Exploring Supersymmetric CP Violation after LHC Run 2 with Electric Dipole Moments and B Observables

We consider the prospects for measuring distinctive signatures of the CP-violating phases in the minimal supersymmetric extension of the Standard Model (MSSM) in light of the limits on sparticle masses from searches at the LHC. We use the CPsuperH code to evaluate model predictions and scan the parameter space using a geometric approach that maximizes CP-violating observables subject to the current upper limits on electric dipole moments (EDMs). We focus on the possible CP-violating asymmetry $A_{\mathrm{CP}}$ in $b \rightarrow s \gamma $ decay and on a possible CP-violating contribution to the $B_s - {\overline{B}}_s$ mass difference $\Delta M^{NP}_{B_s}$, as well as future measurements of the EDMs of the proton, neutron and electron. We find that the current LHC and EDM limits are consistent with values of $A_{\mathrm{CP}}$, $\Delta M^{NP}_{B_s}$ and the proton EDM that are measurable with the Belle-II detector, LHCb and a proposed measurement of the proton EDM using a storage ring, respectively. Measurement of a non-zero proton EDM would constrain $A_{\mathrm{CP}}$ significantly, but it and a CP-violating contribution to $\Delta M^{NP}_{B_s}$ could still be measurable, along with neutron and electron EDMs. A more accurate measurement of $A_{\mathrm{CP}}$ with the current central value would favour stop and chargino masses within reach of future LHC runs as well as a potentially measurable value of $\Delta M^{NP}_{B_s}$.