The Optimal Strategy for ${\epsilon }^{\prime }/\epsilon$ 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 ${\epsilon }^{\prime }/\epsilon$ in the Standard Model (SM). In particular, I emphasize the importance of the correct matching of the long-distance and short-distance contributions to ${\epsilon }^{\prime }/\epsilon$, 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 ${\epsilon }^{\prime }/\epsilon$ 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.

arXiv commentTalk presented at Kaon 2019, Perugia, September 2019. 11 pages, 1 Figure. Few Misprints removed. Additional explanations to Table 1 and formula (4) added. arXiv admin note: substantial text overlap with arXiv:1909.05610

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