The return of kaon flavour physics

Kaon flavour physics has played in the 1960s and 1970s a very important role in the construction of the Standard Model (SM) and in the 1980s and 1990s in SM tests with the help of CP violation in K_L → ππ decays represented by ε_K and the ratio ε/ε. In this millennium, this role has been taken over by B_s,d and D mesons. However, there is no doubt that in the coming years, we will witness the return of kaon flavour physics with the highlights being the measurements of the theoretically clean branching ratios for the rare decays K⁺ → π⁺νν¯ and K_L → π⁰νν¯, and the improved SM predictions for the ratio ε/ε, for ε_K and the K⁰–K^{¯ 0} mixing mass di erence ∆M_K. Theoretical progress on the decays K_L,S → µ⁺µ⁻ and K_L → π⁰⁺⁻ is also expected. They are all very sensitive to new physics (NP) contributions and the correlations between them should help us to identify new dynamics at very short distance scales. These studies will be enriched when theory on the K → ππ isospin amplitudes ReA₀ and ReA₂ improves. This paper summarizes several aspects of this exciting field. In particular, we emphasize the role of the Dual QCD approach in getting the insight in the numerical Lattice QCD results on K⁰–K^{¯ 0} mixing and K → ππ decays.