$ε'/ε$ at $O(p^4)$ in the Chiral Expansion

After updating the determination of the combination of Kobayashi-Maskawa elements Im $V^*_{ts}V_{td}$ according to a new estimate of the parameter $\hat B_K$, we study the CP-violating ratio $\epsilon'/\epsilon$ by means of hadronic matrix elements computed to ${\cal O}(p^4)$ in the chiral expansion and NLO Wilson coefficients. It is the first time that this order in chiral perturbation theory is included in the analysis. The most important effect of this improved study is the substantial reduction of the contribution of the electroweak penguin operator $< Q_{8} >_2$ and accordingly a reduced cancellation between the latter and the gluonic penguin operator $< Q_{6} >_0$. The ratio $\epsilon'/\epsilon$ is thus larger than previously estimated and its predicted value enjoys a smaller uncertainty. Values positive and of the order of $1 \times 10^{-3}$ are preferred even though a vanishingly small value cannot be excluded: we find $\epsilon'/\epsilon = 1.5 ^{+1.9}_{-1.0} \times 10^{-3}$ and $\epsilon'/\epsilon = 1.2 ^{+1.8}_{-0.8} \times 10^{-3}$ for the CP violating phase in the first and second quadrants respectively. They give the averaged value $1.3 ^{+1.9}_{-1.0} \times 10^{-3}$.