quantum field theory - Expected consequence of the term $theta F^{munu}tilde{F}_{munu}$ in the Standard Model

There is a coupling in the standard model of the form $\theta F^{\mu\nu}\tilde{F}_{\mu\nu}$ where $F^{\mu\nu}$ is the QCD field strength. I've read that $\theta<10^{-8}$, which is speculated to be related to Peccei-Quinn symmetry.

1. 
   

   What would be the consequences of this term if $\theta$ were not small? In particular, I know that this term is CP-violating. How will this CP-violation be manifested in experiments?

   
   
   


2. 
   

   How do we know $\theta<10^{-8}$?

   
   

Answer

To answer point $2$, $\theta$ is derived from the neutron elecric dipole moment that is measured to be like $<10^{-18}\,\text{e}\cdot\text{m}$. You can prove that the dipole moment is proportional to $\theta$ and from that you can get your upper limit for $\theta$. See Donoghue, Golowich, Holstein - "Dynamics of the Standard Model", pages 44-45 for more details.

As far as your first question is concerned, a value of $\theta$ different from $0$ would make $CP$ not a symmetry for QCD, but I don't really know what effect this could have in detail.