The Relevance of the Dipole Penguin Operators in $ε'/ε$

Abstract

The standard model contribution to $ε'/ε$ of the magnetic- and electric-dipole penguin operators $Q_{11} = \frac{g_s}{16π^2} \, m_s \: \bar{s}\, σ_{μν} t^a G^{μν}_a (1-γ_5 )\, d $ and $Q_{12} = \frac{eQ_d}{16π^2}\, m_s \: \bar{s}\, σ_{μν} F^{μν} (1-γ_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 $ε'/ε$ comparable to that of other operators so far considered, and should therefore be consistently included in the analysis.