Corrections to the box-diagram amplitude due to kaon mass

Abstract

The $K^0$-K${¯}^0$ mixing amplitude is calculated without using the standard zero-external-momentum approximation. The resulting corrections [∼($m_k$ ${\mathrm{}}^2$/$m_c$ ${\mathrm{}}^2$) ln ($m_c$ ${\mathrm{}}^2$/$m_s$ ${\mathrm{}}^2$)] are numerically significant for the real part of the amplitude. In the imaginary part of the amplitude the effects of similar corrections are less important. Implications for Δ$m_k$ and ε are discussed.