The Coefficient \eta_3 of the |\Delta S|=2 Hamiltonian in the Next-To-Leading Order

Abstract

I present the calculation of the QCD short distance coefficient ${\eta }_3$ of the $|\Delta S|=2$-hamiltonian in the next-to-leading order (NLO) of renormalization group improved perturbation theory. It involves the two-loop mixing of bilocal structures composed of two $|\Delta S|=1$ operators into $|\Delta S|=2$ operators. The next-to-leading order corrections enhance ${\eta }_3$ by 27\% to ${\eta }_3=0.47\text{errorpm}0.030.04$ thereby affecting the phenomenology of the CP-parameter ${ϵ}_K$ sizeably. ${\eta }_3$ depends on the physical input parameters $m_t$, $m_c$ and ${\Lambda }_{MSbar}$ only weakly. The quoted error stems from factorization scale dependences, which have reduced compared to the old leading log result. We further discuss some field theoretical aspects of the calculation such as the renormalization group equation for Green's functions with two operator insertions and the renormalization scheme dependence caused by the presence of evanescent operators. This article is based on work done in collaboration with U.~Nierste.

Comments: 8 pages, LaTeX2e using the packages espcrc2, graphix, subeqn. The complete PostScript file is available under ftp://feynman.t30.physik.tu-muenchen.de/pub/preprints/desy-96-100.ps.gz , the source under ftp://feynman.t30.physik.tu-muenchen.de/pub/preprints/desy-96-100.tar.gz . To appear in the proceedings of the workshop ``QCD and QED in Higher Orders'', Rheinsberg, Germany, April 1996