Resonant electromagnetic leptogenesis with coherent heavy-neutrino evolution

Abstract

We study TeV-scale electromagnetic leptogenesis generated by the gauge-invariant neutrino-dipole operators $O_{NB}$ and $O_{NW}$. The benchmark Wilson coefficients are specified at the renormalization scale $κ_N=M_1=1\,\mathrm{TeV}$ and related to their values at $κ_{\rm match}=3\,\mathrm{TeV}$ through the coupled one-loop $ν$SMEFT evolution. The collision network contains the symmetric-phase $1\leftrightarrow3$ and crossed $2\leftrightarrow2$ processes generated by the linear field-strength vertices and the VEV-induced two-body $γ$, $Z$, and $W$ channels through the electroweak crossover. We use a factorized leading-moment, momentum-averaged Markovian treatment for two $2\times2$ heavy-flavor density matrices, one for each helicity. Pole-resummed two-state effective couplings enter the lepton and antilepton collision tensors, while the off-diagonal density matrices describe coherent evolution and collision damping. Three resolved flavor charges are coupled to a finite-rate sphaleron equation, yielding the frozen baryon yield $Y_B^{\rm FO}$. For the benchmark $\tilde m^{\rm EM}_1=3.97\times10^{-2}\,\mathrm{eV}$, the decay-only pole prescription, in which only decay contributions enter the absorptive pole matrix, gives the locally optimized positive near-resonant maximum $Y_B^{\rm FO}=+5.50\times10^{-5}$ at $ΔM=1.29\times10^{-11}\,\mathrm{GeV}$. Adding the thermally averaged crossed-scattering moment to the pole matrix defines the decay-plus-scattering prescription and shifts the maximum to $Y_B^{\rm FO}=+8.44\times10^{-5}$ at $ΔM=1.83\times10^{-11}\,\mathrm{GeV}$. The corresponding signed mass-splitting curves cross the observed value $Y_B^{\rm obs}$ at $ΔM=1.68\times10^{-5}\,\mathrm{GeV}$ and $2.34\times10^{-5}\,\mathrm{GeV}$.