabilizing proton decay rates and ensuring gauge anomaly cancellation (Kajiyama et al., 2010, Nevzorov, 2017, Chun et al., 2020).
• Higgs Relaxation and Electromagnetic Effects: In Higgs relaxation scenarios, time-dependent Higgs VEVs induce effective chemical potentials for $B+L$ violating processes, with CP violation and lepton asymmetry generated analogously to electromagnetic baryogenesis through higher-dimensional operators involving gauge fields (Yang et al., 2015).

7. Outlook and Limitations

Electromagnetic leptogenesis, particularly in the low-scale, non-resonant regime, faces strong “structural” suppressions due to operator dimension, loop matching, and the necessity of gauge invariance (Takada, 9 Sep 2025). Quasi-degenerate heavy neutrinos with self-energy resonant enhancement offer a plausible path to realistic baryogenesis, but require precise mass tuning and can be sensitive to washout processes. Multicomponent models may simultaneously address baryon asymmetry, neutrino masses, dark matter, and even dark energy, but are subject to correlated constraints from laboratory searches, astrophysical data, and cosmological measurements.

The continued interplay of theory, precision cosmic observations, and future experimental probes of dipole transitions, LFV, dark matter, and primordial magnetic fields will test the breadth of possible electromagnetic contributions to the origin of the baryon asymmetry.