Paper detail

Asymptotic properties of CP violation in the Standard Model

We present the analysis of the renormalization based evolution of the CP-violation observables obtained from the $C$ matrix introduced by Jarlskog. We show that the observables $\vert\det C\vert$ and $\operatorname{Tr}C^{2}$ decrease very fast with the energy and their value is reduced at the Planck's scale by 5 and 3 orders of magnitude with respect to their low energy values. On the other hand the Jarlskog's CKM matrix rephasing invariant $J$ increases with energy and at the Planck's scale is 25 % larger than at low energy. The absolute value of the coefficient $a_{CP}\sim \det C/(\operatorname{Tr}C^{2})^{3/2}$ decreases with energy and at the Planck's scale it is 12 % smaller than at low energy. We also find that the pattern of the eigenvalues of the $C$ matrix is such that two eigenvalues almost cancel each other and their absolute values are much bigger than the absolute value of the third eigenvalue. The low rate of the CP-violation is a consequence of this pattern of the eigenvalues.