The Dual QCD @ Work

Abstract

The Dual QCD (DQCD) framework, based on the ideas of 't Hooft and Witten, and developed by Bill Bardeen, Jean-Marc Gerard and myself in the 1980s is not QCD, a theory of quarks and gluons, but a successful low energy approximation of it when applied to $K\to\pi\pi$ decays and $K^0-\bar K^0$ mixing. After years of silence, starting with 2014, this framework has been further developed in order to improve the SM prediction for the ratio $\epsilon'/\epsilon$, the $\Delta I=1/2$ rule and $\hat B_K$. Most importantly, this year it has been used for the calculation of all $K\to\pi\pi$ hadronic matrix elements of BSM operators which opened the road for the general study of $\epsilon'/\epsilon$ in the context of the SM effective theory (SMEFT). This talk summarizes briefly the past successes of this framework and discusses recent developments which lead to a master formula for $\epsilon'/\epsilon$ valid in any extension of the SM. This formula should facilitate the search for new physics responsible for the $\epsilon'/\epsilon$ anomaly hinted by 2015 results from lattice QCD and DQCD.