The Optimal Strategy for $\varepsilon'/\varepsilon$ in the SM: 2019

Abstract

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 $\varepsilon'/\varepsilon$ in the Standard Model (SM). In particular, I emphasize the importance of the correct matching of the long-distance and short-distance contributions to $\varepsilon'/\varepsilon$, which presently is only achieved by RBC-UKQCD lattice QCD collaboration and by the analytical Dual QCD approach. An mportant 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 $\mu_c$ in $m_c(\mu_c)$ in the case of QCD penguin (QCDP) contributions and $\mu_t$ in $m_t(\mu_t)$ in the case of electroweak penguin (EWP) contributions play the most important roles. Presently the error on $\varepsilon'/\varepsilon$ is dominated by the uncertainties in the QCDP parameter $B_6^{(1/2)}$ and the isospin-breaking parameter $\hat\Omega_\text{eff}$ We present a table illustrating this. To be published online by the Institute of Physics Proceedings.