${\epsilon }^{\prime }/\epsilon$ at $O(p^4)$ in the Chiral Expansion

Abstract

After updating the determination of the combination of Kobayashi-Maskawa elements $\Im V_{td}{V}_{ts}^{\ast }$ according to our new estimate of the parameter ${\hat{B}}_K$, we study the CP-violating ratio ${\epsilon }^{\prime }/\epsilon$ 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 ${\epsilon }^{\prime }/\epsilon$ is thus larger than previously estimated and its predicted value enjoys a smaller uncertainty. We find ${\epsilon }^{\prime }/\epsilon =1.7_{-1.0}^{+1.4}\times 10^{-3}$. Values positive and of the order of $10^{-3}$ are therefore preferred.

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

References in corpus (1)

• The Delta I = 1/2 Rule and B_K at O(p^4) in the Chiral Expansion

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