Constraints on explicitCPviolation from the Brookhaven muong−2experiment

We use the recently derived $\mathrm{CP}$ phase dependent analytic results for the supersymmetric electroweak correction to $g_{\mu }-2$ to constrain the explicit $\mathrm{CP}$ phases in softly broken supersymmetry using the new physics effect seen in the $g-2$ Brookhaven measurement. It is shown that the BNL data strongly constrain the $\mathrm{CP}$ violating phase ${\theta }_{\mu }$ (the phase of the Higgs mixing parameter $\mu )$ and ${\xi }_2$ [the phase of the SU(2) gaugino mass $m_2]$ and as much as 60–90 % of the region in the ${\xi }_2-{\theta }_{\mu }$ plane is eliminated over a significant region of the MSSM parameter space by the BNL constraint. The region of $\mathrm{CP}$ phases not excluded by the BNL experiment allows for large phases and for a satisfaction of the EDM constraints via the cancellation mechanism. We find several models with large $\mathrm{CP}$ violation which satisfy the EDM constraint via the cancellation mechanism and produce an $a_{\mu }^{\mathrm{SUSY}}$ consistent with the new physics signal seen by the Brookhaven experiment. The sparticle spectrum of these models lies within reach of the planned accelerator experiments.