Theoretical Predictions for Neutron and Electron Dipole Moments

Abstract

Just to get a feeling of possible values of the neutron EDM d_n, let us start with a naive estimate as follows:

$$\begin{gathered} d{\text{n/e}} \approx {\text{m}}_{\text{p}}^{{\text{ - 1}}} \times Gm_\pi ^2 \times \eta \hfill \\ {\text{ }} \approx 2 \times {10^{ - 14}}{\text{cm}} \times {\text{2}} \times {\text{1}}{{\text{0}}^{{\text{ - 7}}}} \times 2 \times {10^{ - 3}} \hfill \\ \end{gathered} $$

(5.1)

$$ \approx {10^{ - 24}} - {10^{ - 23}}cm.$$

(5.2)

The first term here, the Compton wavelength of a proton, is a normal scale, that of a nucleon magnetic moment. The second one is the characteristic relative magnitude of weak interactions in hadronic processes (the typical momenta used to construct a dimensionless factor from the Fermi weak interaction constant G are assumed to be comparable to the pion mass m_π). Finally, one may expect that the CP-odd part of the weak interaction is somehow suppressed as compared to the CP-even one. As a natural value of this suppression factor η we take, for the third term, the ratio of the CP-odd and CP-even amplitudes in the decays of K⁰ mesons.