Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1993-10-19
Nucl.Phys. B419 (1994) 292-322
Physics
High Energy Physics
High Energy Physics - Phenomenology
30 pages and 9 figures (available as uuencoded tarred postscript files), LaTeX, TUM-T31-40/93
Scientific paper
10.1016/0550-3213(94)90044-2
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 $0.834 \le \eta_1^{\rm LO} \le 1.138$. 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 $\eta_1$ reduces considerably the theoretical uncertainty related to the choice of renormalization scales.
Herrlich Stefan
Nierste Ulrich
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