Paper detail

Electric Dipole Moment from QCD $θ$ and How It Vanishes for Mixed States

In a previous paper [1], we studied the $η'$ mass and formulated its chirally symmetric coupling to fermions which induces electric dipole moment (EDM). Here we calculate the EDM to one-loop. It is finite, having no ultraviolet divergence while its infrared divergence is canceled by soft photon emission processes \emph{exactly} as for $θ=0$. The coupling does not lead to new divergences (not present for $\sinθ=0$) in soft photon processes either. Furthermore, as it was argued previously [1], the EDM vanishes if suitable mixed quantum states are used. This means that in a quantum theory based on such mixed states, a strong bound on EDM will not necessarily lead to a strong bound such as $|\sin θ|\lesssim 10^{-11}$ . This fact eliminates the need to fine-tune $θ$ or for the axion field.