Electric Dipole Moment of the Neutron in theV−AeiφTheory of Weak Interactions

We estimate the electric dipole moment $d$ of the neutron in a theory where weak interactions are mediated by an intermediate boson and where $\mathrm{CP}$ violation arises from phase angles between vector and axial-vector currents. Following the dispersion-theoretic tadpole model of Babu and Suzuki, we evaluate $d$ in terms of the ${\pi }^0$ and $\eta$ photoproduction amplitudes and the strengths of the ${\pi }^0$ and $\eta$ tadpoles. The strengths of these tadpoles are evaluated in the soft-pion and soft-$\eta$ limits, respectively, by making use of the hypothesis of partially conserved axial-vector current, current algebra, and Weinberg's sum rules. The result is found to diverge logarithmically with the mass of the intermediate boson. The contribution of the $\eta$ tadpole is found to be negligible for most cases, when compared with that of the ${\pi }^0$ tadpole. Making reasonable estimates of the photoproduction amplitudes, the dipole moment is found to be $\mathrm{}\left|d\right|\mathrm{}\simeq 0.9(sin\phi +0.06\mathrm{}sin\xi )\times {10}^{-19\mathrm{}}$ e cm if the mass of the intermediate boson is 5 BeV; $\phi$ and $\xi$ are the phase angles associated with the strangeness-conserving and strangeness-violating axial-vector currents, respectively.