Tuesday, July 9, 2019

quantum field theory - Why is the $theta$ term of QCD violating charge and parity (CP) symmetries?


From the non-trivial nature of the QCD vacuum, the Lagrangian is augmented with a term like



\begin{equation} \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu} \end{equation}


where $ \tilde{G}^{a,\mu \nu} = \frac{1}{2} \epsilon^{\mu \nu \rho \sigma} G^a_{ \rho \sigma} $ is the dual field strength tensor. This term is said to violate CP, giving rise to the strong CP problem.


I understand the CP violation comes from the epsilon tensor in the dual field strength but I am looking for a simple straightforward demonstration of the CP violating nature of a term like $G \tilde{G}$.




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