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

Abstract

In a previous paper [1], we studied the ${\eta }^{\prime }$ 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 $\theta =0$. The coupling does not lead to new divergences (not present for $\sin \theta =0$) 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 $|\sin \theta |\lesssim 10^{-11}$ . This fact eliminates the need to fine-tune $\theta$ or for the axion field.

Comments: 16 pages, 1 figure