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arXiv · hep-ph/9310311

Enhancement of the $K_L$ -- $K_S$ Mass Difference by Short Distance QCD Corrections Beyond Leading Logarithms

S. Herrlich·U. Nierste
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Abstract

We calculate the next-to-leading order short distance QCD corrections to the coefficient $η_1$ of the effective $ΔS = 2$ hamiltonian in the standard model. This part dominates the short distance contribution $(Δm_K)^{\rm SD}$ to the $K_L$ -- $K_S$ mass difference. The next-to-leading order result enhances $η_1$ and $(Δm_K)^{\rm SD}$ 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 $0.922 \le η_1^{\rm NLO} \le 1.419$ compared to $0.834 \le η_1^{\rm LO} \le 1.138$. For $B_K = 0.7$ this corresponds to 48 -- 75 \% of the experimentally observed mass difference. The inclusion of next-to- leading order corrections to $η_1$ reduces considerably the theoretical uncertainty related to the choice of renormalization scales.

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S. Herrlich, U. Nierste. 1993-10-19. Enhancement of the $K_L$ -- $K_S$ Mass Difference by Short Distance QCD Corrections Beyond Leading Logarithms. https://doi.org/10.1016/0550-3213(94)90044-2

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