Electroweak sphalerons in the reduced minimal 3-3-1 model
  We calculate the electroweak sphaleron rates in the reduced minimal 3-3-1 (RM331) model. In the context of the early Universe, this model undergoes a sequence of two first-order phase transitions, $SU(3) \rightarrow SU(2)$ at the TeV scale and $SU(2)\rightarrow U(1)$ at the $10^2$ GeV scale, as the Universe cools down from the hot big bang. By a thin-wall approximation, we show that for each phase transition in this sequence, the sphaleron rate is larger than the cosmological expansion rate at temperatures higher than the critical temperature, and after the phase transition, the sphaleron process is decoupled. This may provide baryon-number violation (B violation) necessary for baryogenesis in the relationship with nonequilibrium physics in the early Universe. 
Vo Quoc Phong, Hoang Ngoc Long, Vo Thanh Van, Nguyen Chi Thanh
hep-ph