Non-leptonic kaon decays at large $N_c$
4-2-011 - TH common room
Computing non-leptonic kaon decay and mixing amplitudes in the SM, taking properly into account non-perturbative QCD effects, is a notoriously difficult problem: reliable predictions for $\epsilon'/\epsilon$, or of the $\Delta I=1/2$ enhancement rule, remain elusive after several decades of study. After a brief introduction to the difficulties faced by non-perturbative computations, I will discuss how some light on the anatomy of the problem enhancement can be obtained by studying the large-$N_c$ scaling of the relevant amplitudes. We find that the subleading 1/$N_c$ corrections in $B_K$ are small, but those in the $K \to \pi\pi$ amplitudes are large and fully anti-correlated in the I = 0, 2 isospin channels. We briefly comment on the implications for the $\Delta I=1/2$ rule.