Leptogenesis for Pedestrians

TL;DR

This work provides an analytic description of thermal leptogenesis, linking the generated baryon asymmetry to neutrino mass parameters via the seesaw framework. By solving simplified Boltzmann equations for decays, inverse decays, and Delta L = 1 scatterings, it derives explicit expressions for the efficiency factor and the CP-violating asymmetry, and it identifies the temperature $T_B$ where the asymmetry is mainly produced. The key contributions include analytic bounds on the heavy neutrino mass $M_1$ and the initial temperature $T_i$, as well as an upper bound on light-neutrino masses around $m_i \,\lesssim\,0.12\,{\rm eV}$, with sensitivity to the mass ordering and possible resonant effects. The results provide a framework for evaluating the viability of leptogenesis across neutrino-mass parameter space and highlight the importance of corrections beyond simple Boltzmann treatments, especially in the transition between weak and strong washout regimes.

Abstract

During the process of thermal leptogenesis temperature decreases by about one order of magnitude while the baryon asymmetry is generated. We present an analytical description of this process so that the dependence on the neutrino mass parameters becomes transparent. In the case of maximal CP asymmetry all decay and scattering rates in the plasma are determined by the mass M_1 of the decaying heavy Majorana neutrino, the effective light neutrino mass tilde{m}_1 and the absolute mass scale bar{m} of the light neutrinos. In the mass range suggested by neutrino oscillations, m_{sol} \simeq 8*10^{-3} eV \lesssim \tilde{m}_1 \lesssim m_{atm} \simeq 5*10^{-2} eV, leptogenesis is dominated just by decays and inverse decays. The effect of all other scattering processes lies within the theoretical uncertainty of present calculations. The final baryon asymmetry is dominantly produced at a temperature T_B which can be about one order of magnitude below the heavy neutrino mass M_1. We also derive an analytical expression for the upper bound on the light neutrino masses implied by successful leptogenesis.

Figures (13)

• Figure 1: The dilation factor. The dashed line is the analytical expression Eq. (\ref{['Dapprox']}) to be compared with the numerical result (solid line).
• Figure 2: Out of equilibrium decays. $N_1$ number density, efficiency factor and decay temperature $T_{\rm d} = M_1/z_{\rm d}$ for $K=10^{-2}$ and $K=10^{-4}$.
• Figure 3: Comparison analytical (dashed lines) and numerical (solid lines) results for heavy neutrino production and $B-L$ asymmetry in the case of zero initial abundance, $N_{N_1}^{\rm i}=0$, for weak washout (top) and strong washout (bottom); $|\varepsilon_1|=10^{-6}$.
• Figure 4: Strong washout: comparison between analytical and numerical (full lines) results. Inverse decays are in equilibrium in the temperature range $z_{\rm in} \leq z \leq z_{\rm out} \sim z_B$; $|\varepsilon_1| = 10^{-6}$.
• Figure 5: $z_B$ as function of the decay parameter $\beta K$. The case studied in this section corresponds to $\beta=1$. The solid red line is the numerical solution of eq. (\ref{['z0a']}), the dotted black line shows the asymptotic solution (\ref{['lam']}), and the blue dashed line is the interpolation (\ref{['interpol']}).