The Relevance of the Dipole Penguin Operators in ${ϵ}^{\prime }/ϵ$

Abstract

The standard model contribution to ${ϵ}^{\prime }/ϵ$ of the magnetic- and electric-dipole penguin operators $Q_{11}=\frac{g_s}{16{\pi }^2}{m}_s\bar{s}{\sigma }_{\mu \nu }{t}^a{G}_a^{\mu \nu }(1-{\gamma }_5)d$ and $Q_{12}=\frac{e{Q}_d}{16{\pi }^2}{m}_s\bar{s}{\sigma }_{\mu \nu }{F}^{\mu \nu }(1-{\gamma }_5)d$ is discussed. While the electromagnetic penguin $Q_{12}$ seems to have a vanishingly small matrix element, we find that the gluonic dipole operator $Q_{11}$ may give a contribution to ${ϵ}^{\prime }/ϵ$ comparable to that of other operators so far considered, and should therefore be consistently included in the analysis.

Comments: 14 pages, LATEX, CERN-TH.7097/93 and SISSA 174/93/EP, (alternative evaluation of the hadronic matrix element and new tables)