The anatomy of [formula omitted] in the standard model

Abstract

We perform a detailed renormalization group analysis of the ratio ε′ ε for 50 GeV < m t < 250 GeV including the contributions from the gluon penguin, photon penguin, Z 0-penguin and neutral Higgs penguin diagrams as well as from π 0− η− η′ mixing and current-current operators. The final result for the Wilson coefficient functions with full O( α QED ) corrections taken into account can be written in a compact and transparent form. Using the constraints on m t and the phase δ coming from the data on ε and B 0− B 0 mixing, we investigate the dependence of the resulting ε′ ε ratio on the values of m t, Λ QCD, B K, m s(1 GeV), F B and the ratio Γ( b → u) Γ( b → c) . The presence of Z 0-diagrams suppresses strongly ε′ ε for large values of m t. For m t ≃ O(100 GeV) the standard model is milliweak wity typical values ε′ ε ≃ (1.0 ± 0.5) × 10 −3 . For m t ≃ O(220 GeV) it behaves like a superweak theory with | ε′ ε |≃0 and negative values for larger m t. These two distinct regions of m t, “milliweak” and “superweak” respectively, are the two regions of m t favoured by the data on ϵ and B 0− B 0 mixing.