$ε'/ε$ at $O(p^4)$ in the Chiral Expansion

Details $ε'/ε$ at $O(p^4)$ in the Chiral Expansion $ε'/ε$ at $O(p^4)$ in the Chiral Expansion

1997-06-05

arxiv.org/abs/hep-ph/9706260v4

Nucl.Phys. B514 (1998) 93-112

Physics

High Energy Physics

High Energy Physics - Phenomenology

Latex2e, JHEP.cls, 22 pages, 8 figures. Short-distance analysis updated. Introduction and conclusions expanded

Scientific paper

10.1016/S0550-3213(97)00786-4

After updating the determination of the combination of Kobayashi-Maskawa elements $ \Im V_{td}V^*_{ts}$ according to our new estimate of the parameter $\hat B_K$, we study the CP-violating ratio $\epsilon'/\epsilon$ by means of hadronic matrix elements computed to $O(p^4)$ in the chiral expansion. It is the first time that this order in chiral perturbation theory is included. We also discuss the relevance of some $O(p^2)$ terms that are generally neglected in the calculation of the electroweak penguin matrix elements. The most important effect of this improved analysis is the substantial reduction (20%) of the leading electroweak penguin matrix element and accordingly a reduced cancelation between the electroweak and gluon penguin contributions. The ratio $\epsilon'/\epsilon$ is thus larger than previously estimated and its predicted value enjoys a smaller uncertainty. We find $\epsilon'/\epsilon = 1.7 ^{+1.4}_{-1.0} \times 10^{-3}$. Values positive and of the order of $10^{-3}$ are therefore preferred.

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