What can be expected from the further study of $CP$ and $T$ symmetry violation and $CPT$ invariance tests

Different $CP$ and $T$ violation models are discussed in view of using their particular features to experimentally ascertain which of these models are realized in nature. For example, recording the electric dipole moments of the neutron and electron close to their experimental limits or only one or two orders of magnitude smaller would be evidence for the presence of $CP$ violation sources other than the Kobayashi–Maskawa phase in the Standard Model. As for $CPT$ invariance, which predicts, in particular, the equality of the particle and antiparticle masses, the ratio of the difference between the $K^0$ and $\bar K^0$ masses to their sum being below $10^{-18}$ is considered to be the best test of $CPT$ symmetry. However, an extremely small value of this ratio does not necessarily imply extremely small parameters of the CPT violation in $\{K^0,\bar K^0\}$-system decays. The existing data only indicate that these parameters must not exceed $30\%$ of the known $CP$ violation parameter $\eta_+$. Other experiments for high-precision testing of $CPT$ invariance are discussed.