/ at the NLO: 10 Years Later

Abstract

During the last four years several parameters relevant for the analysis of the CP-violating ratio ?'/? improved and/or changed significantly. In particular, the experimental value of ?'/? and the strange quark mass decreased, the uncertainty in the CKM factor has been reduced, and for a value of the hadronic matrix element of the dominant electroweak penguin operator Q8, some consensus has been reached among several theory groups. In view of this situation, ten years after the first analyses of ?'/? at the next-to-leading order, we reconsider the analysis of ?'/? within the SM and investigate what can be said about the hadronic Q6 matrix element of the dominant QCD penguin operator on the basis of the present experimental value for ?'/? and todays values of all other parameters. Employing a conservative range for the reduced electroweak penguin matrix element R8 = 1.0?0.2 from lattice QCD, and present values for all other input parameters, on the basis of the current world average for ?'/?, we obtain the reduced hadronic matrix element of the dominant QCD penguin operator R6 = 1.23?0.16 implying Q60NDR(mc) ? ??0.8?Q82NDR(mc). We compare these results with those obtained in large-Nc approaches in which generally R6 ? R8 and Q60NDR(mc) is chirally suppressed relatively to Q82NDR(mc). We present the correlation between R6 and R8 that is implied by the data on ?'/? provided new physics contributions to ?'/? can be neglected.