We apply the vacuum-background-field method and the modified renormalization-group equation in the energy region $\mu <1\mathrm{}$ GeV to correct the Wilson coefficients in the $\Delta S=1\mathrm{}$ effective weak Hamiltonian responsible for $K\to 2\pi$ decays. We find that the change of $C_{\pm }$ results in an enhancement to the $\Delta I=\frac{1}{2}$ amplitude by a factor of 2 at the scale $\mu =0.6\mathrm{}$ GeV for $K\to 2\pi$ decays.

• Received 9 May 1989

DOI:https://doi.org/10.1103/PhysRevD.40.3627