Resonating the Cosmic Void: A First-Principles Approach to Electromagnetic Leptogenesis
Schwinger--Keldysh formulation of electromagnetic leptogenesis in an EFT framework
This paper presents a comprehensive effective field theory (EFT) pipeline for TeV-scale electromagnetic leptogenesis (EMLG). By employing the Schwinger-Keldysh formulation, it derives density-matrix quantum kinetic equations (QKEs) that unify decay and scattering processes, demonstrating that resonantly enhanced dipole operators can explain the observed baryon asymmetry while suppressing conflicting neutrino Yukawa interactions.
Executive Summary
TL;DR: This work bridges the gap between high-scale UV completions and electroweak-scale baryon production by providing a rigorous EFT pipeline for Electromagnetic Leptogenesis (EMLG). By leveraging the Schwinger-Keldysh (CTP) formalism, the author resolves long-standing ambiguities in scattering vs. decay double-counting, proving that TeV-scale right-handed neutrinos with enhanced dipole moments can indeed generate the observed matter-antimatter asymmetry.
Academic Context: This is a significant "theoretical cleanup" and extension work. It moves EMLG from a qualitative proposal to a quantitative, gauge-invariant EFT framework, placing it firmly within the coordinates of SMEFT research.
The Dipole Bottleneck: Problem & Motivation
The observed Baryon Asymmetry of the Universe (BAU) requires Sakharov's conditions, often satisfied via the out-of-equilibrium decays of heavy neutrinos. However, standard leptogenesis is frequently "contaminated" by Yukawa couplings that drive unwanted washout.
The author identifies a critical hurdle: if we want a dipole-dominated scenario, we must suppress the renormalizable Higgs-neutrino Yukawa to roughly . Without this, the Yukawa-induced width broadens the resonant regulator and wipes out the delicate dipole-driven CP source. The challenge is constructing a model where this suppression is "natural" rather than fine-tuned, and where the kinetic equations don't fall into the trap of double-counting real intermediate states.
Methodology - The Unified CTP Pipeline
1. UV Matching and RG Evolution
Starting from a -symmetric UV model where heavy states are integrated out at TeV, the author generates dimension-six operators:
u} P_R N) ilde{H} B_{\mu u} $$ $$ \mathcal{O}_{NW} = (\bar{L} \sigma^{\mu u} au^a P_R N) ilde{H} W^a_{\mu u} $$ These are evolved via Renormalization Group Equations (RGEs) down to the electroweak scale ($\sim 150$ GeV). This ensuring the model remains gauge-invariant throughout the "Higgs crossover" window. ### 2. Quantum Kinetic Equations (QKEs) Instead of a naive Boltzmann approach, the author derives density-matrix QKEs from the Kadanoff-Baym equations. The core "How" behind the effectiveness of this paper is the **spectral decomposition** of the collision term.  *Fig 1: One-loop matching onto the dipole operators. The architecture ensures that only dipole-type interactions dominate the early universe plasma.* By using the Schwinger-Keldysh contour, the collision term distinguishes between: * **Pole Contributions**: Physical 1 ↔ 2 decays/inverse decays (time-like momenta). * **Landau-Damping Cut**: 2 ↔ 2 scatterings (space-like momenta). Because these kinematic supports are disjoint, the author can add them together without the standard "Real Intermediate State (RIS) subtraction" headache found in earlier literature. ## Experiments & Results: The Rise and Fall of Asymmetry The resonance condition $\Delta M \simeq \Gamma/2$ is the focal point. Numerical analysis reveals a characteristic "rise and fall" behavior of the baryon yield $Y_B$ relative to the effective electromagnetic neutrino mass $ ilde{m}^{EM}_1$.  *Fig 2: The regulated Breit-Wigner structure of the self-energy loop functions, showing the resonant enhancement essential for TeV-scale viability.* ### Key Quantitative Insights: * **Weak Washout Range**: Below $5 imes 10^{-4}$ eV, the asymmetry scales as $( ilde{m}^{EM}_1)^2$. * **Strong Washout Range**: Above this threshold, inverse decays and scatterings become efficient, eventually suppressing the yield. * **The Observed Goal**: The model successfully crosses the $Y_B \approx 10^{-10}$ line for both thermal and zero initial abundances in the neutrino-oscillation-motivated range ($10^{-2}$ to $10^{-1}$ eV).  *Fig 3: Frozen-out baryon asymmetry vs. dipole coupling strength. The blue curves represent actual yields, demonstrating the overlap with the observed BAU (orange dashed line).* ## Critical Analysis & Conclusion ### Deep Insights The author shows that $\Delta L = 0$ scatterings (often neglected or incorrectly subtracted) are numerically subdominant ($\sim 10^{-5}$ relative to decays) but theoretically vital for a gauge-invariant description. This consistency check provides high confidence in the undiluted yields. ### Limitations & Future Work * **Dilution**: Currently, the model overproduces asymmetry in some regions, necessitating late entropy injection (e.g., from modular decays) to dilute the result down to the observed value. * **Phase Crossover**: The study focuses on the "broken" phase window. A fully continuous treatment across the electroweak crossover (from symmetric to broken) remains a future theoretical frontier. **Summary**: This paper provides the most robust kinetic treatment of electromagnetic leptogenesis to date. By replacing free parameters with an EFT pipeline and resolving quantum double-counting, it elevates dipole-induced leptogenesis from a "toy model" to a rigorous contender for early-universe cosmology.