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The next-to-leading order result enhances $\\eta_1$ and $(\\Delta m_K)^{\\rm SD}$ by 20\\% compared to the leading order estimate. Taking $0.200 \\gev \\le \\laMSb \\le 0.350 \\gev$ and $1.35 \\gev \\le m_c(m_c) \\le 1.45 \\gev$ we obtain $0.922 \\le \\eta_1^{\\rm NLO} \\le 1.419$ compared to $0.834 \\le \\eta_1^{\\rm LO} \\le 1.138$. 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Herrlich, U. Nierste","submitted_at":"1993-10-19T14:30:05Z","abstract_excerpt":"We calculate the next-to-leading order short distance QCD corrections to the coefficient $\\eta_1$ of the effective $\\Delta S = 2$ hamiltonian in the standard model. This part dominates the short distance contribution $(\\Delta m_K)^{\\rm SD}$ to the $K_L$ -- $K_S$ mass difference. The next-to-leading order result enhances $\\eta_1$ and $(\\Delta m_K)^{\\rm SD}$ by 20\\% compared to the leading order estimate. Taking $0.200 \\gev \\le \\laMSb \\le 0.350 \\gev$ and $1.35 \\gev \\le m_c(m_c) \\le 1.45 \\gev$ we obtain $0.922 \\le \\eta_1^{\\rm NLO} \\le 1.419$ compared to $0.834 \\le \\eta_1^{\\rm LO} \\le 1.138$. 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