Seesaw Mechanism Confronting PAMELA in S_4 Flavor Symmetric Extra U(1) Model

Abstract

We study cosmic-ray anomaly observed by PAMELA based on E_6 inspired extra U(1) model with S_4 flavor symmetry. In our model, the lightest flavon has very long lifetime of O(10^18) second which is longer than the age of the universe, but not long enough to explain the PAMELA result O(10^26) sec. Such a situation could be avoidable by considering that the flavon is not the dominant component of dark matters. However non-thermalizing the flavon is needed to obtain proper relic density. This relates reheating temperature of the universe with seesaw mass scale. If we assume this flavon is a particle decaying into positron (or electron), the seesaw mass scale is constrained by reheating temperature. Thus we find an interesting result that the allowed region is around O(10^12) GeV, which is consistent with our original result.