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

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 $N\to\nu+\gamma/Z$, 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 $\mu\propto v/M_{\Psi}^2$ 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 $Y_B^{\rm obs}$.