A direct link between neutrinoless double beta decay and leptogenesis in a seesaw model with $S_4$ symmetry

We study how leptogenesis can be implemented in a seesaw model with $S_4$ flavor symmetry, which leads to the neutrino tri-bimaximal mixing matrix and degenerate right-handed (RH) neutrino spectrum. Introducing a tiny soft $S_4$ symmetry breaking term in the RH neutrino mass matrix, we show that the flavored resonant leptogenesis can be successfully realized, which can lower the seesaw scale much so as to make it possible to probe in colliders. Even though such a tiny soft breaking term is essential for leptogenesis, it does not significantly affect the low energy observables. We also investigate how the effective light neutrino mass $|<m_{ee}> |$ associated with neutrinoless double beta decay can be predicted along with the neutrino mass hierarchies by imposing experimental data of low-energy observables. We find a direct link between leptogenesis and neutrinoless double beta decay characterized by $|<m_{ee}>|$ through a high energy CP phase $phi$, which is correlated with low energy Majorana CP phases. It is shown that our predictions of $|<m_{ee}>|$ for some fixed parameters of high energy physics can be constrained by the current observation of baryon asymmetry.