CP-Violating Phases in SUSY, Electric Dipole Moments, and Linear Colliders

TL;DR

This paper investigates CP-violating phases in the MSSM under stringent EDM constraints, showing that while $|θ_b_mu|$ is typically forced to be small, cancellations among SUSY contributions can allow sizable phases in extended models. It performs comprehensive Monte Carlo scans across mSUGRA-like and general MSSM parameter spaces to map viable regions and quantify tuning needs. It then analyzes how CP-violating phases, particularly $φ_1$ (phase of $M_1$), could be extracted from neutralino/chargino masses and cross sections at a future Linear Collider, including the impact of EDM limits and a minimal observable set; results indicate $φ_1$ could be measured to ≈$0.03π$ with high luminosity, provided some information on $|bμ|$ is available. The study also constructs CP-odd kinematic variables at a linear collider and finds CP asymmetries of order $0.1$–$1.5eta$, which are challenging to observe due to small size and experimental systematics. Overall, the work highlights the delicate balance between EDM constraints, collider observables, and the prospects for unambiguous CP-violation detection in SUSY.

Abstract

We reexamine large CP-violating phases in the general Minimal Supersymmetric Standard Model, as well as more restricted models. We perform a detailed scan over parameter space to find solutions which satisfy the current experimental limits on the electric dipole moments of the electron, neutron and $^{199}$Hg atom, exploring the allowed configurations of phases and masses, and we attempt to quantify the level of tuning of the parameters necessary to populate the regions of cancellations. We then consider the measurement of CP-violating phases at a future linear collider. We find that measurements of chargino and neutralino masses and production cross-sections allow for a determination of $φ_1$(the phase of $M_1$) to a precision of $π/30$, while the EDM constraints require that $θ_μ$ be too small to be measured. Using the EDM constraints we find that the CP-even model parameters and the phase $φ_1$ can be determined at a Linear Collider with $400 \gev$ c.m. energy. As long as some information on the size of $|μ|$ is included in the observables, a measurement of $φ_1$ is guaranteed for $φ_1 > π/10$. To unambiguously identify CP violation, we construct CP-odd kinematical variables at a linear collider. However, the CP asymmetries are rather small, typically about $0.1-1.5%$, and it will be challenging to experimentally observe the predicted asymmetries.

Figures (13)

• Figure 1: Diagrams contributing to the electric dipole moment of the electron. The SUSY phases enter at the crossed vertices.
• Figure 2: Diagram contributing to the electric dipole moment of the down quark. The SUSY phases enter at the crossed vertices.
• Figure 3: mSUGRA solutions satisfying the experimental limits on the electron, neutron and $^{199}$Hg EDMs.
• Figure 4: Parameter sets in the 15-parameter MSSM satisfying the experimental limits on the electron, neutron and $^{199}$Hg EDMs. Open circles suffer from parameter tuning $\Delta X/X$ worse than 1% (see the text). Light (green) dots correspond to configurations with a light Higgs $m_h<113\,\hbox{GeV}$. The tuning parameter $\Delta X/X$ is defined in the text, and corresponds to the maximum variation that the point survives.
• Figure 5: For the 15-parameter MSSM scan, the dependence of the solutions on the light and heavy chargino masses. Open circles suffer from parameter tuning $\Delta X/X$ worse than 1% (see the text). Light (green) dots correspond to configurations with a light Higgs $m_h<113\,\hbox{GeV}$.