Constraining CP-phases in SUSY: an interplay of muon/electron $g-2$ and electron EDM

TL;DR

This paper investigates how measurements of muon and electron g-2 and electron EDM constrain CP-phases in the MSSM, providing upper limits and exploring parameter space cancellations to inform SUSY model building.

Contribution

It derives analytical and numerical upper limits on CP-phases in MSSM using g-2 and EDM data, highlighting the constraints' implications for SUSY models.

Findings

Muon g-2 and electron EDM constrain CP-phases below 1.9×10⁻⁵ radians.

Electron g-2 and EDM constraints limit CP-phases under 3.9×10⁻⁶ radians.

Parameter space cancellations can relax CP-phase constraints by orders of magnitude.

Abstract

The minimal supersymmetric standard model (MSSM) with complex parameters can contribute sizably to muon/electron anomalous magnetic dipole momemnt ($g-2$) and electric dipole moment (EDM). The electron $g-2$ interplays with electron EDM; the muon $g-2$ can also interplay with electron EDM assuming the universality between smuon and selectron masses, either of which can constrain the relevant CP-phases in the MSSM. In this work, we first use such an interplay to derive an approximate analytical upper limit on the relevant CP-phase. Then we extensively scan the parameter space to obtain more accurate upper limits. We obtain the following observations: (i) The muon $g-2$ in the $2\sigma$ range combined with the electron EDM upper limit (assuming the universality between smuon and selectron masses) typically constrains the relevant CP-phase under $1.9\times 10^{-5} (\text{rad})$; (ii) The electron $g-2$ in the $2\sigma$ range (Berkeley) interplays with the electron EDM upper limit (without assuming the universality between smuon and selectron masses) constrains the relevant CP-phase under $3.9\times 10^{-6}(\text{rad})$ (also requiring muon $g-2$ in the allowed $2\sigma$ range). We also find some special cancellations in the parameter space which can relax the constraints by a couple of orders. Such stringent limits on CP-phases may pose a challenge for model building of SUSY, i.e., how to naturally suppress these phases.