# Why is the strong CP term $\theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu}$ never considered for $SU(2)$ or $U(1)$ interactions?

The Lagrangian one would write down naively for QCD is invariant under CP, which is in agreement with all experiments.

Nevertheless, if we add the term

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

where $\tilde{G}^{a,\mu \nu} = \frac{1}{2} \epsilon^{\mu \nu \rho \sigma} G^a_{ \rho \sigma}$ is the dual field strength tensor to the Lagrangian, QCD isn't CP invariant anymore. This is known as the strong CP problem

• Why do we need to consider this term in QCD, and why is it never mentioned in weak- or electromagnetic interactions? (In the literature I was only able to find the nebulous statement that this is because of the topological structure of the QCD ground state)
• This term isn't invariant under parity transformations, so why isn't there a strong P problem, too?