Electromagnetic Leptogenesis -- an EFT-Consistent Analysis via Wilson Coefficients. Part I. Low-Scale, Non-Resonant Regime

TL;DR

This work presents a first-principles EFT analysis of electromagnetic leptogenesis driven by the gauge-invariant dipole operator $O_{NB}$. By performing a one-loop UV matching to determine $C_{NB}$, RG evolving it to the electroweak scale, and mapping to broken-phase dipole couplings, it computes flavour-resolved decay widths and CP asymmetries, then evolves the fully flavoured Boltzmann equations in the $N_1$-dominated regime. The main finding is a strong suppression of the freeze-out baryon asymmetry, $Y_B^{ m FO} \,\lesssim\ 10^{-17}$, arising from the structural scaling $oldsymbol{μ}_{eta i}\propto v/M_ ext{Ψ}^2$ and the loop/RGE factors that suppress both production and washout. The paper argues that resonant enhancements in a quasi-degenerate spectrum could lift this to the observed level, and discusses synergies with direct searches, providing a clear path for future EFT and UV-model investigations.

Abstract

We analyse electromagnetic leptogenesis within the framework of an effective field theory, where the dynamics is governed by the gauge-invariant dipole operator $O_{NB}$. The Wilson coefficient $C_{NB}$ is matched at one loop and renormalisation-group (RG) evolved to the electroweak scale. After electroweak symmetry breaking we compute flavour-dependent two-body decay widths and CP asymmetries for $N\toν+γ/Z$, and solve the fully flavoured Boltzmann equations. In the $N_1$-dominated regime the freeze-out baryon asymmetry is $Y_B^{\rm FO}\lesssim 10^{-17}$, far below the observed value $Y_B^{\rm obs}\simeq 8.7\times 10^{-11}$. The suppression is structural: gauge invariance forces a Higgs insertion; therefore dipole couplings $μ\propto v/M_Ψ^2$ while the matched coefficient $C_{NB}$ is loop-generated and further reduced by RG running. We note that in the quasi-degenerate limit the self-energy resonance can be operative and suggest a plausible path to $Y_B^{\rm obs}$.

Figures (9)

• Figure 1: Workflow of the EFT-consistent analysis adopted in this work.
• Figure 2: First one-loop matching graph for $\mathcal{O}_{NB}$. The $\mathrm{U}(1)_Y$ gauge boson $B_{\mu}$ is emitted from the $\Psi$ line through $+\mathrm{i}g_1Y_{\Psi}\gamma^{\mu}$. The loop contains $\Psi$ and $S$ and attaches via $-\mathrm{i}\lambda_iP_R$ and $-\mathrm{i}\lambda'_jP_R$. The external process is $N_i\to L_{\alpha}+\tilde{H}+B_{\mu}$. The mirror graph $i\leftrightarrow j$ produces the antisymmetric combination $(\lambda_i\lambda'_j-\lambda_j\lambda'_i)$. The amplitude is UV-finite; emission from the scalar line is purely longitudinal and cancels by the Ward--Takahashi identity, so only the fermion line induces the dipole.
• Figure 3: Two-body decays of a right-handed neutrino $N_i$ induced by the dipole operator $\mathcal{O}_{NB}$, which after EWSB reduces to a dimension-five operator. The wavy line denotes the neutral gauge boson, the photon (left) or the $Z$ boson (right). Decays into final states containing a charged lepton are forbidden by charge conservation. Grey blobs indicate that the effective vertices encode the heavy-field information through the Wilson coefficient $C_{NB}$.
• Figure 4: Vertex contributions. The contribution is represented by two types of graphs, (a) and (b). Left: particle content, external four-momenta and vertices. Right: the common momentum routing used for the loop integrations.
• Figure 5: Self-energy contributions. The contribution is likewise given by two types of graphs, (a) and (b). Left: particle content, external four-momenta and vertices. Right: the common momentum routing used for the loop integrations.