Updated Constraints from Electric Dipole Moments in the MSSM with R-Parity Violation

TL;DR

This work tackles CP violation in the MSSM with trilinear RPV by re-evaluating two-loop Barr–Zee EDM contributions, using a generic gauge framework and a CKM-based SM CP phase. It cross-checks analytic results against the literature, clarifies flavor-basis conventions, and derives updated constraints on RPV couplings from the latest electron and neutron EDM measurements. A key outcome is a testable correlation between neutron and proton EDMs that arises when down-type quark dipole moments dominate, offering a distinctive signature for future EDM experiments. The study also maps out how constraints vary with slepton and sneutrino masses and discusses regions where cancellations weaken electron bounds but leave neutron bounds stronger, guiding future explorations of the RPV parameter space. Overall, the results sharpen the limits on LLE and LQD couplings in the RPV-MSSM and motivate direct proton EDM measurements as a critical probe of these CP-violating interactions.

Abstract

We revisit the electric dipole moments (EDMs) of quarks and leptons in the Minimal Supersymmetric Standard Model (MSSM) with trilinear $R$-parity violation (RPV). In this framework, EDMs are induced at the two-loop level via RPV interactions. We perform a comprehensive recalculation of several classes of Barr-Zee type diagrams in a general $R_ξ$ gauge. While we find general agreement with previous analytic results in the literature, our work provides a valuable independent cross-check of the complicated calculations. We also point out some subtleties in the intermediate steps and in the choice of the flavor basis for the numerical evaluation of the expressions. By confronting the theoretical predictions with the latest experimental limits on EDMs, we derive updated constraints on combinations of RPV couplings. We highlight an approximate, testable correlation between the proton and neutron EDM that emerges within the considered class of RPV models, offering a distinctive signature for future EDM experiments.

Figures (7)

• Figure 1: Example Barr--Zee diagrams with lepton or quark loops, that contribute to lepton and quark EDMs (left and center) or quark chromo EDMs (right).
• Figure 2: Example Barr--Zee diagrams with slepton or squark loops, that contribute to lepton and quark EDMs (left and center) or quark chromo EDMs (right).
• Figure 3: Example two-loop diagrams involving neutralinos, charginos, and gluinos that contribute to lepton and quark EDMs (left and center) or quark chromo EDMs (right). In the first and third panels, we do not indicate the arrows on the neutrino fermion lines, as their directions are reversed depending on whether the left- or right-handed sfermion is considered.
• Figure 4: Constraints on combinations of RPV couplings in their complex plane, derived from the current 95% CL experimental bounds on the electron (blue contours) and neutron (red contours) EDMs with all sfermion masses involved in the calculation specified to be 1 TeV. The shaded blue and red regions indicate parameter space disfavored by the respective EDM limits.
• Figure 5: Contour plots illustrating the 95% CL constraints on four representative combinations of RPV couplings as functions of the charged slepton and sneutrino masses. Panels (a) and (b) correspond to constraints derived from the electron EDM, while panels (c) and (d) show those from the neutron EDM. In all plots, the masses of other relevant supersymmetric particles in the first loop are assumed to be $1$ TeV.