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

TL;DR

This paper discusses the optimal strategy for evaluating the $ ext{Re}(rac{ ext{ε}'}{ ext{ε}})$ ratio in the Standard Model, emphasizing correct matching of contributions, inclusion of NNLO corrections, and the impact of isospin-breaking and QED effects.

Contribution

It provides a comprehensive strategy for precise $ ext{Re}(rac{ ext{ε}'}{ ext{ε}})$ calculation, highlighting the importance of matching, higher-order corrections, and current uncertainties.

Findings

Matching of long- and short-distance contributions is crucial.

NNLO QCD corrections significantly reduce scheme and scale dependence.

Uncertainties are dominated by $B_6^{(1/2)}$ and $ ext{Ω}_ ext{eff}$ parameters.

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.