Higgs-Higgsino-Gaugino Induced Two Loop Electric Dipole Moments

TL;DR

This work addresses electric dipole moments (EDMs) in the MSSM with heavy sfermions, where one-loop contributions are suppressed and two-loop Higgs–gauge mediated diagrams become crucial. It derives complete analytic expressions for two-loop Barr-Zee type diagrams involving a chargino–neutralino loop exchanged with Higgs and gauge bosons, including $ZA^0$ and $WH^\pm$ channels, and provides explicit formulas with loop functions $j(r,r')$. Numerical analysis under electroweak baryogenesis–motivated benchmarks shows these new contributions often dominate the EDMs of the electron and neutron, with $d_e$ mainly from $\gamma H^0$, $\gamma A^0$, and $WH^\pm$ and $d_n$ from $ZA^0$, $ZH^0$, and $WH^\pm$, while the results scale with $\sin\phi_\mu$ and are sensitive to $\tan\beta$ and $m_{A^0}$. The findings have significant implications for EDM searches and the viability of MSSM electroweak baryogenesis, highlighting the need to include these contributions in phenomenological analyses.

Abstract

We compute the complete set of Higgs-mediated chargino-neutralino two-loop contributions to the electric dipole moments (EDMs) of the electron and neutron in the minimal supersymmetric standard model (MSSM). We study the dependence of these contributions on the parameters that govern CP-violation in the MSSM gauge-gaugino-Higgs-Higgsino sector. We find that contributions mediated by the exchange of W H^\pm and Z A^0 pairs, where H^\pm and A^0 are the charged and CP-odd Higgs scalars, respectively, are comparable to or dominate over those mediated by the exchange of neutral gauge bosons and CP-even Higgs scalars. We also emphasize that the result of this complete set of diagrams is essential for the full quantitative study of a number of phenomenological issues, such as electric dipole moment searches and their implications for electroweak baryogenesis.

Figures (5)

• Figure 1: All the two-loop diagrams with chargino-neutralino loop mediated by Higgs bosons. (Mirror graphs are not displayed.)
• Figure 2: A break-up of the various Higgs-mediated chargino-neutralino two-loop contributions to the electron (left) and neutron (right) electric dipole moment. Black lines correspond to positive values, red lines to negative values. In the right panel we show the various down-quark contributions times a factor 4/3, as well as the global up-quark contribution (times a factor -1/3). All SUSY parameters, except $\tan\beta$, are fixed to the reference setup.
• Figure 3: Exclusion limits for the electron (left) and neutron (right) electric dipole moment, on the ($\tan\beta,m_{A^0}$) plane, for $M_1=145$ GeV, $M_2=290$ GeV, $\mu=300$ GeV and for various values of the CP violating phase $|\sin\phi_\mu|$. For each value of $|\sin\phi_\mu|$, parameter space points below the corresponding line are excluded, while those above the line are allowed.
• Figure 4: Exclusion limits for the electron (left) and neutron (right) electric dipole moment, on the ($M_1,\mu$) plane. We assume the gaugino unification mass relation $M_2\simeq2M_1$, and vary the CPV phase $\sin\phi_\mu$ (see the text for further details on the model assumptions). In the upper right corner of the left panel we also show the contour of electron EDM equal to $10^{-27}$ e cm, for maximal CPV phase.
• Figure 5: Exclusion limits for the electron (left) and neutron (right) electric dipole moment, on the ($M_2,\mu$) plane. We assume here the anomaly-mediated SUSY breaking gaugino mass relation $M_1\simeq3M_2$. In the upper right corner of the left panel we also show the contour of electron EDM equal to $10^{-27}$ e cm, for maximal CPV phase.