Upper Bounds on epsilon'/epsilon Parameters B_6^{(1/2)} and B_8^{(3/2)} from Large N QCD and other News

TL;DR

This paper uses large N QCD methods to derive upper bounds on parameters B_6^{(1/2)} and B_8^{(3/2)}, aligning with recent lattice results, and discusses implications for epsilon'/epsilon and other kaon decay parameters.

Contribution

It provides new theoretical bounds on B_6^{(1/2)} and B_8^{(3/2)} using large N QCD, consistent with lattice findings, and explores their impact on CP violation in kaon decays.

Findings

B_6^{(1/2)} < B_8^{(3/2)} < 1 from large N analysis

Lattice results support the large N pattern of matrix elements

SM prediction for epsilon'/epsilon is roughly half the experimental value

Abstract

We demonstrate that in the large N approach developed by the authors in collaboration with Bardeen, the parameters B_6^{(1/2)} and B_8^{(3/2)} parametrizing the K\to\pi\pi matrix elements <Q_6>_0 and <Q_8>_2 of the dominant QCD and electroweak operators receive both negative O(1/N) corrections such that B_6^{(1/2)} < B_8^{(3/2)}<1 in agreement with the recent lattice results of the RBC-UKQCD collaboration. We also point out that the pattern of the size of the hadronic matrix elements of all QCD and electroweak penguin operators Q_i contributing to the K\to \pi \pi amplitudes A_0 and A_2, obtained by this lattice collaboration, provides further support to our large N approach. In particular, a very precise lattice result for the matrix element <Q_8>_0 implies for the corresponding parameter B_8^{(1/2)}=1.0\pm 0.2 to be compared with large N value B_8^{(1/2)}=1.1\pm 0.1. We discuss briefly the implications of these findings for the ratio epsilon'/epsilon. In fact, with the precise value for B_8^{(3/2)} from RBC-UKQCD collaboration, our upper bound on B_6^{(1/2)} implies epsilon'/epsilon in the SM roughly by a factor of two below its experimental value (16.6\pm 2.3)\times 10^{-4}. We also briefly comment on the parameter \hat B_K and the \Delta I=1/2$ rule.