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

Abstract

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 ${\ensuremath{\pi}}^{0}$ and $\ensuremath{\eta}$ photoproduction amplitudes and the strengths of the ${\ensuremath{\pi}}^{0}$ and $\ensuremath{\eta}$ tadpoles. The strengths of these tadpoles are evaluated in the soft-pion and soft-$\ensuremath{\eta}$ 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 $\ensuremath{\eta}$ tadpole is found to be negligible for most cases, when compared with that of the ${\ensuremath{\pi}}^{0}$ tadpole. Making reasonable estimates of the photoproduction amplitudes, the dipole moment is found to be $|d|\ensuremath{\simeq}0.9(sin\ensuremath{\varphi}+0.06sin\ensuremath{\xi})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ e cm if the mass of the intermediate boson is 5 BeV; $\ensuremath{\varphi}$ and $\ensuremath{\xi}$ are the phase angles associated with the strangeness-conserving and strangeness-violating axial-vector currents, respectively.