Abstract
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)x(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) 10^-4, substantially more precise than the recent RBC-UKQCD prediction and 2.9 sigma below the experimental value (16.6+-2.3) 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) 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.
Highlights
A long-standing challenge in making predictions for ε /ε within the Standard Model (SM) and its extensions has been the strong interplay of QCD penguin contributions and electroweak penguin contributions to this ratio
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
We employed 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
Summary
As present calculations by lattice QCD and in [24] are not precise enough, at this moment, we cannot exclude that B6(1/2) could be as large as B8(3/2) and this leads conservatively to the bound in (1.4) For these reasons it is instructive to consider other values of the parameters B6(1/2) and B8(3/2) than those obtained by RBC-UKQCD collaboration which are, consistent with the large-N bound in (1.4). This is an important result as it shows that even if the value of B6(1/2) from lattice calculations would move up in the future, the SM would face difficulty in reproducing the data provided the large-N bound in (1.4) is respected With these results at hand, we are in the position to summarise the present picture of the estimate of ε /ε in the SM:.
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