Improved anatomy of ε′/ε in the Standard Model

Abstract: We present a new analysis of the ratio ε′/ε within the Standard Model (SM) using a formalism that is manifestly independent of the values of leading (V − A) ⊗ (V − A) QCD penguin, and EW penguin hadronic matrix elements of the operators Q₄, Q₉, and Q₁₀, 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 → ππ amplitudes. As a result of this and the high precision now available for CKM and quark mass parameters, to high accuracy ε′/ε depends only on two non-perturbative parameters, B₆ ^(1/2) and B₈ ^(3/2), and perturbatively calculable Wilson coefficients. Within the SM, we are separately able to determine the hadronic matrix element 〈Q₄〉₀ from CP-conserving data, significantly more precisely than presently possible with lattice QCD. Employing B₆ ^(1/2) = 0.57 ± 0.19 and B₈ ^(3/2) = 0.76 ± 0.05, extracted from recent results by the RBC-UKQCD collaboration, we obtain ε′/ε = (1.9 ± 4.5) × 10⁻⁴, substantially more precise than the recent RBC-UKQCD prediction and 2.9 σ below the experimental value (16.6 ± 2.3) × 10⁻⁴, with the error being fully dominated by that on B₆ ^(1/2). Even discarding lattice input completely, but employing the recently obtained bound B₆ ^(1/2) ≤ B₈ ^(3/2) ≤ 1 from the large-N approach, the SM value is found more than 2 σ below the experimental value. At B₆ ^(1/2) = B₈ ^(3/2) = 1, varying all other parameters within one sigma, we find ε′/ε = (8.6 ± 3.2) × 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.