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

Abstract

We study electromagnetic leptogenesis (EMLG) in the low-scale, resonant regime within a fully effective-field-theory (EFT)--consistent framework. Starting from a UV Lagrangian and performing a one-loop matching to obtain the gauge-invariant dipole operator $O_{NB}$ with its Wilson coefficient $C_{NB}$, we implement the Pilaftsis--Underwood resummation for the self-energy contributions to the CP asymmetries and evolve a flavour covariant transport system across the electroweak window. In the quasi-degenerate limit $M_m-M_i\simeq\varGamma_m/2$, the CP-odd source acquires a Breit--Wigner--form enhancement whereas the washout saturates, with the freeze-out baryon asymmetry achieving $Y_B^{\rm FO}\gtrsim 10^{-10}$ across the strong-washout regime, comfortably above the observed value $Y_B^{\rm obs}\simeq 8.7\times 10^{-11}$. This establishes resonant EMLG at $O(100)~{\rm GeV}$ as a viable EFT-based mechanism for the baryon asymmetry of the Universe.

Figures (6)

• Figure 1: Workflow of the EFT-consistent analysis adopted in this work. In the resonant analysis we evaluate CP sources with the resummed self-energy loop functions $\tilde{f}_{S_a}$, $\tilde{f}_{S_b}$, and evolve the flavour covariant transport system.
• Figure 2: Loop functions $f_{V_a}(x)$, $f_{S_a}(x)$, $f_{S_b}(x)$. The self-energy pieces $f_{S_a}(x)$ and $f_{S_b}(x)$ diverge as $x\to 1$, i.e. in the quasi-degenerate limit $M_i\simeq M_m$. We keep flavour resolution throughout, since under flavour summation one of the self-energy pieces, $f_{S_b}(x)$, drops out.
• Figure 3: Time evolution in the resonant regime for $\tilde{m}_1^{\rm EM}=10^{-3}~{\rm eV}$, where $\tilde{m}_1^{\rm EM}$ is defined in eq. (\ref{['eq:2.21']}). The blue curve shows the depletion of $Y_{N_1}$, normalised to its value at $z=z_{\rm EW}$. The CP-odd source is computed from the PU-resummed self-energy functions $\tilde{f}_{S_{a,b}}$ at fixed dipole couplings $\mu_{\alpha 1}$. The flavour asymmetries $Y_{\Delta\alpha}$ (dashed orange for $e$, dash-dotted green for $\mu$, dotted magenta for $\tau$) grow monotonically. The $\tau$ suppression in this benchmark originates from the small rephasing invariant Yasaman_Farzan_2007, $\mathcal{J}_{\tau}^{(12)}=\mathop{\mathrm{Im}}\nolimits[*]{\mu_{\tau 1}^{\ast}\mu_{\tau 2}(\mu^{\dagger}\mu)_{12}}$. This $\tau$ suppression is not a universal prediction and may be absent for different $\tilde{m}_1^{\rm EM}$ values.
• Figure 4: The freeze-out baryon asymmetry $Y_B^{\rm FO}$ as a function of the effective mass $\tilde{m}_1^{\rm EM}$. At the reference point $\tilde{m}_1^{\rm EM}=0.24~{\rm eV}$, we fix $M_2$ by $\Delta M\simeq\varGamma_2/2$ and thereafter vary $\tilde{m}_1^{\rm EM}$ by rescaling $\mu_{\alpha 1}$, recomputing $\varGamma_1$ and the CP sources. For the weak-washout regime $\tilde{m}_1^{\rm EM}\lesssim 4.15\times 10^{-4}~{\rm eV}$, the yield grows rapidly, $Y_B^{\rm FO}\propto(\tilde{m}_1^{\rm EM})^2$, since $\varepsilon^{\rm res}\propto\mu^2$ and $D\propto K\propto\mu^2$. For the strong-washout regime $\tilde{m}_1^{\rm EM}\gtrsim 4.15\times 10^{-4}~{\rm eV}$, the CP source saturates and the washout $W(z_f)\sim 1$ drives a plateau; here we denote by $z_f$ the freeze-out of the washout. The horizontal dashed orange line marks $Y_B^{\rm obs}\simeq 8.7\times 10^{-11}$2020AA...641A...6P; the vertical dashed green lines show the oscillation-motivated neutrino-mass window Esteban:2024eli. Over the mass window we obtain $Y_B^{\rm FO}\gtrsim 10^{-9}$, with a global upper envelope $Y_B^{\rm FO}\lesssim 10^{-8}$ (more stringently $Y_B^{\rm FO}\lesssim 4\times 10^{-9}$).
• Figure 5: The two types of Feynman graphs (a) and (b) for the self-energy contributions in EMLG. In each case, the left panel shows the particle species involved in the reaction, the four-momenta, and the vertices, while the right panel indicates the directions of the four-vectors $k,p,q,q_1,q_2$.