We present new results for the matrix elements of the Q6 and Q4 penguin operators, evaluated in a large-Nc approach which incorporates important O(Nc2nf/Nc) unfactorized contributions. Our approach shows analytic matching between short- and long-distance scale dependences within dimensional renormalization schemes, such as MS. Numerically, we find that there is a large positive contribution to the ΔI = 1/2 matrix element of Q6 and hence to the direct CP-violation parameter ∈′/∈. We also present results for the ΔI = 1/2 rule in K → ππ amplitudes, which incorporate the related and important "eye-diagram" contributions of O(N c21/NC) from the Q2 operator (i.e. the penguin-like contraction). The results lead to an enhancement of the ΔI = 1/2 effective coupling. The origin of the large unfactorized contributions which we find is discussed in terms of the relevant scales of the problem. © SISSA/ISAS 2003.
|Journal||Journal of High Energy Physics|
|Publication status||Published - 1 May 2003|
- 1/N Expansion
- Chiral Lagrangians
- Kaon Physics