The Optimal Strategy for ϵ ^′/ϵ in the SM: 2019

Following the recent analysis done in collaboration with Jason Aebischer and Christoph Bobeth, I summarize the optimal, in our view, strategy for the present evaluation of the ratio ϵ ^′/ϵ in the Standard Model. In particular, I emphasize the importance of the correct matching of the long-distance and short-distance contributions to ϵ ^′/ϵ, which presently is only achieved by RBC-UKQCD lattice QCD collaboration and by the analytical Dual QCD approach. An important role play also the isospin-breaking and QED effects, which presently are best known from chiral perturbation theory, albeit still with a significant error. Finally, it is essential to include NNLO QCD corrections in order to reduce unphysical renormalization scheme and scale dependences present at the NLO level. Here _c in m _c ( _c ) in the case of QCD penguin contributions and _t in m _t ( _t ) in the case of electroweak penguin contributions play the most important roles. Presently the error on ϵ ^′/ϵ is dominated by the uncertainties in the QCDP parameter and the isospin-breaking parameter IMG ALIGN="MIDDLE" ALT="$hat Ω {{\rm{eff}}}$" SRC="JPCS-1526-1-012019eqn-02.gif". We present a table illustrating this.