Parity of theta term of Lagrangian

[illuminates]

I have a very simple question. Let's consider the theta term of Lagrangian:
$$L = \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu}$$
Investigate parity of this term:
$$P(G_{\mu \nu}^a)=+G_{\mu \nu}^a$$
$$P( \tilde{G}^{a, \mu \nu} ) =-G_{\mu \nu}^a$$
It is obvious. But what about $\theta$? If $\theta$ is simple number then
$$P(\theta)=\theta$$
And in such case we have:
$$P(L)=-L$$
So Lagrangian is P-odd quantity. Is it normal? Is in physics P-odd Lagrangians somewhere else? What about week interaction? Is week interaction conserve parity of Lagrangian?

 

[illuminates]

it seems the topic is needed to shift in "High Energy, Nuclear, Particle Physics".

 

[PeterDonis]

it seems the topic is needed to shift in "High Energy, Nuclear, Particle Physics".

Thread has been moved.

 

[Orodruin]

The SU(2) of electroweak interactions break parity maximally as it is a V-A type interaction. It does not include interactions with right-handed particles.

 

[illuminates]

The SU(2) of electroweak interactions break parity maximally as it is a V-A type interaction. It does not include interactions with right-handed particles.

Thank you for replying. Would you say my reasoning above is true?

 

[Urs Schreiber]

So Lagrangian is P-odd quantity. Is it normal?

By the way, this parity behaviour of the theta-term is the basis for the Vafa-Witten mechanism, supposed to explain that classically $\theta = 0$. See Vafa-Witten 84.