S. Herrlich | Searcharxiv

arXiv1994

Next-to-leading order short distance QCD corrections to the effective $ΔS = 2$ Hamiltonian, implications for the $K_L$-$K_S$ mass difference

We report on the results of a calculation of next-to leading order short distance QCD corrections to the coefficient $η_1$ of the effective $ΔS = 2$ Lagrangian in the standard model and discuss the uncertainties inherent in such a calculation. As a phenomenological application we comment on the contributions of short distance physics to the ${\rm K}_{\rm L}$--${\rm K}_{\rm S}$ mass difference. This report is based on research work done in collaboration with Ulrich Nierste.

hep-ph↗

arXiv1993

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

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.

hep-ph↗