  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.
