The K ---> pi pi Decays in the Large n Limit: Quark Evolution

Aug, 1986
25 pages
Published in:
  • Nucl.Phys.B 293 (1987) 787-811
  • Published: 1987
Report number:
  • MPI-PAE/PTh-45/86

Citations per year

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Abstract: (Elsevier)
We use the large- N limit to obtain a consistent picture of the K → ππ amplitudes, A (K → ππ ). We emphasize that the full evaluation of A (K → ππ ) should include two contributions: (i) the evolution from M W down to μ ≅ O(1 GeV) done in the quark picture and (ii) the evolution from μ ≅ O(1 GeV) down to low energy O( λ QCD , m π , m K ) which must be done in the meson picture. Using chiral perturbation theory at the tree level, we confirm that the matrix elements of the dominant Q 6 penguin operator are enhanced by an order of magnitude over those of the current-current operators. We identify an additional (with respect to standard estimates) enhancement of the penguin contributions to the real parts of A (K → ππ ) relevant for the ΔI = 1 2 rule, which comes from an imcomplete GIM cancellation above the charm quark mass. The corresponding contributions to the imaginary parts and to the ratio ε' ε are found to be slightly suppressed. Performing the short distance analysis to first nontrivial order in 1/ N , we demonstrate its validity and simplicity. We obtain encouraging results for A (K → ππ ) amplitudes and point out that further improvements can be obtained through the inclusion of the low energy meson evolution which is presented in a separate publication. We find ε′ ε ≅ 5 · 10 −3 for m t = 40 GeV.
  • K: NONLEPTONIC DECAY
  • NONLEPTONIC DECAY: K
  • EXPANSION 1/N
  • QUARK
  • PERTURBATION THEORY: CHIRAL
  • ISOSPIN: SELECTION RULE
  • SELECTION RULE: ISOSPIN
  • CP: violation
  • RENORMALIZATION GROUP
  • FIELD THEORY: OPERATOR PRODUCT EXPANSION