The Strong CP Problem

The QCD Lagrangian presented so far has discrete global symmetries under C (charge), P (parity) and T (time reversal). The most general Lagrangian with SU(Nc) gauge symmetry contains one more term

${\mathcal{L}}_{\theta }=\frac{\theta g_s^2}{32{\pi }^2}tr[F_{\mu \nu }{\tilde{F}}^{\mu \nu }]\text{ with }{\tilde{F}}^{\mu \nu }={ϵ}^{\mu \nu \rho \sigma }{F}_{\rho \sigma }$

This term violates CP symmetry and can contribute non-perturbatively. Current experimental bounds on neutron dipole moment indicate that $\theta <10^{-10}$. The fact that this term is very small (almost zero) is called the strong CP problem.