The Relevance of the Dipole Penguin Operators in $\epsilon'/\epsilon$

Abstract

The standard model contribution to $\epsilon'/\epsilon$ 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^{\mu\nu}_a (1-\gamma_5 )\, d $ and $Q_{12} = \frac{eQ_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 $\epsilon'/\epsilon$ comparable to that of other operators so far considered, and should therefore be consistently included in the analysis.