Factorization Approach for the ¢ I = 1=2 Rule and "0=" in Kaon Decays

Hai-Yang Cheng

《Chinese Journal of Physics》 38卷6期 (2000/12) Pp. 1044-1062

並列摘要

The ¢ I = 1=2 rule and direct CP violation ”0=” in kaon decays are studied within the framework of the effective Hamiltonian approach in conjunction with generalized factorization for hadronic matrix elements. We identify two principal sources responsible for the enhancement of ReA0=ReA2: the vertex-type as well as penguin-type corrections to the matrix elements of four-quark operators, which render the physical amplitude renormalization-scale and -scheme independent, and the nonfactorized effect due to soft-gluon exchange, which is needed to suppress the ¢ I = 3=2 K ! 1/4 1/4 amplitude. Contrary to the chiral approach which is limited to light meson decays and fails to reproduce the A2 amplitude, the aforementioned approach for dealing with scheme and scale issues is applicable to heavy meson decays. We obtain ReA0=ReA2 = 13 ¡ 15 if ms(1 GeV) lies in the range 125 ¡ 175 MeV. The bag parameters Bi, which are often employed to parametrize the scale and scheme dependence of hadronic matrix elements, are calculated in two different renormalization schemes. It is found that B8^(2) and B6^(0) , both of order 1.5 at ^¹ =1 GeV, are nearly °5 scheme independent, whereas B 3;5;7^(0) as well as B7^(2) show a sizable scheme dependence. Moreover, only B 1;3;4^(0) exhibit a significant ms dependence, while the other B-parameters are almost ms independent. For direct CP violation, we obtain ”0=” = (0:5 ¡ 1:3) £ 10¡^3 if ms(1 GeV) = 150 MeV and ”0=” = (0:8 ¡ 2:0) £ 10¡^3 if ms is as small as indicated by some recent lattice calculations.