New QCD-estimate of the kaon penguin matrix elements and

Abstract

Firstly, we use the recent ALEPH/OPAL data on the V-A spectral functions for fixing the continuum threshold with which the first and second Weinberg sum rules should be satisfied in the chiral limit. Then, we predict the values of the low-energy constants m_{\pi^+}-m_{\pi^0}, {L}_{10}, and test the values of the electroweak kaon penguin matrix elements <Q^{3/2}_{8,7}>_{2\pi} obtained from DMO--like sum rules. Secondly, we use the data on the \tau-total hadronic width R_{\tau,V/A} for extracting <Q_8^{3/2}_{2\pi}>, in the {MS}\bar scheme, and propose some new sum rules for < Q_7^{3/2}>_{2\pi} in the chiral limit, where the latter require more accurate data for the spectral functions near the $\tau$-mass. Thirdly, we analyze the effects to the matrix element <Q_6^{1/2}>_{2\pi}, of the S_2\equiv(\bar uu+\bar dd) component of the I=0 scalar meson, with its parameters fixed from QCD spectral sum rules. Our results should stimulate a further attention on the r\^ole of the (expected large) gluonium component of the I=0 scalar meson and of the associated operator in the K--->\pi\pi amplitude. Finally, using our previous determinations, we deduce, in the Standard Model (SM), the conservative upper bound for the CP-violating ratio: \epsilon'/\epsilon < (22\pm 9) 10^{-4}, which is in agreement with the present measurements.