Electric Dipole Moments in the MSSM Reloaded

TL;DR

This work performs a comprehensive, CP-violating MSSM EDM computation for Tl, neutron, Hg, and deuteron, incorporating all one-loop diagrams, the dominant Barr–Zee two-loop effects, the CP-odd Weinberg operator, and Higgs-mediated four-fermion operators. It advances prior treatments by resumming CP-violating Higgs-boson mixing and including threshold corrections to light-quark Yukawas, with analytic results implemented in CPsuperH2.0. The study demonstrates that sizeable CP-violating phases can be consistent with current EDM limits due to intricate cancellations across contributions, and it shows that the deuteron EDM provides particularly strong sensitivity to these phases. By applying the framework to CPX, trimixing, and MCPMFV scenarios, the paper maps viable regions of parameter space and clarifies how future EDM measurements, especially of the deuteron, can probe otherwise unconstrained CP-violating observables. These insights have implications for interpreting LHC-era CP violation and guiding low-energy searches for new physics.

Abstract

We present a detailed study of the Thallium, neutron, Mercury and deuteron electric dipole moments (EDMs) in the CP-violating Minimal Supersymmetric extension of the Standard Model (MSSM). We take into account the complete set of one-loop graphs, the dominant Higgs-mediated two-loop diagrams, the complete CP-odd dimension-six Weinberg operator and the Higgs-mediated four-fermion operators. We improve upon earlier calculations by including the resummation effects due to CP-violating Higgs-boson mixing and to threshold corrections to the Yukawa couplings of all up- and down-type quarks and charged leptons. As an application of our study, we analyse the EDM constraints on the CPX, trimixing and Maximally CP- and Minimally Flavour-Violating (MCPMFV) scenarios. Cancellations may occur among the CP-violating contributions to the three measured EDMs arising from the 6 CP-violating phases in the MCPMFV scenario, leaving open the possibility of relatively large contributions to other CP-violating observables. The analytic expressions for the EDMs are implemented in an updated version of the code CPsuperH2.0.

Figures (28)

• Figure 1: Generic Feynman diagram for the EDM $(d^E_f)^\chi$ of the fermion $f$ induced by $\chi$ exchange effects. The photon line can be attached to the sfermion $\tilde{f'}$ line, or to the $\chi$ line if $\chi=\tilde{\chi}^\pm_i$.
• Figure 2: Typical Feynman diagrams for $(d^{\,G})^{\tilde{g}}$ and $(d^{\,G})^{H}$. The $H_i$ lines denote all three neutral Higgs bosons including CP-violating Higgs-boson mixing. Heavy dots indicate resummation of threshold corrections to the corresponding Yukawa couplings.
• Figure 3: The functional dependence of $z_q | H(z_1,z_2,z_q) |$ on $z_q$ for several values of $z_s\equiv z_1=z_2$. When $z_s \leq 4$, $H(z_1,z_2,z_q)$ becomes negative when $z_q$ is larger than a specific value.
• Figure 4: Feynman diagrams for CP-odd four-fermion operators. The $H_i$ line denotes all three neutral Higgs bosons including CP-violating Higgs-boson mixing. Heavy dots indicate resummation of threshold corrections to the corresponding Yukawa couplings.
• Figure 5: Barr-Zee diagrams: the $H_i$ lines denote all three neutral Higgs bosons, including CP-violating Higgs-boson mixing, and heavy dots indicate resummation of threshold corrections to the corresponding Yukawa couplings.