Improved anatomy of ε′/ε in the Standard Model

We present a new analysis of the ratio epsilon'/epsilon within the Standard Model (SM) using a formalism that is manifestly independent of the values of leading (V - A) circle times (V - A) QCD penguin, and EW penguin hadronic matrix elements of the operators Q(4), Q(9), and Q(10), and applies to the SM as well as extensions with the same operator structure. It is valid under the assumption that the SM exactly describes the data on CP-conserving K -> pi pi amplitudes. As a result of this and the high precision now available for CKM and quark mass parameters, to high accuracy epsilon'/epsilon depends only on two non-perturbative parameters, B-6((1/2)) and B-8((3/2)), and perturbatively calculable Wilson coefficients. Within the SM, we are separately able to determine the hadronic matrix element < Q(4)>(0) from CP-conserving data, significantly more precisely than presently possible with lattice QCD. Employing B-6((1/2)) = 0.57 +/- 0.19 and B-8((3/2)) = 0.76 +/- 0.05, extracted from recent results by the RBC-UKQCD collaboration, we obtain epsilon'/epsilon = (1.9 +/- 4.5) x 10(-4), substantially more precise than the recent RBC-UKQCD prediction and 2.9 sigma below the experimental value (16.6 +/- 2.3) x 10(-4), with the error being fully dominated by that on B-6((1/2)). Even discarding lattice input completely, but employing the recently obtained bound B-6((1/2)) <= B-8((3/2)) <= 1 from the large-N approach, the SM value is found more than 2 sigma below the experimental value. At B-6((1/2)) = B-8((3/2)) = 1, varying all other parameters within one sigma, we find epsilon'/epsilon = (8.6 +/- 3.2) x 10(-4). We present a detailed anatomy of the various SM uncertainties, including all sub-leading hadronic matrix elements, briefly commenting on the possibility of underestimated SM contributions as well as on the impact of our results on new physics models.