We investigate the sensitivity of the next generation of flavor-based low-energy experiments to probe the supersymmetric parameter space in the context of the phenomenological MSSM (pMSSM), and examine the complementarity with direct searches for Supersymmetry at the 13 TeV LHC in a quantitative manner. To this end, we enlarge the previously studied pMSSM parameter space to include all physical non-zero CP-violating phases, namely those associated with the gaugino mass parameters, Higgsino mass parameter, and the tri-linear couplings of the top quark, bottom quark and tau lepton. We find that future electric dipole moment and flavor measurements can have a strong impact on the viability of these models even if the sparticle spectrum is out of reach of the 13 TeV LHC. In particular, the lack of positive signals in future low-energy probes would exclude values of the phases between ${cal O}(10^{-2})$ and ${cal O}(10^{-1})$. We also find regions of parameter space where large phases remain allowed due to cancellations. Most interestingly, in some rare processes, such as BR($B_s to mu^+ mu^-$ ), we find that contributions arising from CP-violating phases can bring the potentially large SUSY contributions into better agreement with experiment and Standard Model predictions.
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