Estimatingɛ′/ɛin the standard model independent ofImλt

The $\mathrm{CP}$-violating parameter ${\varepsilon }^{\prime }/\varepsilon$ is estimated in a novel way by including the explicit computation of $\varepsilon$ in the ratio as opposed to the usual procedure of taking its value from experiment. This approach has the advantage of being independent of the determination of the CKM parameters $\mathrm{Im}{\lambda }_t$ and of showing more directly the dependence on the long-distance parameters. The matrix elements are taken from the chiral quark model approach, the parameters of which have been recently determined by an updated fit of the $\mathrm{CP}$-conserving amplitudes entering the $\Delta I=1/2\mathrm{}$ rule. By sampling the ranges of the experimental inputs according to a normal distribution and those of the theoretical uncertainties according to a flat one, it is found that ${\varepsilon }^{\prime }/\varepsilon =(2.5\mathrm{}\pm 0.9)\times {10}^{-3},$ in agreement with the current experimental data. A more conservative estimate $0.9\times {10}^{-3}<{\varepsilon }^{\prime }/\varepsilon <5.8\mathrm{}\times {10}^{-3}$ is found by considering the smallest and the largest values obtained by taking a flat distribution for all inputs.