Upper bounds on rare K and B decays from minimal flavour violation

We study the branching ratios of rare K and B decays in models with minimal flavour violation, using the presently available information from the universal unitarity triangle analysis and from the measurements of Br (B → X_s γ), Br(B → X_s l⁺l^-) and Br(K⁺ → π⁺ νν̄). We find the following upper bounds: Br(K⁺ → π⁺ νν̄) < 11.9 × 10^-11, Br(K_L → π⁰ νν̄) < 4.6 × 10^-11, Br(K_L→ μ⁺μ^-)_SD < 1.4 × 10^-9, Br(B → X_s νν̄) < 5.2 × 10^-5 Br(B → X_d νν̄) < 2.2 × 10^-6, Br(B_s → μ⁺ μ^-) < 7.4 × 10^-9, Br(B_d → μ⁺ μ^-) < 2.2 × 10^-10 at 95% probability. We analyze in detail various possible scenarios with positive or negative interference of Standard Model and new physics contributions, and show how an improvement of experimental data corresponding to the projected 2010 B factory integrated luminosities will allow to disentangle and test these different possibilities. Finally, anticipating that subsequently the leading role in constraining this kind of new physics will be taken over by the rare decays K⁺ → π⁺ νν̄, K_L → π⁰ νν̄ and B_s,d → μ⁺ μ^-, that are dominated by the Z⁰-penguin function C, we also present plots for several branching ratios as functions of C. We point out an interesting triple correlation between K⁺ → π⁺ νν̄, B → X_s γ and B → X_sl⁺l^- present in MFV models.