Reheating era leptogenesis in models with a seesaw mechanism

Observed baryon asymmetry can be achieved not only by the decay of right-handed neutrinos but also by the scattering processes in the reheating era. In the latter scenario, new physics in high energy scale does not need to be specified, but only two types of the higher dimensional operator of the standard model particles are assumed in the previous work. In this paper, we examine the origin of the higher dimensional operators assuming models with a certain seesaw mechanism at the high energy scale. The seesaw mechanism seems to be a simple realization of the reheating era leptogenesis because the lepton number violating interaction is included. We show that the effective interaction giving $CP$ violating phases is provided in the several types of models and also the reheating era leptogenesis actually works in such models. Additionally, we discuss a possibility for lowering the reheating temperature in the radiative seesaw models, where the large Yukawa coupling is naturally realized.

Figure 1

Interference between tree and one-loop diagram for the lepton number violation scattering process.

Figure 2

A process that gives the operator $(\overline{L_i}\tilde{\mathrm{\Phi }})(\overline{L_j}\tilde{\mathrm{\Phi }})/{\mathrm{\Lambda }}_1$ in the type-I (-III) seesaw model.

Figure 3

Processes that give the operator $(\overline{L_i}{\gamma }^{\mu }{L}_j)(\overline{L_k}{\gamma }_{\mu }{L}_l)/{\mathrm{\Lambda }}_2^2$.

Figure 4

The allowed parameter space of $T_R$ as a function of $M_R$ in the type-I seesaw model for $R=1$ and $R=10$ with normal mass ordering. In the right panel, the effect of the ${\epsilon }_2$ term is omitted in the Boltzmann equation.

Figure 5

The allowed parameter space of $T_R$ as a function of $M_R$ in the type-I seesaw model for $R=10^3$ and $R=10^4$ with normal mass ordering. In the right panel, the effect of ${\epsilon }_2$ term is omitted in the Boltzmann equation.

Figure 6

The allowed parameter space of $T_R$ as a function of $M_R$ in the type-I seesaw model for $R=1$ and $R=10$ with inverted mass ordering. In the right panel, the effect of ${\epsilon }_2$ term is omitted in the Boltzmann equation.

Figure 7

The allowed parameter space of $T_R$ as a function of $M_R$ in the type-I seesaw model for $R=1$ and $R=10$ with inverted mass ordering. In the right panel, the effect of the ${\epsilon }_2$ term is omitted in the Boltzmann equation.

Figure 8

In the scotogenic radiative seesaw mechanism, $(\overline{L_i}\tilde{\mathrm{\Phi }})(\overline{L_j}\tilde{\mathrm{\Phi }})/{\mathrm{\Lambda }}_1$ is derived by loop processes.

Figure 9

The allowed parameter space of $T_R$ as a function of $M_R$ in the Ma model with normal mass ordering. In the right panel, the effect of the ${\epsilon }_2$ term is omitted in the Boltzmann equation.

Figure 10

The allowed parameter space of $T_R$ as a function of $M_R$ in the Ma model with normal mass ordering. In the right panel, the effect of the ${\epsilon }_2$ term is omitted in the Boltzmann equation.

Figure 11

A schematic picture for the energy densities of inflaton ${\rho }_{\text{inflaton}}$ and of radiation ${\rho }_{\text{radiation}}$ during the reheating process. The horizontal axis is the scale factor of the universe $a$.