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

TL;DR

This paper calculates the electric dipole moment (EDM) induced by QCD $ heta$ term, showing it is finite and vanishes for mixed states, challenging the necessity of fine-tuning $ heta$ or axion fields.

Contribution

It demonstrates that the QCD $ heta$-induced EDM is finite and vanishes in mixed quantum states, offering a new perspective on the strong CP problem.

Findings

EDM is finite and free of ultraviolet divergence.

Infrared divergence cancels with soft photon emission.

EDM vanishes for suitable mixed states, reducing constraints on $ heta$.

Abstract

In a previous paper [1], we studied the $\eta'$ 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.