Theta Vacua, QCD Sum Rules, and the Neutron Electric Dipole Moment

We present a detailed study of the electric dipole moment of the neutron induced by a vacuum theta angle within the framework of QCD sum rules. At next-to-next-to leading order in the operator product expansion, we find the result $d_n(\th) = 1.2\times 10^{-16}\bar \theta e\cdot cm$, to approximately 40% precision. With the current experimental bound this translates into a limit on the theta parameter of $|\bar \theta|<6\times 10^{-10}$. We compare this result with the long-standing estimates obtained within chiral perturbation theory, and observe a numerical similarity, but also significant differences in the source of the dominant contribution.