The Breakdowns of $S_N$ Symmetries and Violation of CP Symmetry

In this article we study how the breakdowns of $S_N$ permutation symmetry bring CP violation (CPV) into electroweak interactions explicitly. The CPV strength thus derived varies with various $S_N$ symmetries. In the case $N = 3$, CP symmetry is always conserved. If the $S_3$ symmetries were broken down into some residual $S_2$ symmetries as the back ground temperature ${\bf T}$ of the universe decreased as the universe expended, along with it came the violation of CP symmetry in some special cases. The very strong strength of CPV predicted in these cases produced much more BAU than current standard model do. That solves partly the BAU discrepancy between particle physics and cosmology since we can attribute most of them to be generated in some BAU-productive eras in the early universe. Considering we do not see any such $S_N$ symmetries in our present universe, a non-symmetric CKM matrix is given to describe the real world we are living in, consequently. It proves that standard model alone is enough to generate CP violation which fit experimental values as good as to the order of ${\bf O(10^{-2})}$ at tree level.