Updated analysis ofɛ′/ɛin the standard model with hadronic matrix elements from the chiral quark model

We discuss the theoretical and experimental status of the $\mathrm{CP}$ violating ratio ${\varepsilon }^{\prime }/\varepsilon .$ We revise our 1997 standard-model estimate—based on hadronic matrix elements computed in the chiral quark model up to ${O(p}^4)$ in the chiral expansion—by including an improved statistical analysis of the uncertainties and updated determination of the Cabibbo-Kobayashi-Maskawa elements and other short-distance parameters. Using normal distributions for the experimental input data we find $\mathrm{Re}{\varepsilon }^{\prime }/\varepsilon =(2.2\mathrm{}\pm 0.8)\times {10}^{-3},$ whereas a flat scanning gives $0.9\times {10}^{-3}<\mathrm{Re}\mathrm{}{\varepsilon }^{\prime }/\varepsilon <4.8\mathrm{}\times {10}^{-3}.$ Both results are in agreement with the current experimental data. The key element in our estimate is, as before, the fit of the $\Delta I=1/2\mathrm{}$ rule, which allows us to absorb most of the theoretical uncertainties in the determination of the model-dependent parameters in the hadronic matrix elements. Our semiphenomenological approach leads to numerical stability against variations of the renormalization scale and scheme dependence of the short- and long-distance components. The same dynamical mechanism at work in the selection rule also explains the larger value obtained for ${\varepsilon }^{\prime }/\varepsilon$ with respect to other estimates. A coherent picture of $\overrightarrow{K}\pi \pi$ decays is thus provided.