A few thoughts on $\theta$ and the electric dipole moments

Abstract

I highlight a few thoughts on the contribution to the dipole moments from the so-called $\theta$ parameter. The dipole moments are known can be generated by $\theta$. In fact, the renowned strong $\mathcal{C}\mathcal{P}$ problem was formulated as a result of non-observation of the dipole moments. What is less known is that there is another parameter of the theory, the ${\theta }_{QED}$ which becomes also a physical and observable parameter of the system when some conditions are met. This claim should be contrasted with conventional (and very naive) viewpoint that the ${\theta }_{\mathrm{QED}}$ is unphysical and unobservable. A specific manifestation of this phenomenon is the so-called Witten effect when the magnetic monopole becomes the dyon with induced electric charge $e^{\prime }=-e\frac{{\theta }_{QED}}{2\pi }$. We argued that the similar arguments suggest that the electric magnetic dipole moment $\mu$ of any microscopical configuration in the background of ${\theta }_{QED}$ generates the electric dipole moment $⟨d_{\mathrm{ind}}⟩$ proportional to ${\theta }_{QED}$, i.e. $⟨d_{\mathrm{ind}}⟩=-\frac{{\theta }_{\mathrm{QED}}\cdot \alpha }{\pi }\mu$. We also argue that many $\mathcal{C}\mathcal{P}$ correlations such as $⟨{\vec{B}}_{\mathrm{ext}}\cdot \vec{E}⟩=-\frac{\alpha {\theta }_{\mathrm{QED}}}{\pi }{\vec{B}}_{\mathrm{ext}}^2$ will be generated in the background of an external magnetic field ${\vec{B}}_{\mathrm{ext}}$ as a result of the same physics.

arXiv comment6 pages. arXiv admin note: text overlap with arXiv:1702.00012

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