10 14 10 15 10 16 10 17 m$_{M}$ GLYPH<LBracket1> GeV GLYPH<RBracket1> 10 GLYPH<Minus> 8 10 GLYPH<Minus> 6 10 GLYPH<Minus> 4 0.01 1 r r$_{3}$ FIG. 2: The three solid blue curves give r/r$_{3}$ as a function of the messenger scale for N$_{M}$ = 1 (upper), N$_{M}$ = 3 (middle) and N$_{M}$ = 10 (lower). The three pairs of horizontal lines give upper bounds on r/r$_{3}$ and correspond to the following flavor scenarios for the gravity-mediated contributions: (i) Full anarchy (solid, pink) – Eq. (5.14) with tan β = 3; (ii) Anarchy with vanishing or Yukawa-like A -terms (dashed, green) – Eq. (5.7); (iii) FN structure (dotted, black) – Eq. (4.3). For a given number of messengers and a given flavor scenario, FCNC and CP constraints give an upper bound on the messenger scale, which can be read from the crossing point of the corresponding blue and horizontal curves. related by ( m max M )$_{A}$$_{∼}$$_{0}$$_{,Y}$ ∼ ( m$_{d}$/m$_{s}$ ) 1 / 4 ( m max M )$_{FN}$. In both cases, In the fully anarchical case, the EDM constraints yield a stronger bound: Measurements in low energy experiments of flavor-changing and of CP-violating processes will complement direct searches for new physics. Our goal in this work has been to under- stand concrete ways in which such complementarity will take effect. In order to do that, we chose to work in a specific framework, which is supersymmetry where the soft breaking terms receive dominant contributions from gauge-mediation and sub-dominant contributions from 22 VI. CONCLUSIONS m$_{M}$/m$_{Pl}$ ∼ < 10 − 5 (full anarchy) . (5.25) m$_{M}$/m$_{Pl}$ ∼ < 10 − 3 (FN , or anarchy with A ∼ 0 ,Y ) . (5.24)