CP Violation and the Muon Anomaly in N=1 Supergravity

The one loop supersymmetric electro-weak correction to the anomalous magnetic moment of the muon is derived in the minimal N=1 supergravity unification with two CP violating phases. A numerical analysis of the CP violating effects on $g_{\mu}-2$ is carried out with the cancellation mechanism to guarantee the satisfaction of the experimental limits on the electric dipole moments of the electron and on the neutron. It is found that the effects of the CP phases can significantly affect the supersymmetric electro-weak correction to $g_{\mu}-2$, and that the numerical size of such a correction can be as large or larger than the Standard Model electro-weak correction to $g_{\mu}-2$. These results are of import for the new Brookhaven experiment which is expected to increase the sensitivity of the $g_{\mu}-2$ measurements by a factor of 20 and allow for a test of the electro-weak correction in the near future.