Leptogenesis from the Dirac CP-violating phase in the minimal left-right symmetric model

Abstract

Leptogenesis from low-energy CP violation provides a vital link between neutrino physics and the observed baryon asymmetry of the universe. However, this connection is typically obscured by unknown high-energy parameters. In this work, we investigate thermal leptogenesis in the Minimal Left-Right Symmetric Model with generalized parity as the left-right symmetry, where the hermiticity of the Dirac neutrino coupling allows the right-handed mixing matrix $V_\mathrm{R}$ to be determined with minimal assumptions. We show that for a real $V_\mathrm{R}$, these conditions favor CP-conserving Majorana phases, leaving the Dirac CP-violating phase ($δ$) as the sole source of asymmetry. By numerically exploring all four leptogenesis scenarios, we demonstrate that $δ$ alone can generate the observed baryon asymmetry with the correct sign within specific regions of the parameter space. The results exhibit a high sensitivity to the neutrino mass ordering and the lightest neutrino mass, providing a stringent, testable framework for future experimental measurements of the CP phase and neutrino mass scale.

Figures (4)

• Figure 1: The real-trace contours ($\text{Im} \text{Tr} (S^n) = 0$ for $n = 1, 2, 3$) are plotted for two $V_\mathrm{R}$ mixing angles, using two sets of randomly chosen values for $\gamma_{12}$ and $\delta$. The intersection of the three lines (for a given set of inputs) indicates a simultaneous solution to the three constraints.
• Figure 2: Values of $\mathrm{Im} \text{Tr}(S^n)$ for $n=1,2,3$ are calculated using randomly sampled values of $\alpha_{31}$ and $\alpha_{21}$ for three different choices of real $V_\mathrm{R}$. The "$V_\mathrm{R}=V_\mathrm{L}$" case refers to a real $V_\mathrm{R}$ matrix with mixing angles equal to those of $V_\mathrm{L}$.
• Figure 3: Values of $\mathrm{Im} \mathrm{Tr}(S^n)$ for $n=1,2,3$, calculated using randomly sampled values of $\alpha_{21}$ and $V_\mathrm{R}$ mixing angles, with $\alpha_{31}$ fixed to $n\pi$.
• Figure 4: Predicted values of the baryon asymmetry as a function of the Dirac CP-violating phase for both mass orderings of light neutrinos in each scenario (labeled S1 through S4). The left panel corresponds to normal ordering (NO), while the right panel corresponds to inverted ordering (IO). In each plot, three benchmark values of the lightest neutrino mass are shown. The green shaded region represents the $3\sigma$ experimental bound on the baryon asymmetry, while the light yellow shaded region indicates the $3\sigma$ range for $\delta$ from NuFIT 6.1 Esteban:2024eli, with the darker yellow sub-region representing the $1\sigma$ range.