Electromagnetic leptogenesis -- an EFT-consistent analysis via Wilson coefficients. Part III. Probing light-neutrino masses and low-energy observables

Abstract

In this third part of our EFT-consistent analysis of electromagnetic leptogenesis, we confront the dipole operator that sources the baryon asymmetry with constraints from light-neutrino masses and low-energy observables. Starting from the UV completion and one-loop-matched Wilson coefficient $C_{NB}$ of the gauge-invariant operator $O_{NB}=(\bar{L}\sigma^{\mu\nu}P_RN)\tilde{H}B_{\mu\nu}$, we compute the radiatively induced Weinberg operator $O_5$ and derive the light Majorana mass matrix generated by a double insertion of $O_{NB}$. For the benchmarks that realise successful resonant electromagnetic leptogenesis at the electroweak scale, these contributions yield neutrino masses far below the scale implied by neutrino oscillation data, so that the observed neutrino masses must originate from additional interactions such as one of the seesaw mechanisms, and only in extreme corners of parameter space do they saturate the cosmological bound on $\sum m_{\nu}$. We also show that no additional Dirac neutrino mass is generated at one loop by the dipole operator alone. Furthermore, we derive the charged-lepton dipole operator $O_{e\gamma}$ in LEFT, accounting for one-loop operator mixing in the symmetric phase and two-loop Barr-Zee-type graphs in the broken phase, and evolve its Wilson coefficient $C_{e\gamma}$ down to the muon and electron mass scales using QED renormalisation-group equations. The resulting analytic upper bounds on $\mathrm{BR}(\mu\to e\gamma)$, the electron EDM, and $(g-2)_{\mu}$ lie many orders of magnitude below current experimental sensitivities throughout the BAU-compatible region. Electromagnetic leptogenesis in this EFT framework is therefore robust against present constraints from light-neutrino masses and low-energy dipole probes.