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CP violation (CPV) and the baryon asymmetry of the universe (BAU) are two ofthe most significant unresolved problems in physics. This article presentsfurther research on the CPV problem in the standard model (SM) with thirty-twocandidate sets of the ten "natural" parameters that exhibit the same CKMperformance. These parameters are considered "natural" because they consistsolely of the Yukawa couplings and the vacuum expectation value (VEV) of theunique Higgs doublet in the SM. We then investigate the CPV problem and the BAUproblem using the Jarlskog measure of CPV, $\Delta_{CP}=J(m^2_t -m^2_c)(m^2_t-m^2_u)(m^2_c -m^2_u)(m^2_b -m^2_s)(m^2_b -m^2_d)(m^2_s -m^2_d)/ T^{12}$, giventhat CP symmetry is violated following the breakdowns of $S_N$ symmetries.Subsequently, we perform numerical tests in a simplified scenario where eightof the ten parameters are fixed, and the remaining two parameters are allowedto vary from their $S_2$-symmetric values ${\bf (x,~y)}=(-1,~1)$ to theircurrent values in all thirty-two parameter sets. To estimate the enhancement ofCPV in such processes, we propose a ratio $R_{\Delta} \equiv \Delta_{CP} /\Delta^{(0)}_{CP}$ between the running $\Delta_{CP}$ and its current value,denoted by $\Delta^{(0)}_{CP}$, which is approximately $10^{-20}$. In allthirty-two cases, the three-dimensional (3D) plots of $R_{\Delta}$ exhibit manyregions that stick out of the $R_{\Delta}=10^{10}$ plane, especially in regionsvery close to ${\bf (x,~y)}=(-1,~1)$. These results demonstrate that the$S_N$-breaking Standard Model is already sufficient to violate CP symmetryexplicitly and generate a significant amount of BAU. Furthermore, it solvesexisting problems without creating new ones.

BAU production in the $S_N$-breaking Standard Model