Electric Dipole Moments Do Not Require the CP-violating Phases of Supersymmetry To Be Small

TL;DR

This work demonstrates that in the general MSSM, electric dipole moment bounds do not necessitate tiny CP-violating phases. By performing a fully general one-loop EDM calculation with seven physical phases and allowing light superpartners, the authors show that cancellations among chargino, neutralino, and gluino contributions can accommodate large phases while satisfying experimental EDM limits. The analysis reveals that electron and neutron EDM constraints induce specific correlations among phases (notably $\varphi_\mu$ with $\varphi_1$ and $\varphi_{A_e}$ for the electron, and with $\varphi_3$ for the neutron), and these cancellations become milder as the SUSY spectrum grows heavier or $\mu$ increases. The findings have broad implications for interpreting SUSY parameters, dark matter properties, and collider signatures, and underscore the importance of directly measuring CP-violating phases to uncover the mechanism of SUSY breaking.

Abstract

We report the first fully general numerical calculation of the neutron and electron dipole moments, including the seven significant phases. We find that there are major regions in the parameter space where none of the phases are required to be small, contrary to the conventional wisdom. The electric dipole moments (EDM's) do provide useful constraints, allowing other regions of parameter space to be carved away. We keep all superpartner masses light so agreement with experimental limits arises purely from interesting relations among soft breaking parameters.

Figures (7)

• Figure 1: One loop Feynman diagrams contributing to the calculation of the electric dipole moments in the MSSM. The gluon and photon line can originate on any internal leg carrying corresponding charge.
• Figure 2: Illustration of the cancellation mechanism in the EDM calculation. See the discussion in the text. Frame a includes the contributions to the electron dipole moment arising from neutralino and chargino loops contributions to the $C_1$ Wilson coefficient for varying $\varphi_{\mu}$, $\varphi_{1}\sim \pi$ and values of $\varphi_{A_e}$ sampled randomly. A standard set of parameters (see text) with $\mu=700\, {\rm GeV}$ was used. Frame b shows the neutron EDM contribution from the gluino loop graph projection into $C_1$ and $C_2$ ($\tilde{g_1}$ and $\tilde{g_1}$, from the chargino loop contribution to $C_1$ ($\tilde{C_1}$) and from the gluino-top-stop graph contributing through the purely gluonic operator Wilson coefficient $C_3$ ($G$). In this case, the standard set of parameters is adopted with $\mu=300\, {\rm GeV}$, $\varphi_{3}\sim \pi$ and $\varphi_{A_q}\sim 0$ for $q=u,d,t$. In both cases the natural cancellations can give a total of order the experimental limits for most or all of $\varphi_{\mu}$. If the cancellation effects were not included one would conclude that all phases would have to be of order $10^{-2}$ to not exceed the experimental limits.
• Figure 3: Plots of regions allowed by the electron (filled circles) and neutron (open circles) EDM limits in the $\varphi_{\mu}-\varphi_{1}$ plane (frame a) and the $\varphi_{\mu}-\varphi_{3}$ plane (frame b). A value of $\mu=450\, {\rm GeV}$ was chosen together with the standard parameter set and all phases were sampled randomly.
• Figure 4: Same as Fig. 3, but for $\mu=60\, {\rm GeV}$ and the standard set of parameters. Again, all phases were varied randomly.
• Figure 5: Frame a shows variation of the $\varphi_{\mu}$ allowed region with $\mu$ for the standard set of parameters and other phases sampled randomly. The values of $A=A_e=A_u=A_d=A_t$ were also varied from $-500\,{\rm GeV}$ to $500\,{\rm GeV}$. Open (full) circles denote points allowed by the neutron (electron) EDM limit. Frame b demonstrates variation of the $\varphi_{\mu}$ range allowed by the electron EDM limits with the values of $A$ for $\mu=450\, {\rm GeV}$.