We present a detailed analysis together with numerical calculations on one-loop contributions to the neutron, deuteron, and mercury electric dipole moment from supersymmetry without $R$ parity, focusing on the quark-scalar loop contributions. Being proportional to top Yukawa and top mass, such contributions are often large, and since these are proportional to hitherto unconstrained combinations of bilinear and trilinear $R$-parity violating (RPV) parameters, they are all the more interesting. Complete formulas are given for the various contributions through the quark dipole operators including the contribution from the color dipole operator. The contribution from the color dipole operator is found to be a similar order in magnitude when compared to the electric dipole operator and should be included in any consistent analysis. Analytical expressions illustrating the explicit role of the $R$-parity violating parameters are given following perturbative diagonalization of mass-squared matrices for the scalars. Dominant contributions come from the combinations $B_i^{*}{\lambda }_{ij1}^{\prime }$ for which we obtain robust bounds. It turns out that neutron and deuteron electric dipole moments (EDMs) receive much stronger contributions than the mercury EDM and any null result at the future deuteron EDM experiment or Los Alamos neutron EDM experiment can lead to extraordinary constraints on RPV parameter space. Even if $R$-parity violating couplings are real, Cabibbo-Kobayashi-Maskawa (CKM) phase does induce RPV contribution and for some cases such a contribution is as strong as the contribution from phases in the $R$-parity violating couplings. Hence, we have bounds directly on $|B_i^{*}{\lambda }_{ij1}^{\prime }|$ even if the RPV parameters are all real. Interestingly, even if slepton mass and/or ${\mu }_0$ is as high as 1 TeV, it still leads to neutron EDM that is an order of magnitude larger than the sensitivity at the Los Alamos experiment. Since the results are not much sensitive to $\tan \beta$, our constraints will survive even if other observables tighten the constraints on $\tan \beta$.

• Received 29 December 2006

DOI:https://doi.org/10.1103/PhysRevD.76.013003