New approach to nonleptonic weak interactions. II. Application to strange- and charm-meson decays

The constraints obtained in I for the asymptotic two-body meson matrix elements of the weak nonleptonic Hamiltonian are related to the physical $K\to \pi \pi$ and $D\to \overline{K}\pi$ decay amplitudes by using a soft-pion approximation in the infinite-momentum frame of the parent particle. In this new milder extrapolation, a part of the so-called surface terms survives in addition to the usual equal-time-commutator term and plays a significant role, especially for the $D\to \overline{K}\pi$ decays. However, to the approximation in which only the ground-state-meson contribution is kept in the surface terms, the $\left| \Delta \overrightarrow{\mathrm{I}} \right|=\frac{1}{2}$ rule for the $K\to 2\pi$ decays and the 6 ⊕ 6* rule [in exact SU(3) symmetry] for the $D\to \overline{K}\pi$ decays are shown to hold exactly and the amplitudes predict a reasonable value for the ratio of the rates, $\frac{\Gamma (K_S^0\to {\pi }^{+}{\pi }^{-})}{\Gamma (D^0\to K^{-}{\pi }^{+})}$. A semiquantitative scenario is also drawn, which suggests that the $L=1\mathrm{}$ meson contribution to the surface terms plays an important role for the violation of these selection rules and yields the right order of magnitude for the violation of the $\left| \Delta \overrightarrow{\mathrm{I}} \right|=\frac{1}{2}$ rule in $K\to 2\pi$ decays. For the $D\to \overline{K}\pi$ decays it leads to a more significant violation of the 6 ⊕ 6* rule.