Importance of CP violation

Question

To explain the matter-antimatter assymmetry, CP should be violated according to Sakharov conditions. Charge conjugation is required as matter and antimatter have opposite charges but why Parity Violation? Is it because they have opposite chirality as well? Isn't it model dependent?

Answer 1

You understand that $\mathcal C$ violation is required, as if it weren't, processes related by $\mathcal C$ that violated baryon number conservation would balance, i.e. $$ P \to Q B \qquad \mathcal C:\qquad \overline P \to \overline Q \, \overline B $$ would result in no net baryon number violation. In these expressions, $B$ is a fermion carrying baryon number, $Q$ is a fermion uncharged under baryon number, and $P$ is a necessarily a boson, which cannot carry baryon number.

Understanding that $\mathcal{CP}$ violation is required is only slightly more subtle. If it were conserved, $\mathcal{CP}$ symmetric processes would balance baryon number, i.e $$ P \to Q_L B_L \qquad \mathcal{CP}:\qquad \overline P \to \overline Q_R \overline B_R $$ and $L \leftrightarrow R$, would balance, even if they were both $\mathcal C$ violating.

Thus we require $\mathcal C$ and $\mathcal{CP}$ violation. $\mathcal{CP}$ symmetry could relate processes such that the sum of independently $\mathcal C$ violating processes conserved baryon number.

We could have began with fermion to boson and fermion; the argument would have been identical.