Renormalization group running triggered tri-resonant leptogenesis within neutrino flavor-symmetry models

TL;DR

This work investigates tri-resonant leptogenesis within four representative neutrino flavor-symmetry frameworks in the MSSM, where three initially degenerate right-handed neutrinos acquire mass splittings via renormalization-group running between the flavor-symmetry scale $Λ_{FS}$ and the leptogenesis scale $M_0$. The authors deploy the density-matrix formalism to compute flavor-resolved CP asymmetries and track the evolution of right-handed neutrino abundances and lepton asymmetries, using MSSM RGEs to determine the splittings. Across TM1, modular ${ m A}_4$, ${ m S}_4$, and ${ m A}_5$ models, they identify parameter regions in $(M_0, aneta)$ that reproduce the observed BAU $η_B$, with $M_0$ ranging from roughly $10^7$ GeV to above $10^{13}$ GeV depending on the model. The results illustrate that, under the stringent flavor constraints of these models, successful leptogenesis tends to occur at relatively high scales, and TeV-scale leptogenesis is generally incompatible with the studied constructions. This highlights the viability of RG-triggered tri-resonant leptogenesis in tightly constrained flavor-model contexts and guides expectations for future experimental tests and model-building directions.

Abstract

In this paper, we have studied the consequences of some representative neutrino flavor-symmetry models for tri-resonant leptogenesis (which is realized by having three nearly degenerate right-handed neutrinos). To be specific, we have considered a neutrino flavor-symmetry model realizing the TM1 mixing and modular ${\rm A}^{}_4$, ${\rm S}^{}_4$ and ${\rm A}^{}_5$ symmetry models that have a right-handed neutrino mass matrix $M^{}_{\rm R}$ as shown in Eq.~(\ref{6}) which gives three exactly degenerate right-handed neutrino masses and consequently prohibits the leptogenesis mechanism to work successfully. For these models, we study the scenario that the desired right-handed neutrino mass splittings for leptogenesis to work are generated from the renormalization-group running effects. In such a scenario, we explore the parameter space that allows for the reproduction of the observed baryon-antibaryon asymmetry of the Universe.

Figures (12)

• Figure 1: For the TM1 model in section 3, the mass splittings among the three right-handed neutrinos generated from the RGE effects, as functions of $M^{}_0$ for the benchmark values of $\tan \beta =10$ and 50.
• Figure 2: For the TM1 model in section 3, the resulting CP asymmetries for the decays of $N^{}_{I}$ as functions of $M^{}_0$ and $\tan \beta$.
• Figure 3: For the TM1 model in section 3, the resulting $\eta^{}_{\rm B}$ as functions of $M^{}_0$ for some benchmark values of $\tan \beta$. The horizontal gray dashed line shows the observed value of $\eta^{}_{\rm B}$.
• Figure 4: For the modular ${\rm A}^{}_4$ symmetry model in section 4, the resulting CP asymmetries for the decays of $N^{}_{I}$ as functions of $M^{}_0$ for the benchmark value of $\tan \beta = 30$ in the NO (left panel) and IO (right panel) cases.
• Figure 5: For the modular ${\rm A}^{}_4$ symmetry model in section 4, the resulting CP asymmetries for the decays of $N^{}_{I}$ as functions of $\tan \beta$ for the benchmark value of $M^{}_0= 10^{12}$ GeV in the NO (left panel) and IO (right panel) cases.