Effective Hamiltonian forΔS=1weak nonleptonic decays in the six-quark model

Abstract

Strong-interaction corrections to the nonleptonic weak-interaction Hamiltonian are calculated in the leading-logarithmic approximation using quantum chromodynamics. Starting with a six-quark theory, the $W$ boson, $t$ quark, $b$ quark, and $c$ quark are successively considered as "heavy" and the effective Hamiltonian calculated. The resulting effective Hamiltonian for strangeness-changing nonleptonic decays involves $u$, $d$, and $s$ quarks and has possible $\mathrm{CP}$-violating pieces both in the usual $\mathrm{}(V-A)\mathrm{}\times \mathrm{}(V-A)\mathrm{}$ terms and in induced, "penguin"-type terms. Numerically, the $\mathrm{CP}$-violating compared to $\mathrm{CP}$-conserving parts of the latter terms are close to results calculated on the basis of the lowest-order "penguin" diagram.